def desired_highpass():
ripple_low = 0.01
ripple_high = 0.05
# Normalized frequencies vector
F = [0, 0.5, 0.6, 1]
# Desired amplitudes of each point listed in 'F'
Amp = [0, 1]
# Weights vector
W = [1/ripple_low, 1/ripple_high]
M = get_M(ripple_low, ripple_high, 0.5, 0.6)
h = remez(M+1, F, Amp, W, Hz=fs)
A_w = get_amplitude_func(h, 1)
plt.figure()
plt.plot(h)
plt.title("h[n] is GLP filter of type I.")
plt.grid()
plt.legend()
w = np.linspace(-2 * math.pi, 2 * math.pi, 4096)
A = []
for i in w:
A.append(A_w(i))
w /= math.pi
plt.figure()
plt.plot(w, A)
plot_plus("A(w)")
def desired_bandpass():
ripple_low = 0.02
ripple_medium = 0.05
ripple_high = 0.01
# Normalized frequencies vector
F = [0, 0.3, 0.4, 0.7, 0.8, 1]
# Desired amplitudes of each point listed in 'F'
Amp = [0, 0, 1, 1, 0, 0]
# Weights vector
W = [1 / ripple_low, 1 / ripple_medium, 1 / ripple_high]
h = firls(M + 1, F, Amp, W)
A_w = get_amplitude_func(h, 1)
plt.figure()
plt.plot(h)
plt.title("h[n] is GLP filter of type I.")
plt.grid()
plt.legend()
w = np.linspace(-2 * math.pi, 2 * math.pi, 4096)
A = []
for i in w:
A.append(A_w(i))
w /= math.pi
plt.figure()
plt.plot(w, A)
plot_plus("A(w)")
def ex_7():
(M, window) = get_kaiser_window(ripple, delta_w)
# We know that h is simmetric.
# Therefore, it depends on M whether its a type I or II filter.
# k indicates the frequency range to take into account.
if (M % 2 == 0):
filter_type = 1
k = 1
else:
filter_type = 2
k = 2
h_ideal = ideal_lowpass_truncated(w_c, M)
h = np.multiply(h_ideal, window)
A_w = get_amplitude_func(h, filter_type)
plt.figure()
plt.plot(h_ideal)
plt.title("Impulse response corresponds to a type " + str(filter_type) +
" filter.")
plt.grid()
plt.figure()
w = np.linspace(-k * math.pi, k * math.pi, 4096)
A = []
for i in w:
A.append(A_w(i))
w /= math.pi
plt.plot(w, A)
plot_plus(title="Freq. response")
def ex_1():
# Cutoff frequency
w_c = math.pi / 2
# Frequency domain
w = np.linspace(-1 * math.pi, math.pi, 4096)
# Phase delay variations
for M in [10, 100, 1000]:
# Index of truncated sinc function
n_trunc = np.linspace(0, M, endpoint=True, num=M+1)
# Impulse response of truncated sinc function
h_trunc = (w_c / math.pi) * np.sinc((w_c / math.pi) * (n_trunc - M/2))
# Amplitude function of truncated sinc function
A_w_trunc = get_amplitude_func(h_trunc, 1)
y_trunc = []
for i in w:
y_trunc.append(A_w_trunc(i))
plt.plot(w, y_trunc, label="M = " + str(M))
y_ideal = [0] * 4096
for i in xrange(1024, 3072):
y_ideal[i] = 1
plt.plot(w, y_ideal, label="Ideal frequency response")
plt.title("Amplitude function of truncated sinc")
plt.legend()
plt.grid()
plt.show()
def ex_17():
h1 = diferentiator(M1)
h2 = diferentiator(M2)
A_w1 = get_amplitude_func(h1, 4)
A_w2 = get_amplitude_func(h2, 3)
plt.figure()
plt.plot(h1)
plt.title("h1[n] corresponds to type IV filter.")
plt.grid()
plt.legend()
plt.figure()
plt.plot(h2)
plt.title("h2[n] corresponds to type III filter.")
plt.grid()
plt.legend()
w = np.linspace(-2 * math.pi, 2 * math.pi, 4096)
A1 = []
A2 = []
for i in w:
A1.append(A_w1(i))
A2.append(A_w2(i))
w /= math.pi
plt.figure()
plt.plot(w, A1)
plt.title("A1(w)")
plt.grid()
plt.legend()
plt.figure()
plt.plot(w, A2)
plt.title("A2(w)")
plt.grid()
plt.legend()
plt.show()
def ex_4():
M = 80
h = get_impulse_response(M)
A_w = get_amplitude_func(h, 1)
w = np.linspace(-1 * math.pi, math.pi, 4096)
A = []
for i in w:
A.append(A_w(i))
w /= math.pi
plt.figure()
plt.plot(h)
plt.title("Impulse response corresponds to a type I filter")
plt.grid()
plt.legend()
plt.figure()
plt.plot(w, A)
plot_plus(title="Freq. response")
def ex_12():
window = np.hamming(M + 1)
h_ideal = ideal_multiband_truncated(gains, freqs, M)
h = np.multiply(h_ideal, window)
A_w = get_amplitude_func(h, 1)
plt.figure()
plt.plot(h, label="h[n]")
w = np.linspace(-1 * math.pi, math.pi, 4096)
A = []
for i in w:
A.append(A_w(i))
w /= math.pi
plt.figure()
plt.plot(w, A)
plot_plus("Freq. response")
def ex_5():
M = 25
h = get_impulse_response(M)
A_w = get_amplitude_func(h, 2)
plt.figure()
plt.plot(h)
plt.title("Impulse response corresponds to a type II filter")
plt.grid()
plt.legend()
plt.figure()
w = np.linspace(-2 * math.pi, 2*math.pi, 4096)
A = []
for i in w:
A.append(A_w(i))
w/= math.pi
plt.plot(w, A)
plot_plus(title="Freq. response", xlabel="$\omega/\pi$", ylabel="A($\omega$)")
def ex_16():
h_ideal = ideal_hilbert_transformer_truncated(M)
h = np.multiply(h_ideal, window)
A_w = get_amplitude_func(h, 4)
plt.figure()
plt.plot(h)
plt.title("h[n] corresponds to type III filter.")
plt.grid()
plt.legend()
w = np.linspace(-2 * math.pi, 2 * math.pi, 4096)
A = []
for i in w:
A.append(A_w(i))
w /= math.pi
plt.figure()
plt.plot(w, A)
plot_plus("Freq. response")