# scipy.signal.spectrogram

scipy.signal.spectrogram(x, fs=1.0, window=('tukey', 0.25), nperseg=None, noverlap=None, nfft=None, detrend='constant', return_onesided=True, scaling='density', axis=-1, mode='psd')

  Compute a spectrogram with consecutive Fourier transforms.

  Spectrograms can be used as a way of visualizing the change of a nonstationary signal’s frequency 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. 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 Tukey window with shape parameter of 0.25.

    nperseg int, optional

      Length of each segment. Defaults to None, but if window is str or tuple, is set to 256, and if window is array_like, is set to the length of the window.

    noverlap int, optional

      Number of points to overlap between segments. If None, `noverlap = nperseg // 8`. Defaults to None.

    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 ‘constant’.

    return_onesided bool, optional

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

    scaling{ ‘density’, ‘spectrum’ }, optional

      Selects between computing the power spectral density (‘density’) where Sxx has units of V**2/Hz and computing the power spectrum (‘spectrum’) where Sxx has units of V**2, if x is measured in V and fs is measured in Hz. Defaults to ‘density’.

    axis int, optional

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

    mode str, optional

      Defines what kind of return values are expected. Options are [‘psd’, ‘complex’, ‘magnitude’, ‘angle’, ‘phase’]. ‘complex’ is equivalent to the output of `stft` with no padding or boundary extension. ‘magnitude’ returns the absolute magnitude of the STFT. ‘angle’ and ‘phase’ return the complex angle of the STFT, with and without unwrapping, respectively.

  Returns:
    f ndarray

      Array of sample frequencies.

    t ndarray

      Array of segment times.

    Sxx ndarray

      Spectrogram of x. By default, the last axis of Sxx corresponds to the segment times.

  See also

  `periodogram`

    Simple, optionally modified periodogram

  `lombscargle`

    Lomb-Scargle periodogram for unevenly sampled data

  `welch`

    Power spectral density by Welch’s method.

  `csd`

    Cross spectral density by Welch’s method.

  Notes

  An appropriate amount of overlap will depend on the choice of window and on your requirements. In contrast to welch’s method, where the entire data stream is averaged over, one may wish to use a smaller overlap (or perhaps none at all) when computing a spectrogram, to maintain some statistical independence between individual segments. It is for this reason that the default window is a Tukey window with 1/8th of a window’s length overlap at each end.

  New in version 0.16.0.

  References

  [1]

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

  Examples

      >>> import numpy as np
      >>> from scipy import signal
      >>> from scipy.fft import fftshift
      >>> import matplotlib.pyplot as plt
      >>> rng = np.random.default_rng()

  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 = rng.normal(scale=np.sqrt(noise_power), size=time.shape)
      >>> noise *= np.exp(-time/5)
      >>> x = carrier + noise

  Compute and plot the spectrogram.

      >>> f, t, Sxx = signal.spectrogram(x, fs)
      >>> plt.pcolormesh(t, f, Sxx, shading='gouraud')
      >>> plt.ylabel('Frequency [Hz]')
      >>> plt.xlabel('Time [sec]')
      >>> plt.show()

  Note, if using output that is not one sided, then use the following:

      >>> f, t, Sxx = signal.spectrogram(x, fs, return_onesided=False)
      >>> plt.pcolormesh(t, fftshift(f), fftshift(Sxx, axes=0), shading='gouraud')
      >>> plt.ylabel('Frequency [Hz]')
      >>> plt.xlabel('Time [sec]')
      >>> plt.show()