FFT of 0s and 1s signal

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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.

By posting your answer, you agree to the privacy policy and terms of service. Questions Tags Users Badges Unanswered. Signal Processing Stack Fourier analysis of binary signals using dft is a question and answer site for practitioners of the art and science of signal, image and video processing. Join them; it only takes a minute: Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top.

FFT of random binary data. I am trying to make sense of FFTs and binary data. Some things I would like to understand the significance of: What should be the average amplitude of the data, post-FFT? How can this help me find my y-scale? The output will depend on the exact type of random law that creates the binary points. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name.

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4 Aggregation- and Distance-based (Error) Models Aggregation-based specifications 8 of a theory. So far we have focussed on the majority specification of a numerical theory like Cumulative Prospect Theory.

To illustrate how the same approach can apply to theories that do not rely on numerical utility values, let us consider a simple lexicographic heuristic (see, e.Tversky, 1969 ). If the chance of winning is similar in both gambles (within 5 percentage points), prefer the gamble with the higher gain.