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# scipy.signal.cheb1ord

scipy.signal.cheb1ord(wp, ws, gpass, gstop, analog=False, fs=None)

  Chebyshev type I filter order selection.

  Return the order of the lowest order digital or analog Chebyshev Type I filter that loses no more than gpass dB in the passband and has at least gstop dB attenuation in the stopband.

  Parameters:
    wp, ws float

      Passband and stopband edge frequencies.

      For digital filters, these are in the same units as fs. By default, fs is 2 half-cycles/sample, so these are normalized from 0 to 1, where 1 is the Nyquist frequency. (wp and ws are thus in half-cycles / sample.) For example:

      > - Lowpass: wp = 0.2, ws = 0.3

      > - Highpass: wp = 0.3, ws = 0.2

      > - Bandpass: wp = [0.2, 0.5], ws = [0.1, 0.6]

      > - Bandstop: wp = [0.1, 0.6], ws = [0.2, 0.5]

      For analog filters, wp and ws are angular frequencies (e.g., rad/s).

    gpass float

      The maximum loss in the passband (dB).

    gstop float

      The minimum attenuation in the stopband (dB).

    analog bool, optional

      When True, return an analog filter, otherwise a digital filter is returned.

    fs float, optional

      The sampling frequency of the digital system.

      New in version 1.2.0.

  Returns:
    ord int

      The lowest order for a Chebyshev type I filter that meets specs.

    wn ndarray or float

      The Chebyshev natural frequency (the “3dB frequency”) for use with `cheby1` to give filter results. If fs is specified, this is in the same units, and fs must also be passed to `cheby1`.

  See also

  `cheby1`

    Filter design using order and critical points

  `buttord`

    Find order and critical points from passband and stopband spec

  `cheb2ord`, `ellipord`
  `iirfilter`

    General filter design using order and critical frequencies

  `iirdesign`

    General filter design using passband and stopband spec

  Examples

  Design a digital lowpass filter such that the passband is within 3 dB up to 0.2*(fs/2), while rejecting at least -40 dB above 0.3*(fs/2). Plot its frequency response, showing the passband and stopband constraints in gray.

      >>> from scipy import signal
      >>> import matplotlib.pyplot as plt
      >>> import numpy as np

      >>> N, Wn = signal.cheb1ord(0.2, 0.3, 3, 40)
      >>> b, a = signal.cheby1(N, 3, Wn, 'low')
      >>> w, h = signal.freqz(b, a)
      >>> plt.semilogx(w / np.pi, 20 * np.log10(abs(h)))
      >>> plt.title('Chebyshev I lowpass filter fit to constraints')
      >>> plt.xlabel('Normalized frequency')
      >>> plt.ylabel('Amplitude [dB]')
      >>> plt.grid(which='both', axis='both')
      >>> plt.fill([.01, 0.2, 0.2, .01], [-3, -3, -99, -99], '0.9', lw=0) # stop
      >>> plt.fill([0.3, 0.3,   2,   2], [ 9, -40, -40,  9], '0.9', lw=0) # pass
      >>> plt.axis([0.08, 1, -60, 3])
      >>> plt.show()