# Can Reassigned-STFT be an invertible transform? Algorithm for “Signal => Reassigned-STFT => masking => Reassigned-ISTFT => Output signal”

It is well known in DSP that this is a successful method to modify audio signals:

Signal => STFT => masking => ISTFT => Output signal


For example, given a signal x[n], one can compute abs(S[t, k]) the magnitude at time-frame t and frequency bin k, modify this magnitude, then perform an inverse STFT (using IFFT with Overlapp Add method), and get a modified signal. Remark: If the FFT size is 4096, then S is just a matrix of format T x 4096, where T is the number of timeframes.

Now I've read about Reassignment method using phase information, and seen in various audio programs how it helps to have a much sharper spectrogram. Example here and here:

## Question:

Is there a similar practical algorithm for STFT with reassignment?

Is STFT-with-reassignement an invertible transform?

Signal => STFT-with-reassignment => masking => ISTFT-with-reassignment  => Output signal


In particular, if FFT size is 4096, what's the size of the STFT-with-reassignment matrix S2?

Still T x 4096? Or another format? Can I do masking on this matrix? (to remove or attenuate certain frequency bins in some time frames) Can I perform a standard "inverse STFT" on this S2?

Would you have such an algorithm?

• Hi, is this question about whether an implementation of STFT-with-reassignment is available in some toolkit? It kind of overlaps with the question about subdividing the frequency domain space in which case it would be good to keep just one of them (?) – A_A Sep 28 '18 at 10:41
• @A_A no, phase reassignment is a totally different thing, it's not just about tiling the timefrequency plane imho. btw you can have reassignement on a standard regular stft, with rectangular tiling of timefrequency plane. – g6kxjv1ozn Sep 28 '18 at 20:50