## FFT of 0s and 1s signal

5 stars based on 37 reviews

Say I have a series of random binary data, which is measured with a repetition rate of Hz interval time of 0. I have a total of points, which corresponds to a total measurement time of about 31 seconds. I would like to be able to learn more about what I would expect an FFT of this data to look like. The maximum peak is obtained in the case where there is only one non-null frequency in the analysis.

Fourier analysis of binary signals using dft should first try to understand the DFT for deterministic data. You must remember that the DFT is not real but a complex signal. If you are insterested only in magnitudes, of course you can take the squared absolute value of it.

Now, if the signal is random, this is equivalent of getting a Periodogram, which is an estimate of the Spectral density of the signal. The "spectrum" not random of a random signal is the fourier transform, not of the signal itself, but of the autocorrelation function. Informally, it measures how much "energy" the signal has in each frequency band. So, the answer of your question is not simple. The only simple property that could help is is the Parseval fourier analysis of binary signals using dft Another property for deterministic signals is that the zero frequency value of the DFT is the mean value of the signal, properly normalized.