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Fonction firls - module scipy.signal

Signature de la fonction firls

def firls(numtaps, bands, desired, weight=None, nyq=None, fs=None) 

Description

firls.__doc__

    FIR filter design using least-squares error minimization.

    Calculate the filter coefficients for the linear-phase finite
    impulse response (FIR) filter which has the best approximation
    to the desired frequency response described by `bands` and
    `desired` in the least squares sense (i.e., the integral of the
    weighted mean-squared error within the specified bands is
    minimized).

    Parameters
    ----------
    numtaps : int
        The number of taps in the FIR filter. `numtaps` must be odd.
    bands : array_like
        A monotonic nondecreasing sequence containing the band edges in
        Hz. All elements must be non-negative and less than or equal to
        the Nyquist frequency given by `nyq`.
    desired : array_like
        A sequence the same size as `bands` containing the desired gain
        at the start and end point of each band.
    weight : array_like, optional
        A relative weighting to give to each band region when solving
        the least squares problem. `weight` has to be half the size of
        `bands`.
    nyq : float, optional
        *Deprecated. Use `fs` instead.*
        Nyquist frequency. Each frequency in `bands` must be between 0
        and `nyq` (inclusive). Default is 1.
    fs : float, optional
        The sampling frequency of the signal. Each frequency in `bands`
        must be between 0 and ``fs/2`` (inclusive). Default is 2.

    Returns
    -------
    coeffs : ndarray
        Coefficients of the optimal (in a least squares sense) FIR filter.

    See also
    --------
    firwin
    firwin2
    minimum_phase
    remez

    Notes
    -----
    This implementation follows the algorithm given in [1]_.
    As noted there, least squares design has multiple advantages:

        1. Optimal in a least-squares sense.
        2. Simple, non-iterative method.
        3. The general solution can obtained by solving a linear
           system of equations.
        4. Allows the use of a frequency dependent weighting function.

    This function constructs a Type I linear phase FIR filter, which
    contains an odd number of `coeffs` satisfying for :math:`n < numtaps`:

    .. math:: coeffs(n) = coeffs(numtaps - 1 - n)

    The odd number of coefficients and filter symmetry avoid boundary
    conditions that could otherwise occur at the Nyquist and 0 frequencies
    (e.g., for Type II, III, or IV variants).

    .. versionadded:: 0.18

    References
    ----------
    .. [1] Ivan Selesnick, Linear-Phase Fir Filter Design By Least Squares.
           OpenStax CNX. Aug 9, 2005.
           http://cnx.org/contents/eb1ecb35-03a9-4610-ba87-41cd771c95f2@7

    Examples
    --------
    We want to construct a band-pass filter. Note that the behavior in the
    frequency ranges between our stop bands and pass bands is unspecified,
    and thus may overshoot depending on the parameters of our filter:

    >>> from scipy import signal
    >>> import matplotlib.pyplot as plt
    >>> fig, axs = plt.subplots(2)
    >>> fs = 10.0  # Hz
    >>> desired = (0, 0, 1, 1, 0, 0)
    >>> for bi, bands in enumerate(((0, 1, 2, 3, 4, 5), (0, 1, 2, 4, 4.5, 5))):
    ...     fir_firls = signal.firls(73, bands, desired, fs=fs)
    ...     fir_remez = signal.remez(73, bands, desired[::2], fs=fs)
    ...     fir_firwin2 = signal.firwin2(73, bands, desired, fs=fs)
    ...     hs = list()
    ...     ax = axs[bi]
    ...     for fir in (fir_firls, fir_remez, fir_firwin2):
    ...         freq, response = signal.freqz(fir)
    ...         hs.append(ax.semilogy(0.5*fs*freq/np.pi, np.abs(response))[0])
    ...     for band, gains in zip(zip(bands[::2], bands[1::2]),
    ...                            zip(desired[::2], desired[1::2])):
    ...         ax.semilogy(band, np.maximum(gains, 1e-7), 'k--', linewidth=2)
    ...     if bi == 0:
    ...         ax.legend(hs, ('firls', 'remez', 'firwin2'),
    ...                   loc='lower center', frameon=False)
    ...     else:
    ...         ax.set_xlabel('Frequency (Hz)')
    ...     ax.grid(True)
    ...     ax.set(title='Band-pass %d-%d Hz' % bands[2:4], ylabel='Magnitude')
    ...
    >>> fig.tight_layout()
    >>> plt.show()