pyyeti.dsp.fftfilt

pyyeti.dsp.fftfilt(sig, w, *, axis=-1, bw=None, pass_zero=None, nyq=1.0, mag=0.5, makeplot='no')

Filter time-domain signals using FFT with Gaussian ramps.

Parameters:

• sig (nd array_like) – Signal(s) to filter. Filtering is done along axis axis.

• w (scalar or 1d array_like) – Edge (cutoff) frequencies where 0.0 < w[i] < nyq for all i (w must not include 0.0 or nyq). Can be any length and filter will alternate between pass and stop (starting according to pass_zero). For example, if leaving pass_zero as default, a low pass filter is created for scalar w and a band-pass is created for a 2-element w. Units are relative to the nyq input; so, for example, if nyq is the Nyquist frequency in Hz, w would be in Hz.

• axis (int, optional) – Axis along which to operate.

• bw (scalar, 1d array_like, or None; optional) – Width of each transition region (each up or down ramp). If None, bw = 0.01 * nyq.

• pass_zero (bool or None; optional) – Specifies whether or not the zero frequency will be in a pass band. If None, pass_zero is set to True unless w has two elements. (So the default is low pass and band pass for w with one or two elements.)

• nyq (scalar; optional) – Specifies the Nyquist frequency: sample_rate/2.0

• mag (scalar; optional) – Specifies the target filter magnitude at each w

• makeplot (string or axes object; optional) – Specifies if and how to plot filter function:

  makeplot	Description
  ‘no’	do not plot
  ‘clear’	plot after clearing figure
  ‘add’	plot without clearing figure
  ‘new’	plot in new figure
  axes object	plot in given axes (like ‘add’)

Returns:

• fsig (nd ndarray) – Filtered version of sig

• freq (1d ndarray) – Frequency vector from 0.0 to nyq

• h (1d ndarray) – The frequency domain filter function

Raises:

ValueError – When a ramp will not fit in space as required.

Examples

Make a signal composed of 4 sinusoids, then use fftfilt() to try and recover those sinusoids:

>>> from pyyeti import dsp
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> h = 0.001
>>> t = np.arange(0, 3.0, h)
>>> y1 = 10 + 3.1*np.sin(2*np.pi*3*t)
>>> y2 = 5*np.sin(2*np.pi*10*t)
>>> y3 = 2*np.sin(2*np.pi*30*t)
>>> y4 = 3*np.sin(2*np.pi*60*t)
>>> y = y1 + y2 + y3 + y4
>>> _ = plt.plot(t, y)
>>> _ = plt.title('Signal of 4 sinusoids')

>>> sr = 1/h
>>> nyq = sr/2
>>> _ = plt.figure('Ex1', clear=True, layout='constrained')
>>> _ = plt.figure('Ex2', clear=True, layout='constrained')
>>> for j, (w, pz, yj) in enumerate(((7, None, y1),
...                                 ([7, 18], None, y2),
...                                 ([18, 45], None, y3),
...                                 (45, False, y4))):
...     _ = plt.figure('Ex1')
...     _ = plt.subplot(4, 1, j+1)
...     yf = dsp.fftfilt(y, w, pass_zero=pz, nyq=nyq,
...                      makeplot='add')[0]
...     _ = plt.xlim(0, 75)
...     _ = plt.figure('Ex2')
...     _ = plt.subplot(4, 1, j+1)
...     _ = plt.plot(t, yj, t, yf)