# scipy.signal.firwin

scipy.signal.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).

      New in version 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

      This is the Nyquist frequency. Each frequency in cutoff must be between 0 and nyq. Default is 1.

      Deprecated since version 1.0.0: `firwin` keyword argument nyq is deprecated in favour of fs and will be removed in SciPy 1.12.0.

    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])