Recover timedomain signals by performing inverse shorttime, fast Fourier transform (FFT)
Transforms
dspxfrm3
The Inverse ShortTime FFT block reconstructs the timedomain signal from the frequencydomain output of the ShortTime FFT block using a twostep process. First, the block performs the overlap add algorithm shown below.
$$x\left[n\right]=\frac{L}{W(0)}{\displaystyle \sum _{p=\infty}^{\infty}\left[\frac{1}{N}{\displaystyle \sum _{k=0}^{N1}X\left[pL,k\right]{e}^{j2\pi kn/N}}\right]}$$
Then, the block rebuffers the signal in order to reconstruct the timedomain signal. Depending on the analysis window used by the ShortTime FFT block, the Inverse ShortTime FFT block might or might not achieve perfect reconstruction of the time domain signal.
Connect your complexvalued, singlechannel or multichannel input signal to the X(n,k) port. The block accepts unoriented vector, column vector and matrix input. The block outputs the real or complexvalued, singlechannel or multichannel inverse shorttime FFT at port x(n).
Connect your complexvalued, singlechannel analysis window to the w(n) port. When you select the Assert if analysis window does not support perfect signal reconstruction check box, the block displays an error when the input signal cannot be perfectly reconstructed. The block uses the values you enter for the Analysis window length (W) and Reconstruction error tolerance, or maximum amount of allowable error in the reconstruction process, to determine if the signal can be perfectly reconstructed.
The dspstsa
example
illustrates how to use the ShortTime FFT and Inverse ShortTime FFT blocks to remove
the background noise from a speech signal. To open the dspstsa
model,
type dspstsa
in the MATLAB^{®} command prompt.
Enter the length of the analysis window. This parameter is visible when you select the Assert if analysis window does not support perfect signal reconstruction check box.
Enter the number of samples of overlap for each frame of the ShortTime FFT block's input signal. This value should be the same as the Overlap between consecutive windows (in samples) parameter in the ShortTime FFT block parameters dialog.
Enter the desired frame size of the output signal.
Select this check box when the input to the block is both floating point and conjugate symmetric, and you want realvalued outputs. When you select this check box when the input is not conjugate symmetric, the output of the block is invalid. This parameter cannot be used for fixedpoint signals.
Select this check box to display an error when the analysis window used by the ShortTime FFT block does not support perfect signal reconstruction.
Enter the amount of acceptable error in the reconstruction of the original signal. This parameter is visible when you select the Assert if analysis window does not support perfect signal reconstruction check box.
Port  Supported Data Types 

X(n,k) 

w(n) 

x(n) 

[1] Quatieri, Thomas E. DiscreteTime Speech Signal Processing. Englewood Cliffs, NJ: PrenticeHall, 2001.