Do you know the exact duration in samples of the sleep time? If so, then you can take the un-windowed fft of the 2nd block of N samples, modify the phase of each bin to “undo” the effect of the sleep time; then you can inverse transform this back into the time domain and concatenate the resulting data with the data from the first frame. Then you can take in single length-2N fft (windowed or not, your choice). This assumes the spectrum of the underlying signal is stationary over the time interval 2N+M
Bob
- 666
- 3
- 6