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# scipy.signal.stft

`scipy.signal.``stft`(x, fs=1.0, window='hann', nperseg=256, noverlap=None, nfft=None, detrend=False, return_onesided=True, boundary='zeros', padded=True, axis=-1)

  Compute the Short Time Fourier Transform (STFT).

  STFTs can be used as a way of quantifying the change of a nonstationary signal’s frequency and phase content over time.

  Parameters:

  x : array_like

  > Time series of measurement values

  fs : float, optional

  > Sampling frequency of the x time series. Defaults to 1.0.

  window : str or tuple or array_like, optional

  > Desired window to use. 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.

  nperseg : int, optional

  > Length of each segment. Defaults to 256.

  noverlap : int, optional

  > Number of points to overlap between segments. If None, `noverlap = nperseg // 2`. Defaults to None. When specified, the COLA constraint must be met (see Notes below).

  nfft : int, optional

  > Length of the FFT used, if a zero padded FFT is desired. If None, the FFT length is nperseg. Defaults to None.

  detrend : str or function or False, optional

  > Specifies how to detrend each segment. If `detrend` is a string, it is passed as the type argument to the `detrend` function. If it is a function, it takes a segment and returns a detrended segment. If `detrend` is False, no detrending is done. Defaults to False.

  return_onesided : bool, optional

  > If True, return a one-sided spectrum for real data. If False return a two-sided spectrum. Note that for complex data, a two-sided spectrum is always returned. Defaults to True.

  boundary : str or None, optional

  > Specifies whether the input signal is extended at both ends, and how to generate the new values, in order to center the first windowed segment on the first input point. This has the benefit of enabling reconstruction of the first input point when the employed window function starts at zero. Valid options are `['even', 'odd', 'constant', 'zeros', None]`. Defaults to ‘zeros’, for zero padding extension. I.e. `[1, 2, 3, 4]` is extended to `[0, 1, 2, 3, 4, 0]` for `nperseg=3`.

  padded : bool, optional

  > Specifies whether the input signal is zero-padded at the end to make the signal fit exactly into an integer number of window segments, so that all of the signal is included in the output. Defaults to True. Padding occurs after boundary extension, if boundary is not None, and padded is True, as is the default.

  axis : int, optional

  > Axis along which the STFT is computed; the default is over the last axis (i.e. `axis=-1`).

  Returns:

  f : ndarray

  > Array of sample frequencies.

  t : ndarray

  > Array of segment times.

  Zxx : ndarray

  > STFT of x. By default, the last axis of Zxx corresponds to the segment times.

  See also

  `istft`
    Inverse Short Time Fourier Transform
  `check_COLA`
    Check whether the Constant OverLap Add (COLA) constraint is met
  `welch`
    Power spectral density by Welch’s method.
  `spectrogram`
    Spectrogram by Welch’s method.
  `csd`
    Cross spectral density by Welch’s method.
  `lombscargle`
    Lomb-Scargle periodogram for unevenly sampled data

  Notes

  In order to enable inversion of an STFT via the inverse STFT in `istft`, the signal windowing must obey the constraint of “Constant OverLap Add” (COLA), and the input signal must have complete windowing coverage (i.e. `(x.shape[axis] - nperseg) % (nperseg-noverlap) == 0`). The padded argument may be used to accomplish this.

  The COLA constraint ensures that every point in the input data is equally weighted, thereby avoiding aliasing and allowing full reconstruction. Whether a choice of window, nperseg, and noverlap satisfy this constraint can be tested with `check_COLA`.

  New in version 0.19.0.

  References

  [R265] | Oppenheim, Alan V., Ronald W. Schafer, John R. Buck “Discrete-Time Signal Processing”, Prentice Hall, 1999.

  [R266] | Daniel W. Griffin, Jae S. Limdt “Signal Estimation from Modified Short Fourier Transform”, IEEE 1984, 10.1109/TASSP.1984.1164317

  Examples

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

  Generate a test signal, a 2 Vrms sine wave whose frequency is slowly modulated around 3kHz, corrupted by white noise of exponentially decreasing magnitude sampled at 10 kHz.

      >>> fs = 10e3
      >>> N = 1e5
      >>> amp = 2 * np.sqrt(2)
      >>> noise_power = 0.01 * fs / 2
      >>> time = np.arange(N) / float(fs)
      >>> mod = 500*np.cos(2*np.pi*0.25*time)
      >>> carrier = amp * np.sin(2*np.pi*3e3*time + mod)
      >>> noise = np.random.normal(scale=np.sqrt(noise_power),
      ...                          size=time.shape)
      >>> noise *= np.exp(-time/5)
      >>> x = carrier + noise

  Compute and plot the STFT’s magnitude.

      >>> f, t, Zxx = signal.stft(x, fs, nperseg=1000)
      >>> plt.pcolormesh(t, f, np.abs(Zxx), vmin=0, vmax=amp)
      >>> plt.title('STFT Magnitude')
      >>> plt.ylabel('Frequency [Hz]')
      >>> plt.xlabel('Time [sec]')
      >>> plt.show()

  (Source code)