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# scipy.signal.firwin

`scipy.signal.``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, optional

  > 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, optional

  > Desired window to use. See `scipy.signal.get_window` for a list of windows and required parameters.

  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

  `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])