def SimAperture(self, sz, rad_x, rad_y=None, *, shape='cir'):
## Initialize ##
# Create the Lateral meshes #
xx, yy = np.meshgrid(*_MeshLat(*sz, shift=True))
# Determine boundaries #
if ((shape.lower in ('cir', 'sqr'))
or (rad_y is None)): # Isotropic, only first input #
rad_y = rad_x
# Transform the aperture into pixels, and un-normalize the sinc functions #
rad_x /= USER.RES[0] / (np.pi / 2)
rad_y /= USER.RES[1] / (np.pi / 2)
# Check if lobes need to be puffed up a bit (I don't know why?) #
#if((USER.KER_TYPE == PM.HELIX) and (USER.KER_Z > 1)):
# rad_x *= 4/3
# rad_y *= 4/3
## Calculate Aperture ##
# We work with the Fourier transform directly to prevent edge effects #
if (shape.lower() in ('cir', 'ell')):
apr = sp.sinc(np.sqrt((xx / rad_x)**2 + (yy / rad_y)**2))
elif (shape.lower() in ('sqr', 'rec')):
apr = sp.sinc(xx / rad_x) + sp.sinc(yy / rad_y)
## Output ##
return apr
def slepian(M, width, sym=True):
"""Return the M-point slepian window.
"""
if (M * width > 27.38):
raise ValueError("Cannot reliably obtain slepian sequences for"
" M*width > 27.38.")
if M < 1:
return np.array([])
if M == 1:
return np.ones(1, 'd')
odd = M % 2
if not sym and not odd:
M = M + 1
twoF = width / 2.0
alpha = (M - 1) / 2.0
m = np.arange(0, M) - alpha
n = m[:, np.newaxis]
k = m[np.newaxis, :]
AF = twoF * special.sinc(twoF * (n - k))
[lam, vec] = linalg.eig(AF)
ind = np.argmax(abs(lam), axis=-1)
w = np.abs(vec[:, ind])
w = w / max(w)
if not sym and not odd:
w = w[:-1]
return w
def slepian(M,width,sym=1):
"""Return the M-point slepian window.
"""
if (M*width > 27.38):
raise ValueError, "Cannot reliably obtain slepian sequences for"\
" M*width > 27.38."
if M < 1:
return array([])
if M == 1:
return ones(1,'d')
odd = M % 2
if not sym and not odd:
M = M+1
twoF = width/2.0
alpha = (M-1)/2.0
m = arange(0,M)-alpha
n = m[:,newaxis]
k = m[newaxis,:]
AF = twoF*special.sinc(twoF*(n-k))
[lam,vec] = linalg.eig(AF)
ind = argmax(abs(lam),axis=-1)
w = abs(vec[:,ind])
w = w / max(w)
if not sym and not odd:
w = w[:-1]
return w
def __calc_amplitude_on_meshgrid_one_harmonic(self, harmonic):
x_2D = self.x_2D
y_2D = self.y_2D
r2_2D = self.gamma**2 * (x_2D**2 + y_2D**2)
A = self.wiggler.aux_const + r2_2D
Y = harmonic * self.wiggler.K_peak**2 / 4 / A
X = 2 * harmonic * self.gamma * self.wiggler.K_peak * x_2D / A
sum1 = 0
sum2 = 0
sum3 = 0
p = -self.bessel_cutoff
jv2pm1 = jv(harmonic + 2 * p - 1, X)
for p in range(-self.bessel_cutoff, self.bessel_cutoff + 1):
jvpY = jv(p, Y)
sum1 += jv(harmonic + 2 * p, X) * jvpY
sum2 += jv2pm1 * jvpY
jv2pp1 = jv(harmonic + 2 * p + 1, X)
sum3 += jv2pp1 * jvpY
jv2pm1 = jv2pp1
aux_factor = np.sqrt(self.alpha)*harmonic*self.gamma\
* self.wiggler.N_periods/ A
bessel_part_x = aux_factor \
* (2*self.gamma*x_2D*sum1
- self.wiggler.K_peak*(sum2+sum3))
bessel_part_y = aux_factor * 2 * self.gamma * y_2D * sum1
dw_arr = self.lambda1_um / self.lambda_range - harmonic
L = [(sinc(self.wiggler.N_periods *
(harmonic * r2_2D + dw * A) / self.wiggler.aux_const)) /
np.sqrt(l) * np.sqrt(st) for dw, l, st in zip(
dw_arr, self.lambda_range, self.spectral_transmission)]
L = np.asarray(L)
return bessel_part_x * L, bessel_part_y * L
def firwin(N, cutoff, width=None, window='hamming'):
"""
FIR Filter Design using windowed ideal filter method.
Parameters
----------
N -- order of filter (number of taps)
cutoff -- cutoff frequency of filter (normalized so that 1 corresponds to
Nyquist or pi radians / sample)
width -- if width is not None, then assume it is the approximate width of
the transition region (normalized so that 1 corresonds to pi)
for use in kaiser FIR filter design.
window -- desired window to use. See get_window for a list
of windows and required parameters.
Returns
-------
h -- coefficients of length N fir filter.
"""
from signaltools import get_window
if isinstance(width,float):
A = 2.285*N*width + 8
if (A < 21): beta = 0.0
elif (A <= 50): beta = 0.5842*(A-21)**0.4 + 0.07886*(A-21)
else: beta = 0.1102*(A-8.7)
window=('kaiser',beta)
win = get_window(window,N,fftbins=1)
alpha = N//2
m = numpy.arange(0,N)
h = win*special.sinc(cutoff*(m-alpha))
return h / numpy.sum(h,axis=0)
def sinc(X, Y):
n = len(X)
m = len(Y)
res = np.zeros((n, m))
for i in range(n):
for j in range(m):
res[i][j] = sc.sinc(np.linalg.norm(X[i] - Y[j]))
return res
def test04(self):
"""Test firwin2 when window=None."""
ntaps = 5
# Ideal lowpass: gain is 1 on [0,0.5], and 0 on [0.5, 1.0]
freq = [0.0, 0.5, 0.5, 1.0]
gain = [1.0, 1.0, 0.0, 0.0]
taps = firwin2(ntaps, freq, gain, window=None, nfreqs=8193)
alpha = 0.5 * (ntaps - 1)
m = np.arange(0, ntaps) - alpha
h = 0.5 * sinc(0.5 * m)
assert_array_almost_equal(h, taps)
def test04(self):
"""Test firwin2 when window=None."""
ntaps = 5
# Ideal lowpass: gain is 1 on [0,0.5], and 0 on [0.5, 1.0]
freq = [0.0, 0.5, 0.5, 1.0]
gain = [1.0, 1.0, 0.0, 0.0]
taps = firwin2(ntaps, freq, gain, window=None, nfreqs=8193)
alpha = 0.5 * (ntaps - 1)
m = np.arange(0, ntaps) - alpha
h = 0.5 * sinc(0.5 * m)
assert_array_almost_equal(h, taps)
def firls(N, f, D=None):
"""Least-squares FIR filter.
N -- filter length, must be odd
f -- list of tuples of band edges
Units of band edges are Hz with 0.5 Hz == Nyquist
and assumed 1 Hz sampling frequency
D -- list of desired responses, one per band
"""
if D is None:
D = [1, 0]
assert len(D) == len(f), "must have one desired response per band"
assert N%2 == 1, 'filter length must be odd'
L = (N-1)//2
k = np.arange(L+1)
k.shape = (1, L+1)
j = k.T
R = 0
r = 0
for i, (f0, f1) in enumerate(f):
R += np.pi*f1*sinc(2*(j-k)*f1) - np.pi*f0*sinc(2*(j-k)*f0) + \
np.pi*f1*sinc(2*(j+k)*f1) - np.pi*f0*sinc(2*(j+k)*f0)
r += D[i]*(2*np.pi*f1*sinc(2*j*f1) - 2*np.pi*f0*sinc(2*j*f0))
a = np.dot(np.linalg.inv(R), r)
a.shape = (-1,)
h = np.zeros(N)
h[:L] = a[:0:-1]/2.
h[L] = a[0]
h[L+1:] = a[1:]/2.
return h
def slepian(M, width, sym=True):
"""Return a digital Slepian window.
Used to maximize the energy concentration in the main lobe. Also called
the digital prolate spheroidal sequence (DPSS).
Parameters
----------
M : int
Number of points in the output window. If zero or less, an empty
array is returned.
width : float
Bandwidth
sym : bool, optional
When True, generates a symmetric window, for use in filter design.
When False, generates a periodic window, for use in spectral analysis.
Returns
-------
w : ndarray
The window, with the maximum value always normalized to 1
"""
if (M * width > 27.38):
raise ValueError("Cannot reliably obtain slepian sequences for"
" M*width > 27.38.")
if M < 1:
return np.array([])
if M == 1:
return np.ones(1, 'd')
odd = M % 2
if not sym and not odd:
M = M + 1
twoF = width / 2.0
alpha = (M - 1) / 2.0
m = np.arange(0, M) - alpha
n = m[:, np.newaxis]
k = m[np.newaxis, :]
AF = twoF * special.sinc(twoF * (n - k))
[lam, vec] = linalg.eig(AF)
ind = np.argmax(abs(lam), axis=-1)
w = np.abs(vec[:, ind])
w = w / max(w)
if not sym and not odd:
w = w[:-1]
return w
def slepian(M, width, sym=True):
"""Return a digital Slepian window.
Used to maximize the energy concentration in the main lobe. Also called
the digital prolate spheroidal sequence (DPSS).
Parameters
----------
M : int
Number of points in the output window. If zero or less, an empty
array is returned.
width : float
Bandwidth
sym : bool, optional
When True, generates a symmetric window, for use in filter design.
When False, generates a periodic window, for use in spectral analysis.
Returns
-------
w : ndarray
The window, with the maximum value always normalized to 1
"""
if (M * width > 27.38):
raise ValueError("Cannot reliably obtain slepian sequences for"
" M*width > 27.38.")
if M < 1:
return np.array([])
if M == 1:
return np.ones(1, 'd')
odd = M % 2
if not sym and not odd:
M = M + 1
twoF = width / 2.0
alpha = (M - 1) / 2.0
m = np.arange(0, M) - alpha
n = m[:, np.newaxis]
k = m[np.newaxis, :]
AF = twoF * special.sinc(twoF * (n - k))
[lam, vec] = linalg.eig(AF)
ind = np.argmax(abs(lam), axis=-1)
w = np.abs(vec[:, ind])
w = w / max(w)
if not sym and not odd:
w = w[:-1]
return w
def zeta_squared_error(x1, x2, b):
sum = 0
l = 1
c1 = -2. * numpy.pi / math.log(b)
f = cmath.exp(complex(0, numpy.pi * (x1 + x2)))
fn = f
while True:
oldsum = sum
g = gamma_cache.get((c1, l))
if g is None:
g = gamma(complex(1, c1 * l))
gamma_cache[(c1, l)] = g
sum += g * fn * sinc(l * (x1 - x2))
if oldsum == sum:
break
l += 1
fn *= f
return pow(sum.real, 2)
def run():
n = np.arange(-20, 21, 1)
x = 0.5 * (sinc(n / 2))**2
print("x", x.shape)
fig1 = plt.figure(1, figsize=(15, 8), dpi=98)
fig1.add_subplot(211)
plt.subplot(211, xlabel="n", ylabel="y")
plt.grid("-.")
plt.plot(n, x)
plt.ylim(0, 0.6)
plt.subplot(212, xlabel="n", ylabel="y")
plt.stem(n, x)
plt.ylim(0, 0.6)
ts = 1 / 40
fig2 = plt.figure(2, figsize=(15, 8), dpi=98)
fig2.add_subplot(111)
plt.subplot(111)
t = np.arange(-0.5, 1.5, ts)
print("t", t.shape)
fs = 1 / ts
b = np.hstack((np.zeros((1, 20))[0], t[20:60], np.zeros((1, 20))[0]))
print("b", b.shape)
H = fft(b) / fs
print("H", H.shape)
df = fs / 80
f = np.arange(0, fs, df) - fs / 2
print("f", f.shape)
plt.plot(b, f)
H1 = fftshift(H)
print("H1", H1.shape)
y = x * H1[19:60]
fig3 = plt.figure(3, figsize=(15, 8), dpi=98)
fig3.add_subplot(111)
plt.subplot(111)
plt.stem(n, y, linefmt='r-', basefmt='r-', markerfmt='C3.')
plt.ylim(-0.2, 0.3)
fig1.savefig("./1.png")
fig2.savefig("./2.png")
fig3.savefig("./3.png")
plt.show()
def convert(self, signal: Signal, step: int) -> Signal:
old_sampling_period = (signal.samples[-1] - signal.samples[0]) / len(
signal.samples)
new_sampling_period = (signal.samples[-1] -
signal.samples[0]) / self._sampling_rate.rate
new_samples = []
new_x_values = self.get_signal_x_values(signal, new_sampling_period)
for new_x in new_x_values:
new_value = 0
old_x_values = self.get_arguments(signal)
for old_index in range(len(old_x_values)):
new_value += signal.samples[old_index] * sinc(
new_x / old_sampling_period - old_index)
new_samples.append(new_value)
new_signal = deepcopy(signal)
new_signal.samples = new_samples
new_signal.sampling_frequency = self._sampling_rate.rate
return new_signal
def digit_baseband():
Ts = 1
N_sample = 8 # 每个码元的抽样点数
dt = Ts / N_sample # 抽样时间间隔
N = 1000 # 码元数
T = 1
t = np.arange(0, N * N_sample * dt, dt)
gt1 = np.ones((1, N_sample)) # NRZ非归零波形
gt2 = np.ones((1, N_sample // 2)) # RZ归零波形
gt2 = np.hstack((gt2, np.zeros((1, N_sample // 2))))
mt3 = sinc((t - 5) / Ts).reshape(1,
-1) # sin(pi * t / Ts) / (pi * t / Ts)
gt3 = mt3[0:10 * N_sample].reshape((1, -1))
d = (np.sign(np.random.randn(1, N)) + 1) / 2
data = sigexpand(d, N_sample) # 对序列间隔插入N_sample - 1个0
st1 = convolve(data, gt1)
st2 = convolve(data, gt2)
d = 2 * d - 1 #变成双极性序列
data = sigexpand(d, N_sample)
st3 = convolve(data, gt3)
f1, st1f = T2F(t, st1[:len(t)])
f2, st2f = T2F(t, st2[:len(t)])
f3, st3f = T2F(t, st3[:len(t)])
fig1 = plt.figure(1, figsize=(13, 8), dpi=98)
fig1.add_subplot(321)
plt.subplot(3, 2, 1, ylabel='单极性NRZ波形')
plt.xlim(0, 20) # axis([0 20 - 1.5 1.5]);
plt.ylim(-2, 2) # axis([0 20 - 1.5 1.5]);
plt.grid("-.")
plt.plot(t, st1[0][:len(t)])
fig1.add_subplot(322)
plt.grid("-.")
plt.xlim(-5, 5) # axis([0 20 - 1.5 1.5]);
plt.ylim(-40, 10)
plt.plot(f1, 10 * np.log10(abs(st1f)**2 / T))
fig1.add_subplot(323, ylabel='单极性RZ波形')
plt.grid("-.")
plt.xlim(0, 20)
plt.ylim(-1.5, 1.5)
plt.plot(t, st2[0][:len(t)])
fig1.add_subplot(324, ylabel='单极性RZ功率谱密度(dB/Hz)')
plt.grid("-.")
plt.xlim(-5, 5)
plt.ylim(-40, 10)
plt.plot(f2, 10 * np.log10(abs(st2f)**2 / T))
fig1.add_subplot(325, ylabel='双极性sinc波形', xlabel='t/Ts')
plt.plot(t - 5, st3[0][:len(t)])
plt.grid("-.")
plt.xlim(0, 20)
plt.ylim(-2, 2)
fig1.add_subplot(326, ylabel='sinc波形功率谱密度(dB/Hz)', xlabel='f*Ts')
plt.grid("-.")
plt.xlim(-5, 5)
plt.ylim(-40, 10)
plt.plot(f3[:-1], 10 * np.log10(abs(st3f)**2 / T))
plt.show()
def findfreqs(num, den, N):
m = numpy.arange(0, N)
h = win * special.sinc(cutoff * (m - alpha))
return h / numpy.sum(h, axis=0)
def firwin(self,
numtaps,
cutoff,
window=None,
pass_zero=True,
scale=True,
nyq=1.0,
fs=None):
"""
FIR filter design using the window method. This is more or less the
same as `scipy.signal.firwin` with the exception that an ndarray with
the window values can be passed as an alternative to the window name.
The parameters "width" (specifying a Kaiser window) and "fs" have been
omitted, they are not needed here.
This function computes the coefficients of a finite impulse response
filter. The filter will have linear phase; it will be Type I if
`numtaps` is odd and Type II if `numtaps` is even.
Type II filters always have zero response at the Nyquist rate, so a
ValueError exception is raised if firwin is called with `numtaps` even and
having a passband whose right end is at the Nyquist rate.
Parameters
----------
numtaps : int
Length of the filter (number of coefficients, i.e. the filter
order + 1). `numtaps` must be even if a passband includes the
Nyquist frequency.
cutoff : float or 1D array_like
Cutoff frequency of filter (expressed in the same units as `nyq`)
OR an array of cutoff frequencies (that is, band edges). In the
latter case, the frequencies in `cutoff` should be positive and
monotonically increasing between 0 and `nyq`. The values 0 and
`nyq` must not be included in `cutoff`.
window : ndarray or string
string: use the window with the passed name from scipy.signal.windows
ndarray: The window values - this is an addition to the original
firwin routine.
pass_zero : bool, optional
If True, the gain at the frequency 0 (i.e. the "DC gain") is 1.
Otherwise the DC gain is 0.
scale : bool, optional
Set to True to scale the coefficients so that the frequency
response is exactly unity at a certain frequency.
That frequency is either:
- 0 (DC) if the first passband starts at 0 (i.e. pass_zero
is True)
- `nyq` (the Nyquist rate) if the first passband ends at
`nyq` (i.e the filter is a single band highpass filter);
center of first passband otherwise
nyq : float, optional
Nyquist frequency. Each frequency in `cutoff` must be between 0
and `nyq`.
Returns
-------
h : (numtaps,) ndarray
Coefficients of length `numtaps` FIR filter.
Raises
------
ValueError
If any value in `cutoff` is less than or equal to 0 or greater
than or equal to `nyq`, if the values in `cutoff` are not strictly
monotonically increasing, or if `numtaps` is even but a passband
includes the Nyquist frequency.
See also
--------
scipy.firwin
"""
cutoff = np.atleast_1d(cutoff) / float(nyq)
# Check for invalid input.
if cutoff.ndim > 1:
raise ValueError("The cutoff argument must be at most "
"one-dimensional.")
if cutoff.size == 0:
raise ValueError("At least one cutoff frequency must be given.")
if cutoff.min() <= 0 or cutoff.max() >= 1:
raise ValueError(
"Invalid cutoff frequency {0}: frequencies must be "
"greater than 0 and less than nyq.".format(cutoff))
if np.any(np.diff(cutoff) <= 0):
raise ValueError("Invalid cutoff frequencies: the frequencies "
"must be strictly increasing.")
pass_nyquist = bool(cutoff.size & 1) ^ pass_zero
if pass_nyquist and numtaps % 2 == 0:
raise ValueError(
"A filter with an even number of coefficients must "
"have zero response at the Nyquist rate.")
# Insert 0 and/or 1 at the ends of cutoff so that the length of cutoff
# is even, and each pair in cutoff corresponds to passband.
cutoff = np.hstack(([0.0] * pass_zero, cutoff, [1.0] * pass_nyquist))
# `bands` is a 2D array; each row gives the left and right edges of
# a passband.
bands = cutoff.reshape(-1, 2)
# Build up the coefficients.
alpha = 0.5 * (numtaps - 1)
m = np.arange(0, numtaps) - alpha
h = 0
for left, right in bands:
h += right * sinc(right * m)
h -= left * sinc(left * m)
if type(window) == str:
# Get and apply the window function.
from scipy.signal.signaltools import get_window
win = get_window(window, numtaps, fftbins=False)
elif type(window) == np.ndarray:
win = window
else:
logger.error(
"The 'window' was neither a string nor a numpy array, it could not be evaluated."
)
return None
# apply the window function.
h *= win
# Now handle scaling if desired.
if scale:
# Get the first passband.
left, right = bands[0]
if left == 0:
scale_frequency = 0.0
elif right == 1:
scale_frequency = 1.0
else:
scale_frequency = 0.5 * (left + right)
c = np.cos(np.pi * m * scale_frequency)
s = np.sum(h * c)
h /= s
return h
def __init__(self, a):
"""
a : bandwidth
"""
super(Sinc, self).__init__(domain=(-np.inf, np.inf))
self.timeFunc = lambda t: sinc(a*t)
def findfreqs(num, den, N):
m = np.arange(0,N)
h = win*special.sinc(cutoff*(m-alpha))
return h / np.sum(h,axis=0)
def firwin(numtaps, cutoff, width=None, window='hamming', pass_zero=True,
scale=True, nyq=1.0):
"""
FIR filter design using the window method.
This function computes the coefficients of a finite impulse response filter.
The filter will have linear phase; it will be Type I if `numtaps` is odd and
Type II if `numtaps` is even.
Type II filters always have zero response at the Nyquist rate, so a
ValueError exception is raised if firwin is called with `numtaps` even and
having a passband whose right end is at the Nyquist rate.
Parameters
----------
numtaps : int
Length of the filter (number of coefficients, i.e. the filter
order + 1). `numtaps` must be even if a passband includes the
Nyquist frequency.
cutoff : float or 1D array_like
Cutoff frequency of filter (expressed in the same units as `nyq`)
OR an array of cutoff frequencies (that is, band edges). In the
latter case, the frequencies in `cutoff` should be positive and
monotonically increasing between 0 and `nyq`. The values 0 and
`nyq` must not be included in `cutoff`.
width : float or None
If `width` is not None, then assume it is the approximate width
of the transition region (expressed in the same units as `nyq`)
for use in Kaiser FIR filter design. In this case, the `window`
argument is ignored.
window : string or tuple of string and parameter values
Desired window to use. See `scipy.signal.get_window` for a list
of windows and required parameters.
pass_zero : bool
If True, the gain at the frequency 0 (i.e. the "DC gain") is 1.
Otherwise the DC gain is 0.
scale : bool
Set to True to scale the coefficients so that the frequency
response is exactly unity at a certain frequency.
That frequency is either:
0 (DC) if the first passband starts at 0 (i.e. pass_zero
is True);
`nyq` (the Nyquist rate) if the first passband ends at
`nyq` (i.e the filter is a single band highpass filter);
center of first passband otherwise.
nyq : float
Nyquist frequency. Each frequency in `cutoff` must be between 0
and `nyq`.
Returns
-------
h : 1D ndarray
Coefficients of length `numtaps` FIR filter.
Raises
------
ValueError
If any value in `cutoff` is less than or equal to 0 or greater
than or equal to `nyq`, if the values in `cutoff` are not strictly
monotonically increasing, or if `numtaps` is even but a passband
includes the Nyquist frequency.
Examples
--------
Low-pass from 0 to f::
>>> firwin(numtaps, f)
Use a specific window function::
>>> firwin(numtaps, f, window='nuttall')
High-pass ('stop' from 0 to f)::
>>> firwin(numtaps, f, pass_zero=False)
Band-pass::
>>> firwin(numtaps, [f1, f2], pass_zero=False)
Band-stop::
>>> firwin(numtaps, [f1, f2])
Multi-band (passbands are [0, f1], [f2, f3] and [f4, 1])::
>>>firwin(numtaps, [f1, f2, f3, f4])
Multi-band (passbands are [f1, f2] and [f3,f4])::
>>> firwin(numtaps, [f1, f2, f3, f4], pass_zero=False)
See also
--------
scipy.signal.firwin2
"""
# The major enhancements to this function added in November 2010 were
# developed by Tom Krauss (see ticket #902).
cutoff = np.atleast_1d(cutoff) / float(nyq)
# Check for invalid input.
if cutoff.ndim > 1:
raise ValueError("The cutoff argument must be at most one-dimensional.")
if cutoff.size == 0:
raise ValueError("At least one cutoff frequency must be given.")
if cutoff.min() <= 0 or cutoff.max() >= 1:
raise ValueError("Invalid cutoff frequency: frequencies must be greater than 0 and less than nyq.")
if np.any(np.diff(cutoff) <= 0):
raise ValueError("Invalid cutoff frequencies: the frequencies must be strictly increasing.")
if width is not None:
# A width was given. Find the beta parameter of the Kaiser window
# and set `window`. This overrides the value of `window` passed in.
atten = kaiser_atten(numtaps, float(width)/nyq)
beta = kaiser_beta(atten)
window = ('kaiser', beta)
pass_nyquist = bool(cutoff.size & 1) ^ pass_zero
if pass_nyquist and numtaps % 2 == 0:
raise ValueError("A filter with an even number of coefficients must "
"have zero response at the Nyquist rate.")
# Insert 0 and/or 1 at the ends of cutoff so that the length of cutoff is even,
# and each pair in cutoff corresponds to passband.
cutoff = np.hstack(([0.0]*pass_zero, cutoff, [1.0]*pass_nyquist))
# `bands` is a 2D array; each row gives the left and right edges of a passband.
bands = cutoff.reshape(-1,2)
# Build up the coefficients.
alpha = 0.5 * (numtaps-1)
m = np.arange(0, numtaps) - alpha
h = 0
for left, right in bands:
h += right * sinc(right * m)
h -= left * sinc(left * m)
# Get and apply the window function.
from signaltools import get_window
win = get_window(window, numtaps, fftbins=False)
h *= win
# Now handle scaling if desired.
if scale:
# Get the first passband.
left, right = bands[0]
if left == 0:
scale_frequency = 0.0
elif right == 1:
scale_frequency = 1.0
else:
scale_frequency = 0.5 * (left + right)
c = np.cos(np.pi * m * scale_frequency)
s = np.sum(h * c)
h /= s
return h
def firwin(numtaps, cutoff, width=None, window='hamming', pass_zero=True,
scale=True, nyq=None, fs=None):
"""
FIR filter design using the window method.
This function computes the coefficients of a finite impulse response
filter. The filter will have linear phase; it will be Type I if
`numtaps` is odd and Type II if `numtaps` is even.
Type II filters always have zero response at the Nyquist frequency, so a
ValueError exception is raised if firwin is called with `numtaps` even and
having a passband whose right end is at the Nyquist frequency.
Parameters
----------
numtaps : int
Length of the filter (number of coefficients, i.e. the filter
order + 1). `numtaps` must be odd if a passband includes the
Nyquist frequency.
cutoff : float or 1D array_like
Cutoff frequency of filter (expressed in the same units as `fs`)
OR an array of cutoff frequencies (that is, band edges). In the
latter case, the frequencies in `cutoff` should be positive and
monotonically increasing between 0 and `fs/2`. The values 0 and
`fs/2` must not be included in `cutoff`.
width : float or None, optional
If `width` is not None, then assume it is the approximate width
of the transition region (expressed in the same units as `fs`)
for use in Kaiser FIR filter design. In this case, the `window`
argument is ignored.
window : string or tuple of string and parameter values, optional
Desired window to use. See `scipy.signal.get_window` for a list
of windows and required parameters.
pass_zero : {True, False, 'bandpass', 'lowpass', 'highpass', 'bandstop'}, optional
If True, the gain at the frequency 0 (i.e. the "DC gain") is 1.
If False, the DC gain is 0. Can also be a string argument for the
desired filter type (equivalent to ``btype`` in IIR design functions).
.. versionadded:: 1.3.0
Support for string arguments.
scale : bool, optional
Set to True to scale the coefficients so that the frequency
response is exactly unity at a certain frequency.
That frequency is either:
- 0 (DC) if the first passband starts at 0 (i.e. pass_zero
is True)
- `fs/2` (the Nyquist frequency) if the first passband ends at
`fs/2` (i.e the filter is a single band highpass filter);
center of first passband otherwise
nyq : float, optional
*Deprecated. Use `fs` instead.* This is the Nyquist frequency.
Each frequency in `cutoff` must be between 0 and `nyq`. Default
is 1.
fs : float, optional
The sampling frequency of the signal. Each frequency in `cutoff`
must be between 0 and ``fs/2``. Default is 2.
Returns
-------
h : (numtaps,) ndarray
Coefficients of length `numtaps` FIR filter.
Raises
------
ValueError
If any value in `cutoff` is less than or equal to 0 or greater
than or equal to ``fs/2``, if the values in `cutoff` are not strictly
monotonically increasing, or if `numtaps` is even but a passband
includes the Nyquist frequency.
See Also
--------
firwin2
firls
minimum_phase
remez
Examples
--------
Low-pass from 0 to f:
>>> from scipy import signal
>>> numtaps = 3
>>> f = 0.1
>>> signal.firwin(numtaps, f)
array([ 0.06799017, 0.86401967, 0.06799017])
Use a specific window function:
>>> signal.firwin(numtaps, f, window='nuttall')
array([ 3.56607041e-04, 9.99286786e-01, 3.56607041e-04])
High-pass ('stop' from 0 to f):
>>> signal.firwin(numtaps, f, pass_zero=False)
array([-0.00859313, 0.98281375, -0.00859313])
Band-pass:
>>> f1, f2 = 0.1, 0.2
>>> signal.firwin(numtaps, [f1, f2], pass_zero=False)
array([ 0.06301614, 0.88770441, 0.06301614])
Band-stop:
>>> signal.firwin(numtaps, [f1, f2])
array([-0.00801395, 1.0160279 , -0.00801395])
Multi-band (passbands are [0, f1], [f2, f3] and [f4, 1]):
>>> f3, f4 = 0.3, 0.4
>>> signal.firwin(numtaps, [f1, f2, f3, f4])
array([-0.01376344, 1.02752689, -0.01376344])
Multi-band (passbands are [f1, f2] and [f3,f4]):
>>> signal.firwin(numtaps, [f1, f2, f3, f4], pass_zero=False)
array([ 0.04890915, 0.91284326, 0.04890915])
""" # noqa: E501
# The major enhancements to this function added in November 2010 were
# developed by Tom Krauss (see ticket #902).
nyq = 0.5 * _get_fs(fs, nyq)
cutoff = np.atleast_1d(cutoff) / float(nyq)
# Check for invalid input.
if cutoff.ndim > 1:
raise ValueError("The cutoff argument must be at most "
"one-dimensional.")
if cutoff.size == 0:
raise ValueError("At least one cutoff frequency must be given.")
if cutoff.min() <= 0 or cutoff.max() >= 1:
raise ValueError("Invalid cutoff frequency: frequencies must be "
"greater than 0 and less than fs/2.")
if np.any(np.diff(cutoff) <= 0):
raise ValueError("Invalid cutoff frequencies: the frequencies "
"must be strictly increasing.")
if width is not None:
# A width was given. Find the beta parameter of the Kaiser window
# and set `window`. This overrides the value of `window` passed in.
atten = kaiser_atten(numtaps, float(width) / nyq)
beta = kaiser_beta(atten)
window = ('kaiser', beta)
if isinstance(pass_zero, str):
if pass_zero in ('bandstop', 'lowpass'):
if pass_zero == 'lowpass':
if cutoff.size != 1:
raise ValueError('cutoff must have one element if '
'pass_zero=="lowpass", got %s'
% (cutoff.shape,))
elif cutoff.size <= 1:
raise ValueError('cutoff must have at least two elements if '
'pass_zero=="bandstop", got %s'
% (cutoff.shape,))
pass_zero = True
elif pass_zero in ('bandpass', 'highpass'):
if pass_zero == 'highpass':
if cutoff.size != 1:
raise ValueError('cutoff must have one element if '
'pass_zero=="highpass", got %s'
% (cutoff.shape,))
elif cutoff.size <= 1:
raise ValueError('cutoff must have at least two elements if '
'pass_zero=="bandpass", got %s'
% (cutoff.shape,))
pass_zero = False
else:
raise ValueError('pass_zero must be True, False, "bandpass", '
'"lowpass", "highpass", or "bandstop", got '
'%s' % (pass_zero,))
pass_zero = bool(operator.index(pass_zero)) # ensure bool-like
pass_nyquist = bool(cutoff.size & 1) ^ pass_zero
if pass_nyquist and numtaps % 2 == 0:
raise ValueError("A filter with an even number of coefficients must "
"have zero response at the Nyquist frequency.")
# Insert 0 and/or 1 at the ends of cutoff so that the length of cutoff
# is even, and each pair in cutoff corresponds to passband.
cutoff = np.hstack(([0.0] * pass_zero, cutoff, [1.0] * pass_nyquist))
# `bands` is a 2D array; each row gives the left and right edges of
# a passband.
bands = cutoff.reshape(-1, 2)
# Build up the coefficients.
alpha = 0.5 * (numtaps - 1)
m = np.arange(0, numtaps) - alpha
h = 0
for left, right in bands:
h += right * sinc(right * m)
h -= left * sinc(left * m)
# Get and apply the window function.
from .signaltools import get_window
win = get_window(window, numtaps, fftbins=False)
h *= win
# Now handle scaling if desired.
if scale:
# Get the first passband.
left, right = bands[0]
if left == 0:
scale_frequency = 0.0
elif right == 1:
scale_frequency = 1.0
else:
scale_frequency = 0.5 * (left + right)
c = np.cos(np.pi * m * scale_frequency)
s = np.sum(h * c)
h /= s
return h
import numpy as np from scipy import special import matplotlib.pylab as plt domain = np.linspace(0, 2 *np.pi, 512) sinc_write = special.sinc(domain) plt.plot(domain, sinc_write) plt.show()
def firwin(numtaps, cutoff, width=None, window='hamming', pass_zero=True,
scale=True, nyq=None, fs=None):
"""
FIR filter design using the window method.
This function computes the coefficients of a finite impulse response
filter. The filter will have linear phase; it will be Type I if
`numtaps` is odd and Type II if `numtaps` is even.
Type II filters always have zero response at the Nyquist frequency, so a
ValueError exception is raised if firwin is called with `numtaps` even and
having a passband whose right end is at the Nyquist frequency.
Parameters
----------
numtaps : int
Length of the filter (number of coefficients, i.e. the filter
order + 1). `numtaps` must be odd if a passband includes the
Nyquist frequency.
cutoff : float or 1-D array_like
Cutoff frequency of filter (expressed in the same units as `fs`)
OR an array of cutoff frequencies (that is, band edges). In the
latter case, the frequencies in `cutoff` should be positive and
monotonically increasing between 0 and `fs/2`. The values 0 and
`fs/2` must not be included in `cutoff`.
width : float or None, optional
If `width` is not None, then assume it is the approximate width
of the transition region (expressed in the same units as `fs`)
for use in Kaiser FIR filter design. In this case, the `window`
argument is ignored.
window : string or tuple of string and parameter values, optional
Desired window to use. See `scipy.signal.get_window` for a list
of windows and required parameters.
pass_zero : {True, False, 'bandpass', 'lowpass', 'highpass', 'bandstop'}, optional
If True, the gain at the frequency 0 (i.e., the "DC gain") is 1.
If False, the DC gain is 0. Can also be a string argument for the
desired filter type (equivalent to ``btype`` in IIR design functions).
.. versionadded:: 1.3.0
Support for string arguments.
scale : bool, optional
Set to True to scale the coefficients so that the frequency
response is exactly unity at a certain frequency.
That frequency is either:
- 0 (DC) if the first passband starts at 0 (i.e. pass_zero
is True)
- `fs/2` (the Nyquist frequency) if the first passband ends at
`fs/2` (i.e the filter is a single band highpass filter);
center of first passband otherwise
nyq : float, optional
*Deprecated. Use `fs` instead.* This is the Nyquist frequency.
Each frequency in `cutoff` must be between 0 and `nyq`. Default
is 1.
fs : float, optional
The sampling frequency of the signal. Each frequency in `cutoff`
must be between 0 and ``fs/2``. Default is 2.
Returns
-------
h : (numtaps,) ndarray
Coefficients of length `numtaps` FIR filter.
Raises
------
ValueError
If any value in `cutoff` is less than or equal to 0 or greater
than or equal to ``fs/2``, if the values in `cutoff` are not strictly
monotonically increasing, or if `numtaps` is even but a passband
includes the Nyquist frequency.
See Also
--------
firwin2
firls
minimum_phase
remez
Examples
--------
Low-pass from 0 to f:
>>> from scipy import signal
>>> numtaps = 3
>>> f = 0.1
>>> signal.firwin(numtaps, f)
array([ 0.06799017, 0.86401967, 0.06799017])
Use a specific window function:
>>> signal.firwin(numtaps, f, window='nuttall')
array([ 3.56607041e-04, 9.99286786e-01, 3.56607041e-04])
High-pass ('stop' from 0 to f):
>>> signal.firwin(numtaps, f, pass_zero=False)
array([-0.00859313, 0.98281375, -0.00859313])
Band-pass:
>>> f1, f2 = 0.1, 0.2
>>> signal.firwin(numtaps, [f1, f2], pass_zero=False)
array([ 0.06301614, 0.88770441, 0.06301614])
Band-stop:
>>> signal.firwin(numtaps, [f1, f2])
array([-0.00801395, 1.0160279 , -0.00801395])
Multi-band (passbands are [0, f1], [f2, f3] and [f4, 1]):
>>> f3, f4 = 0.3, 0.4
>>> signal.firwin(numtaps, [f1, f2, f3, f4])
array([-0.01376344, 1.02752689, -0.01376344])
Multi-band (passbands are [f1, f2] and [f3,f4]):
>>> signal.firwin(numtaps, [f1, f2, f3, f4], pass_zero=False)
array([ 0.04890915, 0.91284326, 0.04890915])
""" # noqa: E501
# The major enhancements to this function added in November 2010 were
# developed by Tom Krauss (see ticket #902).
nyq = 0.5 * _get_fs(fs, nyq)
cutoff = np.atleast_1d(cutoff) / float(nyq)
# Check for invalid input.
if cutoff.ndim > 1:
raise ValueError("The cutoff argument must be at most "
"one-dimensional.")
if cutoff.size == 0:
raise ValueError("At least one cutoff frequency must be given.")
if cutoff.min() <= 0 or cutoff.max() >= 1:
raise ValueError("Invalid cutoff frequency: frequencies must be "
"greater than 0 and less than fs/2.")
if np.any(np.diff(cutoff) <= 0):
raise ValueError("Invalid cutoff frequencies: the frequencies "
"must be strictly increasing.")
if width is not None:
# A width was given. Find the beta parameter of the Kaiser window
# and set `window`. This overrides the value of `window` passed in.
atten = kaiser_atten(numtaps, float(width) / nyq)
beta = kaiser_beta(atten)
window = ('kaiser', beta)
if isinstance(pass_zero, str):
if pass_zero in ('bandstop', 'lowpass'):
if pass_zero == 'lowpass':
if cutoff.size != 1:
raise ValueError('cutoff must have one element if '
'pass_zero=="lowpass", got %s'
% (cutoff.shape,))
elif cutoff.size <= 1:
raise ValueError('cutoff must have at least two elements if '
'pass_zero=="bandstop", got %s'
% (cutoff.shape,))
pass_zero = True
elif pass_zero in ('bandpass', 'highpass'):
if pass_zero == 'highpass':
if cutoff.size != 1:
raise ValueError('cutoff must have one element if '
'pass_zero=="highpass", got %s'
% (cutoff.shape,))
elif cutoff.size <= 1:
raise ValueError('cutoff must have at least two elements if '
'pass_zero=="bandpass", got %s'
% (cutoff.shape,))
pass_zero = False
else:
raise ValueError('pass_zero must be True, False, "bandpass", '
'"lowpass", "highpass", or "bandstop", got '
'%s' % (pass_zero,))
pass_zero = bool(operator.index(pass_zero)) # ensure bool-like
pass_nyquist = bool(cutoff.size & 1) ^ pass_zero
if pass_nyquist and numtaps % 2 == 0:
raise ValueError("A filter with an even number of coefficients must "
"have zero response at the Nyquist frequency.")
# Insert 0 and/or 1 at the ends of cutoff so that the length of cutoff
# is even, and each pair in cutoff corresponds to passband.
cutoff = np.hstack(([0.0] * pass_zero, cutoff, [1.0] * pass_nyquist))
# `bands` is a 2-D array; each row gives the left and right edges of
# a passband.
bands = cutoff.reshape(-1, 2)
# Build up the coefficients.
alpha = 0.5 * (numtaps - 1)
m = np.arange(0, numtaps) - alpha
h = 0
for left, right in bands:
h += right * sinc(right * m)
h -= left * sinc(left * m)
# Get and apply the window function.
from .signaltools import get_window
win = get_window(window, numtaps, fftbins=False)
h *= win
# Now handle scaling if desired.
if scale:
# Get the first passband.
left, right = bands[0]
if left == 0:
scale_frequency = 0.0
elif right == 1:
scale_frequency = 1.0
else:
scale_frequency = 0.5 * (left + right)
c = np.cos(np.pi * m * scale_frequency)
s = np.sum(h * c)
h /= s
return h
def calc_stimulus_frame(self, N_first: int = 0, N_frame: int = 10, N_end: int = 10,
init: bool = False) -> np.ndarray:
"""
Calculate a data frame of stimulus `x` with a length of `N_frame` samples,
starting with index `N_first`
Parameters
----------
N_first: int
index of first data point
N_frame: int
number of samples to be generated
init: bool
when init == True, initialize stimulus settings
Returns
-------
x: ndarray
an array with `N` stimulus data points
"""
if init or N_first == 0:
'''intialize title string, y-axis label and some variables'''
# use radians for angle internally
self.rad_phi1 = self.ui.phi1 / 180 * pi
self.rad_phi2 = self.ui.phi2 / 180 * pi
# check whether some amplitude is complex and set array type for xf
# correspondingly.
if (self.ui.ledDC.isVisible and type(self.ui.DC) == complex) or\
(self.ui.ledAmp1.isVisible and type(self.ui.A1) == complex) or\
(self.ui.ledAmp2.isVisible and type(self.ui.A2) == complex):
self.xf = np.zeros(N_frame, dtype=complex)
else:
self.xf = np.zeros(N_frame, dtype=float)
self.H_str = r'$y[n]$' # default
self.title_str = ""
if self.ui.stim == "none":
self.title_str = r'Zero Input Response'
self.H_str = r'$h_0[n]$'
# ------------------------------------------------------------------
elif self.ui.stim == "dirac":
self.title_str = r'Impulse Response'
self.H_str = r'$h[n]$'
elif self.ui.stim == "sinc":
self.title_str = r'Sinc Impulse'
elif self.ui.stim == "gauss":
self.title_str = r'Gaussian Impulse'
elif self.ui.stim == "rect":
self.title_str = r'Rect Impulse'
# ------------------------------------------------------------------
elif self.ui.stim == "step":
if self.ui.chk_step_err.isChecked():
self.title_str = r'Settling Error $\epsilon$'
self.H_str = r'$h_{\epsilon, \infty} - h_{\epsilon}[n]$'
else:
self.title_str = r'Step Response'
self.H_str = r'$h_{\epsilon}[n]$'
# ------------------------------------------------------------------
elif self.ui.stim == "cos":
self.title_str = r'Cosine Stimulus'
elif self.ui.stim == "sine":
self.title_str = r'Sinusoidal Stimulus'
elif self.ui.stim == "exp":
self.title_str = r'Complex Exponential Stimulus'
elif self.ui.stim == "diric":
self.title_str = r'Periodic Sinc Stimulus'
# ------------------------------------------------------------------
elif self.ui.stim == "chirp":
self.title_str = self.ui.chirp_type.capitalize() + ' Chirp Stimulus'
# ------------------------------------------------------------------
elif self.ui.stim == "triang":
if self.ui.but_stim_bl.isChecked():
self.title_str = r'Bandlim. Triangular Stimulus'
else:
self.title_str = r'Triangular Stimulus'
elif self.ui.stim == "saw":
if self.ui.but_stim_bl.isChecked():
self.title_str = r'Bandlim. Sawtooth Stimulus'
else:
self.title_str = r'Sawtooth Stimulus'
elif self.ui.stim == "square":
if self.ui.but_stim_bl.isChecked():
self.title_str = r'Bandlimited Rect. Stimulus'
else:
self.title_str = r'Rect. Stimulus'
elif self.ui.stim == "comb":
self.title_str = r'Bandlim. Comb Stimulus'
# ------------------------------------------------------------------
elif self.ui.stim == "am":
self.title_str = (
r'AM Stimulus: $A_1 \sin(2 \pi n f_1 + \varphi_1)'
r'\cdot A_2 \sin(2 \pi n f_2 + \varphi_2)$')
elif self.ui.stim == "pmfm":
self.title_str = (
r'PM / FM Stimulus: $A_1 \sin(2 \pi n f_1'
r'+ \varphi_1 + A_2 \sin(2 \pi n f_2 + \varphi_2))$')
# ------------------------------------------------------------------
elif self.ui.stim == "formula":
self.title_str = r'Formula Defined Stimulus'
# ==================================================================
if self.ui.noise == "gauss":
self.title_str += r' + Gaussian Noise'
elif self.ui.noise == "uniform":
self.title_str += r' + Uniform Noise'
elif self.ui.noise == "prbs":
self.title_str += r' + PRBS Noise'
elif self.ui.noise == "mls":
self.title_str += r' + max. length sequence'
elif self.ui.noise == "brownian":
self.title_str += r' + Brownian Noise'
# ==================================================================
if self.ui.ledDC.isVisible and self.ui.DC != 0:
self.title_str += r' + DC'
# ----------------------------------------------------------------------
N_last = N_first + N_frame
n = np.arange(N_first, N_last)
# T_S = fb.fil[0]['T_S']
self.T1_idx = int(np.round(self.ui.T1))
# calculate stimuli x[n] ==============================================
if self.ui.stim == "none":
self.xf.fill(0)
# ----------------------------------------------------------------------
elif self.ui.stim == "dirac":
self.xf.fill(0) # = np.zeros(N_frame, dtype=A_type)
if N_first <= self.T1_idx < N_last:
self.xf[self.T1_idx - N_first] = self.ui.A1
# ----------------------------------------------------------------------
elif self.ui.stim == "sinc":
self.xf = self.ui.A1 * sinc(2 * (n - self.ui.T1) * self.ui.f1)\
+ self.ui.A2 * sinc(2 * (n - self.ui.T2) * self.ui.f2)
# ----------------------------------------------------------------------
elif self.ui.stim == "gauss":
self.xf = self.ui.A1 * sig.gausspulse(
(n - self.ui.T1), fc=self.ui.f1, bw=self.ui.BW1) +\
self.ui.A2 * sig.gausspulse(
(n - self.ui.T2), fc=self.ui.f2, bw=self.ui.BW2)
# ----------------------------------------------------------------------
elif self.ui.stim == "rect":
n_rise = int(self.T1_idx - np.floor(self.ui.TW1/2))
n_min = max(n_rise, 0)
n_max = min(n_rise + self.ui.TW1, N_end)
self.xf = self.ui.A1 * np.where((n >= n_min) & (n < n_max), 1, 0)
# ----------------------------------------------------------------------
elif self.ui.stim == "step":
if self.T1_idx < N_first: # step before current frame
self.xf.fill(self.ui.A1)
if N_first <= self.T1_idx < N_last: # step in current frame
self.xf[0:self.T1_idx - N_first].fill(0)
self.xf[self.T1_idx - N_first:].fill(self.ui.A1)
elif self.T1_idx >= N_last: # step after current frame
self.xf.fill(0)
# ----------------------------------------------------------------------
elif self.ui.stim == "cos":
self.xf =\
self.ui.A1 * np.cos(2*pi * n * self.ui.f1 + self.rad_phi1) +\
self.ui.A2 * np.cos(2*pi * n * self.ui.f2 + self.rad_phi2)
# ----------------------------------------------------------------------
elif self.ui.stim == "sine":
self.xf =\
self.ui.A1 * np.sin(2*pi * n * self.ui.f1 + self.rad_phi1) +\
self.ui.A2 * np.sin(2*pi * n * self.ui.f2 + self.rad_phi2)
# ----------------------------------------------------------------------
elif self.ui.stim == "exp":
self.xf =\
self.ui.A1 * np.exp(1j * (2 * pi * n * self.ui.f1 + self.rad_phi1)) +\
self.ui.A2 * np.exp(1j * (2 * pi * n * self.ui.f2 + self.rad_phi2))
# ----------------------------------------------------------------------
elif self.ui.stim == "diric":
self.xf = self.ui.A1 * diric(
(4 * pi * (n-self.ui.T1) * self.ui.f1 + self.rad_phi1*2)
/ self.ui.TW1, self.ui.TW1)
# ----------------------------------------------------------------------
elif self.ui.stim == "chirp":
if self.ui.T2 == 0: # sig.chirp is buggy, T_sim cannot be larger than T_end
T_end = N_end # frequency sweep over complete interval
else:
T_end = self.ui.T2 # frequency sweep till T2
self.xf = self.ui.A1 * sig.chirp(
n, self.ui.f1, T_end, self.ui.f2,
method=self.ui.chirp_type, phi=self.rad_phi1)
# ----------------------------------------------------------------------
elif self.ui.stim == "triang":
if self.ui.but_stim_bl.isChecked():
self.xf = self.ui.A1 * triang_bl(2*pi * n * self.ui.f1 + self.rad_phi1)
else:
self.xf = self.ui.A1 * sig.sawtooth(
2*pi * n * self.ui.f1 + self.rad_phi1, width=0.5)
# ----------------------------------------------------------------------
elif self.ui.stim == "saw":
if self.ui.but_stim_bl.isChecked():
self.xf = self.ui.A1 * sawtooth_bl(2*pi * n * self.ui.f1 + self.rad_phi1)
else:
self.xf = self.ui.A1 * sig.sawtooth(2*pi * n * self.ui.f1 + self.rad_phi1)
# ----------------------------------------------------------------------
elif self.ui.stim == "square":
if self.ui.but_stim_bl.isChecked():
self.xf = self.ui.A1 * rect_bl(
2 * pi * n * self.ui.f1 + self.rad_phi1, duty=self.ui.stim_par1)
else:
self.xf = self.ui.A1 * sig.square(
2 * pi * n * self.ui.f1 + self.rad_phi1, duty=self.ui.stim_par1)
# ----------------------------------------------------------------------
elif self.ui.stim == "comb":
self.xf = self.ui.A1 * comb_bl(2 * pi * n * self.ui.f1 + self.rad_phi1)
# ----------------------------------------------------------------------
elif self.ui.stim == "am":
self.xf = self.ui.A1 * np.sin(2*pi * n * self.ui.f1 + self.rad_phi1)\
* self.ui.A2 * np.sin(2*pi * n * self.ui.f2 + self.rad_phi2)
# ----------------------------------------------------------------------
elif self.ui.stim == "pmfm":
self.xf = self.ui.A1 * np.sin(
2 * pi * n * self.ui.f1 + self.rad_phi1 +
self.ui.A2 * np.sin(2*pi * n * self.ui.f2 + self.rad_phi2))
# ----------------------------------------------------------------------
elif self.ui.stim == "formula":
param_dict = {"A1": self.ui.A1, "A2": self.ui.A2,
"f1": self.ui.f1, "f2": self.ui.f2,
"phi1": self.ui.phi1, "phi2": self.ui.phi2,
"BW1": self.ui.BW1, "BW2": self.ui.BW2,
"f_S": fb.fil[0]['f_S'], "n": n, "j": 1j}
self.xf = safe_numexpr_eval(self.ui.stim_formula, (N_frame,), param_dict)
else:
logger.error('Unknown stimulus format "{0}"'.format(self.ui.stim))
return None
# ----------------------------------------------------------------------
# Add noise to stimulus
noi = 0
if self.ui.noise == "none":
pass
elif self.ui.noise == "gauss":
noi = self.ui.noi * np.random.randn(N_frame)
elif self.ui.noise == "uniform":
noi = self.ui.noi * (np.random.rand(N_frame)-0.5)
elif self.ui.noise == "prbs":
noi = self.ui.noi * 2 * (np.random.randint(0, 2, N_frame)-0.5)
elif self.ui.noise == "mls":
# max_len_seq returns `sequence, state`. The state is not stored here,
# hence, an identical sequence is created every time.
noi = self.ui.noi * 2 * (sig.max_len_seq(int(np.ceil(np.log2(N_frame))),
length=N_frame, state=None)[0] - 0.5)
elif self.ui.noise == "brownian":
# brownian noise
noi = np.cumsum(self.ui.noi * np.random.randn(N_frame))
else:
logger.error('Unknown kind of noise "{}"'.format(self.ui.noise))
if type(self.ui.noi) == complex:
self.xf = self.xf.astype(complex) + noi
else:
self.xf += noi
# Add DC to stimulus when visible / enabled
if self.ui.ledDC.isVisible:
if type(self.ui.DC) == complex:
self.xf = self.xf.astype(complex) + self.ui.DC
else:
self.xf += self.ui.DC
return self.xf[:N_frame]
def __init__(self, a):
super(Sinc, self).__init__(domain=(-np.inf, np.inf))
self.calc = lambda t: sinc(a*t)
import numpy
from matplotlib import pyplot
from ex3a_funcs import fraunhofer, single_slit
from scipy.special import sinc
lam = 500e-9
d = 100e-6
D = 1
L = 5e-3
N = 2**9
A = single_slit(L, d, N)
y, I = fraunhofer(A, L, N)
pyplot.clf()
pyplot.plot(y * d, I, '--', label='Computed')
pyplot.plot(y * d, sinc(d * y)**2, label='Theoretical')
pyplot.xlabel('$y d / (\lambda D)$')
pyplot.ylabel('$I/I_0$')
pyplot.legend()
pyplot.savefig('core_task1.pdf')
def slepian(M, width, sym=True):
"""Return a digital Slepian (DPSS) window.
Used to maximize the energy concentration in the main lobe. Also called
the digital prolate spheroidal sequence (DPSS).
Parameters
----------
M : int
Number of points in the output window. If zero or less, an empty
array is returned.
width : float
Bandwidth
sym : bool, optional
When True, generates a symmetric window, for use in filter design.
When False, generates a periodic window, for use in spectral analysis.
Returns
-------
w : ndarray
The window, with the maximum value always normalized to 1
Examples
--------
Plot the window and its frequency response:
>>> from scipy import signal
>>> from scipy.fftpack import fft, fftshift
>>> import matplotlib.pyplot as plt
>>> window = signal.slepian(51, width=0.3)
>>> plt.plot(window)
>>> plt.title("Slepian (DPSS) window (BW=0.3)")
>>> plt.ylabel("Amplitude")
>>> plt.xlabel("Sample")
>>> plt.figure()
>>> A = fft(window, 2048) / (len(window)/2.0)
>>> freq = np.linspace(-0.5, 0.5, len(A))
>>> response = 20 * np.log10(np.abs(fftshift(A / abs(A).max())))
>>> plt.plot(freq, response)
>>> plt.axis([-0.5, 0.5, -120, 0])
>>> plt.title("Frequency response of the Slepian window (BW=0.3)")
>>> plt.ylabel("Normalized magnitude [dB]")
>>> plt.xlabel("Normalized frequency [cycles per sample]")
"""
if (M * width > 27.38):
raise ValueError("Cannot reliably obtain slepian sequences for"
" M*width > 27.38.")
if M < 1:
return np.array([])
if M == 1:
return np.ones(1, 'd')
odd = M % 2
if not sym and not odd:
M = M + 1
twoF = width / 2.0
alpha = (M - 1) / 2.0
m = np.arange(0, M) - alpha
n = m[:, np.newaxis]
k = m[np.newaxis, :]
AF = twoF * special.sinc(twoF * (n - k))
[lam, vec] = linalg.eig(AF)
ind = np.argmax(abs(lam), axis=-1)
w = np.abs(vec[:, ind])
w = w / max(w)
if not sym and not odd:
w = w[:-1]
return w
def interpolant(t):
return np.sum(signal*sinc((t - ts)/dt))