Module « scipy.signal »

Fonction kaiserord - module scipy.signal

Signature de la fonction kaiserord

def kaiserord(ripple, width) 

Description

kaiserord.__doc__

    Determine the filter window parameters for the Kaiser window method.

    The parameters returned by this function are generally used to create
    a finite impulse response filter using the window method, with either
    `firwin` or `firwin2`.

    Parameters
    ----------
    ripple : float
        Upper bound for the deviation (in dB) of the magnitude of the
        filter's frequency response from that of the desired filter (not
        including frequencies in any transition intervals). That is, if w
        is the frequency expressed as a fraction of the Nyquist frequency,
        A(w) is the actual frequency response of the filter and D(w) is the
        desired frequency response, the design requirement is that::

            abs(A(w) - D(w))) < 10**(-ripple/20)

        for 0 <= w <= 1 and w not in a transition interval.
    width : float
        Width of transition region, normalized so that 1 corresponds to pi
        radians / sample. That is, the frequency is expressed as a fraction
        of the Nyquist frequency.

    Returns
    -------
    numtaps : int
        The length of the Kaiser window.
    beta : float
        The beta parameter for the Kaiser window.

    See Also
    --------
    kaiser_beta, kaiser_atten

    Notes
    -----
    There are several ways to obtain the Kaiser window:

    - ``signal.windows.kaiser(numtaps, beta, sym=True)``
    - ``signal.get_window(beta, numtaps)``
    - ``signal.get_window(('kaiser', beta), numtaps)``

    The empirical equations discovered by Kaiser are used.

    References
    ----------
    Oppenheim, Schafer, "Discrete-Time Signal Processing", pp.475-476.

    Examples
    --------
    We will use the Kaiser window method to design a lowpass FIR filter
    for a signal that is sampled at 1000 Hz.

    We want at least 65 dB rejection in the stop band, and in the pass
    band the gain should vary no more than 0.5%.

    We want a cutoff frequency of 175 Hz, with a transition between the
    pass band and the stop band of 24 Hz. That is, in the band [0, 163],
    the gain varies no more than 0.5%, and in the band [187, 500], the
    signal is attenuated by at least 65 dB.

    >>> from scipy.signal import kaiserord, firwin, freqz
    >>> import matplotlib.pyplot as plt
    >>> fs = 1000.0
    >>> cutoff = 175
    >>> width = 24

    The Kaiser method accepts just a single parameter to control the pass
    band ripple and the stop band rejection, so we use the more restrictive
    of the two. In this case, the pass band ripple is 0.005, or 46.02 dB,
    so we will use 65 dB as the design parameter.

    Use `kaiserord` to determine the length of the filter and the
    parameter for the Kaiser window.

    >>> numtaps, beta = kaiserord(65, width/(0.5*fs))
    >>> numtaps
    167
    >>> beta
    6.20426

    Use `firwin` to create the FIR filter.

    >>> taps = firwin(numtaps, cutoff, window=('kaiser', beta),
    ...               scale=False, nyq=0.5*fs)

    Compute the frequency response of the filter.  ``w`` is the array of
    frequencies, and ``h`` is the corresponding complex array of frequency
    responses.

    >>> w, h = freqz(taps, worN=8000)
    >>> w *= 0.5*fs/np.pi  # Convert w to Hz.

    Compute the deviation of the magnitude of the filter's response from
    that of the ideal lowpass filter. Values in the transition region are
    set to ``nan``, so they won't appear in the plot.

    >>> ideal = w < cutoff  # The "ideal" frequency response.
    >>> deviation = np.abs(np.abs(h) - ideal)
    >>> deviation[(w > cutoff - 0.5*width) & (w < cutoff + 0.5*width)] = np.nan

    Plot the deviation. A close look at the left end of the stop band shows
    that the requirement for 65 dB attenuation is violated in the first lobe
    by about 0.125 dB. This is not unusual for the Kaiser window method.

    >>> plt.plot(w, 20*np.log10(np.abs(deviation)))
    >>> plt.xlim(0, 0.5*fs)
    >>> plt.ylim(-90, -60)
    >>> plt.grid(alpha=0.25)
    >>> plt.axhline(-65, color='r', ls='--', alpha=0.3)
    >>> plt.xlabel('Frequency (Hz)')
    >>> plt.ylabel('Deviation from ideal (dB)')
    >>> plt.title('Lowpass Filter Frequency Response')
    >>> plt.show()