Module « scipy.signal »

Fonction istft - module scipy.signal

Signature de la fonction istft

def istft(Zxx, fs=1.0, window='hann', nperseg=None, noverlap=None, nfft=None, input_onesided=True, boundary=True, time_axis=-1, freq_axis=-2) 

Description

istft.__doc__

Perform the inverse Short Time Fourier transform (iSTFT).

    Parameters
    ----------
    Zxx : array_like
        STFT of the signal to be reconstructed. If a purely real array
        is passed, it will be cast to a complex data type.
    fs : float, optional
        Sampling frequency of the time series. Defaults to 1.0.
    window : str or tuple or array_like, optional
        Desired window to use. If `window` is a string or tuple, it is
        passed to `get_window` to generate the window values, which are
        DFT-even by default. See `get_window` for a list of windows and
        required parameters. If `window` is array_like it will be used
        directly as the window and its length must be nperseg. Defaults
        to a Hann window. Must match the window used to generate the
        STFT for faithful inversion.
    nperseg : int, optional
        Number of data points corresponding to each STFT segment. This
        parameter must be specified if the number of data points per
        segment is odd, or if the STFT was padded via ``nfft >
        nperseg``. If `None`, the value depends on the shape of
        `Zxx` and `input_onesided`. If `input_onesided` is `True`,
        ``nperseg=2*(Zxx.shape[freq_axis] - 1)``. Otherwise,
        ``nperseg=Zxx.shape[freq_axis]``. Defaults to `None`.
    noverlap : int, optional
        Number of points to overlap between segments. If `None`, half
        of the segment length. Defaults to `None`. When specified, the
        COLA constraint must be met (see Notes below), and should match
        the parameter used to generate the STFT. Defaults to `None`.
    nfft : int, optional
        Number of FFT points corresponding to each STFT segment. This
        parameter must be specified if the STFT was padded via ``nfft >
        nperseg``. If `None`, the default values are the same as for
        `nperseg`, detailed above, with one exception: if
        `input_onesided` is True and
        ``nperseg==2*Zxx.shape[freq_axis] - 1``, `nfft` also takes on
        that value. This case allows the proper inversion of an
        odd-length unpadded STFT using ``nfft=None``. Defaults to
        `None`.
    input_onesided : bool, optional
        If `True`, interpret the input array as one-sided FFTs, such
        as is returned by `stft` with ``return_onesided=True`` and
        `numpy.fft.rfft`. If `False`, interpret the input as a a
        two-sided FFT. Defaults to `True`.
    boundary : bool, optional
        Specifies whether the input signal was extended at its
        boundaries by supplying a non-`None` ``boundary`` argument to
        `stft`. Defaults to `True`.
    time_axis : int, optional
        Where the time segments of the STFT is located; the default is
        the last axis (i.e. ``axis=-1``).
    freq_axis : int, optional
        Where the frequency axis of the STFT is located; the default is
        the penultimate axis (i.e. ``axis=-2``).

    Returns
    -------
    t : ndarray
        Array of output data times.
    x : ndarray
        iSTFT of `Zxx`.

    See Also
    --------
    stft: Short Time Fourier Transform
    check_COLA: Check whether the Constant OverLap Add (COLA) constraint
                is met
    check_NOLA: Check whether the Nonzero Overlap Add (NOLA) constraint is met

    Notes
    -----
    In order to enable inversion of an STFT via the inverse STFT with
    `istft`, the signal windowing must obey the constraint of "nonzero
    overlap add" (NOLA):

    .. math:: \sum_{t}w^{2}[n-tH] \ne 0

    This ensures that the normalization factors that appear in the denominator
    of the overlap-add reconstruction equation

    .. math:: x[n]=\frac{\sum_{t}x_{t}[n]w[n-tH]}{\sum_{t}w^{2}[n-tH]}

    are not zero. The NOLA constraint can be checked with the `check_NOLA`
    function.

    An STFT which has been modified (via masking or otherwise) is not
    guaranteed to correspond to a exactly realizible signal. This
    function implements the iSTFT via the least-squares estimation
    algorithm detailed in [2]_, which produces a signal that minimizes
    the mean squared error between the STFT of the returned signal and
    the modified STFT.

    .. versionadded:: 0.19.0

    References
    ----------
    .. [1] Oppenheim, Alan V., Ronald W. Schafer, John R. Buck
           "Discrete-Time Signal Processing", Prentice Hall, 1999.
    .. [2] Daniel W. Griffin, Jae S. Lim "Signal Estimation from
           Modified Short-Time Fourier Transform", IEEE 1984,
           10.1109/TASSP.1984.1164317

    Examples
    --------
    >>> from scipy import signal
    >>> import matplotlib.pyplot as plt
    >>> rng = np.random.default_rng()

    Generate a test signal, a 2 Vrms sine wave at 50Hz corrupted by
    0.001 V**2/Hz of white noise sampled at 1024 Hz.

    >>> fs = 1024
    >>> N = 10*fs
    >>> nperseg = 512
    >>> amp = 2 * np.sqrt(2)
    >>> noise_power = 0.001 * fs / 2
    >>> time = np.arange(N) / float(fs)
    >>> carrier = amp * np.sin(2*np.pi*50*time)
    >>> noise = rng.normal(scale=np.sqrt(noise_power),
    ...                    size=time.shape)
    >>> x = carrier + noise

    Compute the STFT, and plot its magnitude

    >>> f, t, Zxx = signal.stft(x, fs=fs, nperseg=nperseg)
    >>> plt.figure()
    >>> plt.pcolormesh(t, f, np.abs(Zxx), vmin=0, vmax=amp, shading='gouraud')
    >>> plt.ylim([f[1], f[-1]])
    >>> plt.title('STFT Magnitude')
    >>> plt.ylabel('Frequency [Hz]')
    >>> plt.xlabel('Time [sec]')
    >>> plt.yscale('log')
    >>> plt.show()

    Zero the components that are 10% or less of the carrier magnitude,
    then convert back to a time series via inverse STFT

    >>> Zxx = np.where(np.abs(Zxx) >= amp/10, Zxx, 0)
    >>> _, xrec = signal.istft(Zxx, fs)

    Compare the cleaned signal with the original and true carrier signals.

    >>> plt.figure()
    >>> plt.plot(time, x, time, xrec, time, carrier)
    >>> plt.xlim([2, 2.1])
    >>> plt.xlabel('Time [sec]')
    >>> plt.ylabel('Signal')
    >>> plt.legend(['Carrier + Noise', 'Filtered via STFT', 'True Carrier'])
    >>> plt.show()

    Note that the cleaned signal does not start as abruptly as the original,
    since some of the coefficients of the transient were also removed:

    >>> plt.figure()
    >>> plt.plot(time, x, time, xrec, time, carrier)
    >>> plt.xlim([0, 0.1])
    >>> plt.xlabel('Time [sec]')
    >>> plt.ylabel('Signal')
    >>> plt.legend(['Carrier + Noise', 'Filtered via STFT', 'True Carrier'])
    >>> plt.show()