Howtosignalprocessing
- What is inverse short time Fourier transform?
- What are the limitations of Fourier transform of an analog time limited signal?
- Is STFT invertible that is the original signal can be recovered from the transform by the inverse STFT?
- What is the difference between FFT and STFT?
What is inverse short time Fourier transform?
The inverse STFT is a perfect reconstruction of the original signal as long as ∑ m = − ∞ ∞ g a + 1 ( n − m R ) = c ∀ n ∈ ℤ where the analysis window g ( n ) was used to window the original signal and c is a constant. The following figure depicts the steps followed in reconstructing the original signal.
What are the limitations of Fourier transform of an analog time limited signal?
A limitation of the Fourier transform is that it's not truly realizable in practice - we can never sample a function for every x∈R! This can be mitigated by the way we do integrals numerically: we do Riemann sums, which naturally require sampling your function anyway!
Is STFT invertible that is the original signal can be recovered from the transform by the inverse STFT?
The STFT is invertible, that is, the original signal can be recovered from the transform by the inverse STFT. The most widely accepted way of inverting the STFT is by using the overlap-add (OLA) method, which also allows for modifications to the STFT complex spectrum.
What is the difference between FFT and STFT?
FFT has a resolution of 2048 lines, Blackman window, and 50% overlap and STFT also has Block size 2048, FFT size 16K, Blackman window used, and 50% overlap. As we can see, STFT performs better with the same block size (but more calculated lines). We improved frequency resolution for the same amount of scooped data.
