I seek a visual explanation of this. I've already seen the maths, and can derive the proofs - they amount to nill for an intuitive understanding. Any amount of math is welcome, as long as serving to ultimately explain it visually.
Examples of excellent explanations:
- Fourier Transform: the "winding around the circle".
- Convolution: the "input-side algorithm", and how it ties to output-side.
Continuous vs Discrete: both are welcome, but ultimately the discrete case must be explainable. I've long thought of the input-side algorithm myself for continuous convolution, but never completed the picture; real analysis is tricky.
Circular vs linear: a complete explanation ought to cover both, but I'm primarily interested in linear convolution (rather, how the circular of padded signals is equivalent to linear).
Duality: ideally, should be covered (conv in freq domain <=> mult in time domain).
- Only right-padding works, and both inputs are padded; this looks like forcing inputs to correlate with lower and fractional frequencies (and more frequencies) relative to unpadded's frame.
- Something about convolving with shifted deltas and observing modulations of complex sinusoids in other domain; awaiting clarification from @AndyWalls.