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The Discrete Fourier Transform (DFT) is a mapping between a finite set of discrete points in a (primal) domain (time, space) and the dual frequency domain. DFT requires an input sequence which is discrete, such as a sampling from an analogue audio signal.
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Why is frequency resolution dependent on the number of samples? (need for intuition)
This might help...remember that units of frequency are the reciprocal of units of time. As such, effects in the frequency domain track time domain effects inversely. Making your samples take up more …
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do closer peaks Leak more to each other (spectral leakage in FFT)
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 ideal result (images borrowed from https://wirelesspi.com/dft-examples …