Short-time Fourier transform with inverse in Python/Numpy, see https://stackoverflow.com/q/51655119/500207

stft.py

import numpy as np
import numpy.fft as fft


def stft(x, Nwin, Nfft=None):
    """
    Short-time Fourier transform: convert a 1D vector to a 2D array

    The short-time Fourier transform (STFT) breaks a long vector into disjoint
    chunks (no overlap) and runs an FFT (Fast Fourier Transform) on each chunk.

    The resulting 2D array can 

    Parameters
    ----------
    x : array_like
        Input signal (expected to be real)
    Nwin : int
        Length of each window (chunk of the signal). Should be ≪ `len(x)`.
    Nfft : int, optional
        Zero-pad each chunk to this length before FFT. Should be ≥ `Nwin`,
        (usually with small prime factors, for fastest FFT). Default: `Nwin`.

    Returns
    -------
    out : complex ndarray
        `len(x) // Nwin` by `Nfft` complex array representing the STFT of `x`.
    
    See also
    --------
    istft : inverse function (convert a STFT array back to a data vector)
    stftbins : time and frequency bins corresponding to `out`
    """
    Nfft = Nfft or Nwin
    Nwindows = x.size // Nwin
    # reshape into array `Nwin` wide, and as tall as possible. This is
    # optimized for C-order (row-major) layouts.
    arr = np.reshape(x[:Nwindows * Nwin], (-1, Nwin))
    stft = fft.rfft(arr, Nfft)
    return stft


def stftbins(x, Nwin, Nfft=None, d=1.0):
    """
    Time and frequency bins corresponding to short-time Fourier transform.

    Call this with the same arguments as `stft`, plus one extra argument: `d`
    sample spacing, to get the time and frequency axes that the output of
    `stft` correspond to.

    Parameters
    ----------
    x : array_like
        same as `stft`
    Nwin : int
        same as `stft`
    Nfft : int, optional
        same as `stft`
    d : float, optional
        Sample spacing of `x` (or 1 / sample frequency), units of seconds.
        Default: 1.0.

    Returns
    -------
    t : ndarray
        Array of length `len(x) // Nwin`, in units of seconds, corresponding to
        the first dimension (height) of the output of `stft`.
    f : ndarray
        Array of length `Nfft`, in units of Hertz, corresponding to the second
        dimension (width) of the output of `stft`.
    """
    Nfft = Nfft or Nwin
    Nwindows = x.size // Nwin
    t = np.arange(Nwindows) * (Nwin * d)
    f = fft.rfftfreq(Nfft, d)
    return t, f


def istft(stftArr, Nwin):
    """
    Inverse short-time Fourier transform (ISTFT)

    Given an array representing the output of `stft`, convert it back to the
    original samples.

    Parameters
    ----------
    stftArr : ndarray
        Output of `stft` (or something the same size)
    Nwin : int
        Same input as `stft`: length of each chunk that the STFT was calculated
        over.
    
    Returns
    -------
    y : ndarray
        Data samples corresponding to STFT data.
    
    See also:
    stft : the forward transform
    """
    arr = fft.irfft(stftArr)[:, :Nwin]
    return np.reshape(arr, -1)


if __name__ == '__main__':
    sampleRate = 100.0  # Hertz
    N = 1024
    Nwin = 64

    # Generate a chirp: start frequency at 5 Hz and going down at 2 Hz/s
    time = np.arange(N) / sampleRate  # seconds
    x = np.cos(2 * np.pi * time * (5 - 2 * 0.5 * time))

    # Test with Nfft bigger than Nwin
    Nfft = Nwin * 2
    s = stft(x, Nwin, Nfft=Nfft)
    y = istft(s, Nwin)

    # Make sure the stft and istft are inverses. Caveat: `x` and `y` won't be
    # the same length if `N/Nwin` isn't integral!
    maxerr = np.max(np.abs(x - y))
    assert (maxerr < np.spacing(1) * 10)

    # Test `stftbins`
    t, f = stftbins(x, Nwin, Nfft=Nfft, d=1 / sampleRate)
    assert (len(t) == s.shape[0])
    assert (len(f) == s.shape[1])

    try:
        import pylab as plt
        plt.imshow(np.abs(s), aspect="auto", extent=[f[0], f[-1], t[-1], t[0]])
        plt.xlabel('frequency (Hertz)')
        plt.ylabel('time (seconds (start of chunk))')
        plt.title('STFT with chirp example')
        plt.grid()
        plt.show()
    except ModuleNotFoundError:
        pass

Can I use the same implementation on real sensor data for example with 2 columns 'datetime' and 'value' columns. Thanks

These functions take just raw Numpy 1D arrays so yes, give stft the value column and it it will work.

Thanks for the code!