scipy.signal — filtering, convolution, FFT-based analysis: Visual walkthrough

Parent: scipy.signal (topic note)

Step 1 — A signal is just a row of heights

WHAT. Before any formula, look at what a "signal" actually is. We sample the world at even time-steps and write down a number at each step. That's it — a row of heights.

WHY start here. Every symbol later ( $x [n]$ , the sum, the wave) is bookkeeping on top of this row. If the row is clear, the algebra is just describing the picture.

PICTURE.

Figure — scipy.signal — filtering, convolution, FFT-based analysis

Step 2 — Any signal is a pile of spikes

WHAT. Take one bar of the signal — say the bar of height $x [2]$ sitting at slot 2. We can write it as a single spike of height 1 sitting at slot 2, scaled by $x [2]$ .