〰️ FIR Filter Design

Choose the eleven taps of a finite-impulse-response filter so its frequency response approximates an ideal low-pass: gain near one in the passband, near zero in the stopband, with a free transition between. The error sums the gap to the target across a frequency grid. A smooth least-squares filter-design problem. Score is total passband-plus-stopband error, to minimise. 11-D.

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The JS objective is a line-for-line port of example_applications/fir_filter_design and agrees to floating-point tolerance. The curve is the realised magnitude response across frequency; the shaded bands are the passband (target 1) and stopband (target 0) the filter must match.