Efficient FFT (or SFFT) for adjacent parts of signal with overlap? Imaging we have a signal $x$, which is segmented to 50% overlapped vectors $x_1,x_2,..,x_m$ , and we intent to compute FFT of each segment. Is there anyway that we can reduce computation of FFT of each block. I mean, if FFT of $x_1$ has taken and we know $x_2$ has a 50% overlap with $x_1$, so half of $x_2$, have already went through some FFT process.


Is there any method or modification that reuse this information to reduce computations of FFT of each segment based on information of the previous segment?
One method might be to split your length $N$ overlapping FFTs up, so that you compute the $\frac{N}{2}$-point FFT of each block of samples that come in. Then, in order to get the $N$-point FFT that you want, you can combine the last two $\frac{N}{2}$-point results with appropriate twiddle factors.

This would technically do what you want, but in most cases (especially on contemporary PC-like platforms with good FFT libraries), it's not going to be appreciably (if at all) faster than just doing the overlapping $N$-point FFTs.