bundles / scipy 1.17.1 / scipy / signal / _spectral_py / istft

function

`scipy.signal._spectral_py:istft`

source: /scipy/signal/_spectral_py.py :1622

Signature

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

Summary

Perform the inverse Short Time Fourier transform (legacy function).

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 periodic 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).
scaling: {'spectrum', 'psd'}: The default 'spectrum' scaling allows each frequency line of Zxx to be interpreted as a magnitude spectrum. The 'psd' option scales each line to a power spectral density - it allows to calculate the signal's energy by numerically integrating over abs(Zxx)**2.

Returns

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

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):

t \sum w^{2} [n - t H] \neq = 0

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

x [n] = \frac{\sum _{t} x _{t} [ n ] w [ n - t H ]}{\sum _{t} w ^{2} [ n - t H ]}

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 an 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.

Array API Standard Support

istft is not in-scope for support of Python Array API Standard compatible backends other than NumPy.

See dev-arrayapi for more information.

Examples

import numpy as np
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()

✓

`scipy.signal._spectral_py:istft`

Signature

Summary

Parameters

Returns

Notes

Examples

See also

Aliases

Referenced by

This package