def scipy_example(self, time, data, sample_rate=None):
"""
Example from the SciPy Cookboock, see
http://www.scipy.org/Cookbook/FIRFilter
"""
chk.array_1d(time)
chk.array_1d(data)
if not sample_rate:
sample_rate = calc_sample_rate(time)
# ------------------------------------------------
# Create a FIR filter and apply it to data[:,channel]
# ------------------------------------------------
# The Nyquist rate of the signal.
nyq_rate = sample_rate / 2.0
# The desired width of the transition from pass to stop,
# relative to the Nyquist rate. We'll design the filter
# with a 5 Hz transition width.
width = 5.0 / nyq_rate
# The desired attenuation in the stop band, in dB.
ripple_db = 60.0
# Compute the order and Kaiser parameter for the FIR filter.
N, beta = sp.signal.kaiserord(ripple_db, width)
# The cutoff frequency of the filter.
cutoff_hz = 10.0
# Use firwin with a Kaiser window to create a lowpass FIR filter.
taps = sp.signal.firwin(N, cutoff_hz / nyq_rate, window=("kaiser", beta))
# Use lfilter to filter x with the FIR filter.
filtered_x = sp.signal.lfilter(taps, 1.0, data)
# ------------------------------------------------
# Setup the figure parameters
# ------------------------------------------------
figpath = "processing/"
figfile = "filterdesign"
plot = plotting.A4Tuned()
plot.setup(figpath + figfile, nr_plots=3, grandtitle=figfile, figsize_y=20, wsleft_cm=2.0)
# ------------------------------------------------
# Plot the FIR filter coefficients.
# ------------------------------------------------
plot_nr = 1
ax1 = plot.fig.add_subplot(plot.nr_rows, plot.nr_cols, plot_nr)
ax1.plot(taps, "bo-", linewidth=2)
ax1.set_title("Filter Coefficients (%d taps)" % N)
ax1.grid(True)
# ------------------------------------------------
# Plot the magnitude response of the filter.
# ------------------------------------------------
plot_nr += 1
ax2 = plot.fig.add_subplot(plot.nr_rows, plot.nr_cols, plot_nr)
w, h = sp.signal.freqz(taps, worN=8000)
ax2.plot((w / np.pi) * nyq_rate, np.absolute(h), linewidth=2)
ax2.set_xlabel("Frequency (Hz)")
ax2.set_ylabel("Gain")
ax2.set_title("Frequency Response")
ax2.set_ylim(-0.05, 1.05)
# ax2.grid(True)
# in order to place the nex axes inside following figure, first
# determine the ax2 bounding box
# points: a 2x2 numpy array of the form [[x0, y0], [x1, y1]]
ax2box = ax2.get_window_extent().get_points()
# seems to be expressed in pixels so convert to relative coordinates
# print ax2box
# figure size in pixels
figsize_x_pix = plot.figsize_x * plot.dpi
figsize_y_pix = plot.figsize_y * plot.dpi
# ax2 box in relative coordinates
ax2box[:, 0] = ax2box[:, 0] / figsize_x_pix
ax2box[:, 1] = ax2box[:, 1] / figsize_y_pix
# print ax2box[0,0], ax2box[1,0], ax2box[0,1], ax2box[1,1]
# left position new box at 10% of x1
left = ax2box[0, 0] + ((ax2box[1, 0] - ax2box[0, 0]) * 0.15)
bottom = ax2box[0, 1] + ((ax2box[1, 1] - ax2box[0, 1]) * 0.30) # x2
width = (ax2box[1, 0] - ax2box[0, 0]) * 0.35
height = (ax2box[1, 1] - ax2box[0, 1]) * 0.6
# print [left, bottom, width, height]
# left inset plot.
# [left, bottom, width, height]
# ax2a = plot.fig.add_axes([0.42, 0.6, .45, .25])
ax2a = plot.fig.add_axes([left, bottom, width, height])
ax2a.plot((w / np.pi) * nyq_rate, np.absolute(h), linewidth=2)
ax2a.set_xlim(0, 8.0)
ax2a.set_ylim(0.9985, 1.001)
ax2a.grid(True)
# right inset plot
left = ax2box[0, 0] + ((ax2box[1, 0] - ax2box[0, 0]) * 0.62)
bottom = ax2box[0, 1] + ((ax2box[1, 1] - ax2box[0, 1]) * 0.30) # x2
width = (ax2box[1, 0] - ax2box[0, 0]) * 0.35
height = (ax2box[1, 1] - ax2box[0, 1]) * 0.6
# Lower inset plot
# ax2b = plot.fig.add_axes([0.42, 0.25, .45, .25])
ax2b = plot.fig.add_axes([left, bottom, width, height])
ax2b.plot((w / np.pi) * nyq_rate, np.absolute(h), linewidth=2)
ax2b.set_xlim(12.0, 20.0)
ax2b.set_ylim(0.0, 0.0025)
ax2b.grid(True)
# ------------------------------------------------
# Plot the original and filtered signals.
# ------------------------------------------------
# The phase delay of the filtered signal.
delay = 0.5 * (N - 1) / sample_rate
plot_nr += 1
ax3 = plot.fig.add_subplot(plot.nr_rows, plot.nr_cols, plot_nr)
# Plot the original signal.
ax3.plot(time, data, label="original signal")
# Plot the filtered signal, shifted to compensate for the phase delay.
ax3.plot(time - delay, filtered_x, "r-", label="filtered signal")
# Plot just the "good" part of the filtered signal. The first N-1
# samples are "corrupted" by the initial conditions.
ax3.plot(time[N - 1 :] - delay, filtered_x[N - 1 :], "g", linewidth=4)
ax3.set_xlabel("t")
ax3.grid(True)
plot.save_fig()
def fir(self, time, data, **kwargs):
"""
Based on the xxample from the SciPy cook boock, see
http://www.scipy.org/Cookbook/FIRFilter
Parameters
----------
time : ndarray(n)
data : ndarray(n)
plot : boolean, default=False
figpath : str, default=False
figfile : str, default=False
sample_rate : int, default=None
If None, sample rate will be calculated from the given signal
freq_trans_width : float, default=1
The desired width of the transition from pass to stop,
relative to the Nyquist rate.
ripple_db : float, default=10
The desired attenuation in the stop band, in dB.
cutoff_hz : float, default=10
Frequencies above cutoff_hz are filtered out
Returns
-------
filtered_x : ndarray(n - (N-1))
filtered signal
N : float
order of the firwin filter
delay : float
phase delay due to the filtering process
"""
plot = kwargs.get("plot", False)
figpath = kwargs.get("figpath", False)
figfile = kwargs.get("figfile", False)
sample_rate = kwargs.get("sample_rate", None)
# The desired width of the transition from pass to stop,
# relative to the Nyquist rate. We'll design the filter
# with a 5 Hz transition width.
freq_trans_width = kwargs.get("freq_trans_width", 1)
# The desired attenuation in the stop band, in dB.
ripple_db = kwargs.get("ripple_db", 10)
# The cutoff frequency of the filter.
cutoff_hz = kwargs.get("cutoff_hz", 10)
chk.array_1d(time)
chk.array_1d(data)
if not sample_rate:
sample_rate = calc_sample_rate(time)
# ------------------------------------------------
# Create a FIR filter and apply it to data[:,channel]
# ------------------------------------------------
# The Nyquist rate of the signal.
nyq_rate = sample_rate / 2.0
# The desired width of the transition from pass to stop,
# relative to the Nyquist rate. We'll design the filter
# with a 5 Hz transition width.
width = freq_trans_width / nyq_rate
# Compute the order and Kaiser parameter for the FIR filter.
N, beta = sp.signal.kaiserord(ripple_db, width)
# Use firwin with a Kaiser window to create a lowpass FIR filter.
taps = sp.signal.firwin(N, cutoff_hz / nyq_rate, window=("kaiser", beta))
# Use lfilter to filter x with the FIR filter.
filtered_x = sp.signal.lfilter(taps, 1.0, data)
# The phase delay of the filtered signal.
delay = 0.5 * (N - 1) / sample_rate
# # the filtered signal, shifted to compensate for the phase delay.
# time_shifted = time-delay
# # the "good" part of the filtered signal. The first N-1
# # samples are "corrupted" by the initial conditions.
# time_good = time[N-1:] - delay
if plot:
self.plot_fir(figpath, figfile, time, data, filtered_x, N, delay, sample_rate, taps, nyq_rate)
return filtered_x, N, delay
