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Why are my frequency bins oscillating?

This is indeed spectral leakage and specifically the dependency of the leakage on phase. Here is an example of 30 Hz sine with with a random phase. These are 50 frames with a randomized phase. The &...
Hilmar's user avatar
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4 votes

Why are my frequency bins oscillating?

The idea that you're looking for here is spectral leakage. As alluded to in the comments, the DFT bins will undergo different amounts of spectral leakage depending on the initial phase of the tone ...
Baddioes's user avatar
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3 votes

What is the difference between the DFS (Discrete Fourier Series) and DTFS (Discrete-Time Fourier Series)

That's primarily due to inconsistent naming. Typically the term "Discrete Time Fourier Transform" (DTFT) is used for signals that are discrete in time but continuous in Frequency, which is ...
Hilmar's user avatar
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2 votes

What is the difference between the DFS (Discrete Fourier Series) and DTFS (Discrete-Time Fourier Series)

Unless I'm really suffering a brain fart, (8.11, 8.12) and (3.94, 3.95) are mathematically identical. Just take $$W^{kn}_N = e^{jk(2 \pi /N)n} \tag 1$$ and see for yourself. Terminology changes, and ...
TimWescott's user avatar
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1 vote

Constraints on choosing the frequency axis when Fourier transforming non-uniformly sampled data?

Can I choose f arbitrarily? Yes and no. Theoretically, you can perform a "DFT-like" operation with any set of N time samples {t_n} at any set of K frequencies $f_k$ simply as $$X(f_k) = \...
Hilmar's user avatar
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1 vote

do closer peaks Leak more to each other (spectral leakage in FFT)

It's not exactly leakage. If the frequency of interest contains an integer number of cycles, its peak lands right on one of the frequency domain samples, and its nulls land on the others, creating an ...
Cristobol Polychronopolis's user avatar
1 vote

do closer peaks Leak more to each other (spectral leakage in FFT)

Sort of. The leakage has the shape of a Dirichlet Kernel. This similar to a sinc shape so the leakage diminishes with distance. However there is a significant fine structure so it's not monotonic.
Hilmar's user avatar
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