# Inverse Short-Time FFT

Recover time-domain signals by performing inverse short-time fast Fourier transform (FFT)

Libraries:
DSP System Toolbox / Transforms / Matrix Operations

## Description

The Inverse Short-Time FFT block reconstructs the time-domain signal from the frequency-domain output of the Short-Time FFT block using a two-step process. First, the block implements the overlap-add algorithm.

`$x\left[n\right]=\frac{L}{W\left(0\right)}\sum _{p=-\infty }^{\infty }\left[\frac{1}{N}\sum _{k=0}^{N-1}X\left[pL,k\right]{e}^{j2\pi kn/N}\right]$`

Then, the block rebuffers the signal in order to reconstruct the time-domain signal. Depending on the analysis window used by the Short-Time FFT block, the Inverse Short-Time FFT block might or might not achieve perfect reconstruction of the time-domain signal.

## Ports

### Input

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Specify the frequency-domain input signal as a vector or a matrix. The FFT length is equal to the number of rows in the input at the x[nL,k] port. Hence the number of input rows must be greater than or equal to the window length.

Data Types: `single` | `double`
Complex Number Support: Yes

Specify the analysis window at the w[n] port.

Data Types: `single` | `double`
Complex Number Support: Yes

### Output

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The block outputs the inverse short-time FFT output at the port x[n].

Data Types: `single` | `double`
Complex Number Support: Yes

## Parameters

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Enter the length of the analysis window as a positive integer greater than 1.

Enter the number of samples of overlap for each frame of the input signal as a nonnegative integer. This value should be the same as the Overlap between consecutive windows (in samples) parameter in the dialog box of the Short-Time FFT block.

Enter the desired frame size of the output signal as a positive integer.

Select this check box when the input to the block is both floating point and conjugate symmetric and you want real-valued outputs. If 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 fixed-point signals.

Select this check box to display an error when the analysis window used by the Short-Time FFT block does not support perfect signal reconstruction.

A time-domain signal input to the Short-time FFT block cannot be perfectly reconstructed.

To determine if the signal can be perfectly reconstructed, the Inverse Short-time FFT block uses the values you enter in the Analysis window length and Reconstruction error tolerance parameters.

Enter the amount of acceptable error in the reconstruction of the original signal as a real scalar.

#### Dependency

To enable this parameter, select the Assert if analysis window does not support perfect signal reconstruction check box.

## Block Characteristics

 Data Types `double` | `single` Direct Feedthrough `no` Multidimensional Signals `no` Variable-Size Signals `no` Zero-Crossing Detection `no`

## References

[1] Quatieri, Thomas E. Discrete-Time Speech Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 2001.

## Version History

Introduced before R2006a