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Regarding your Edit #2: It is not true that phase estimation requires that frequency be at a bin center. However if a frequency estimate requires interpolation between FFT result bins, so does any …

A DCT is equivalent to a DFT of real data that is doubled and mirrored, thus rendering it symmetric. The DFT of any symmetric real signal has a phase of zero (its all cosines, no antisymmetric sine c …

To extract only the carrier with a band-pass filter, the filter pass-band has to be narrower than the modulating frequencies, or else some of the envelope modulation will "leak" through the filter. A …

Many audio FFT visualizations use log(magnitude) instead of linear, as that makes it easier to find a scale that makes data visible a graph. The energy contained in band that contains multiple FFT …

Those sources can then resonate and exchange energy back to the strummed string, modulating the vibration's amplitude. …

The amplitude peak is hidden between FFT result bins for frequencies that are not exactly integer periodic in the FFT's length. But you can interpolate to find the results for those frequencies. …

If you have enough samples for an FFT, instead of an FFT, try a least squares fit for the 3 parameters (frequency, phase, amplitude) of a pure sinusoid to that sample set. …

For periodic signals, the maximum peak-to-peak amplitude is dependent in the relative phase of each harmonic, as well as their magnitudes. Do you have that information? …

Using a Hilbert transform with a sufficiently narrow-band signal, the low pass filter may not be needed even for continuous envelope estimation.

You can't make an FFT ignore phase (for strictly real input), except for signals which have frequencies that are exactly periodic in the FFT window length. Otherwise, you will have to interpolate to …

The library function log of zero results in a NaN (not a real number, -inf). So the log of a square with a base of zero can't be plotted.

The maximum magnitude has to be interpolated for any sinusoid that is not exactly periodic by an exact integer number of periods in the FFT length. An interpolation is necessary because those frequen …

A mathematical theorem (named after Fourier) says that (non-pathological) signals that are "not a sine" are, for all practical purposes, identical to (or can be accurately described as) the sum of a b …

No. Amplifying only the real part of an FFT result will only amplify signals that are symmetric in the FFT window. What if your desired tone happens to be anti-symmetric in that window?

Other frequencies will show rectangular windowing artifacts (so called "leakage") which will scallop the peak bin amplitude. … There do exist interpolation methods to correct for the amplitude of these between-FFT-bin-center frequencies. …