AI-generated page Every curve computed live Two published tables, quoted

This interactive designer was generated by Claude (Anthropic) for the Wireless 101 course materials. It builds the lab that courses/dsp101/SYLLABUS.md declares at lines 293–294 (“Interactive filter designer with frequency response”) and 335 (“Compare FIR and IIR Filters”).

Nothing here is drawn to look plausible. The coefficients are designed from the real definitions in this file — windowed sinc with real window functions for FIR; a real Butterworth / Chebyshev pole set, a real pre-warped bilinear transform and a real biquad cascade for IIR. Magnitude, phase and group delay come from evaluating those coefficients with complex arithmetic. Passband ripple, transition width and stopband attenuation are measured by searching the computed response, so they are results, not the numbers you typed. The test signal is filtered by real convolution (FIR) and a real recursive difference equation (IIR), and its spectrum is a real radix‑2 FFT.

Quoted, not measured here (labelled published where it appears): the window comparison table — peak side‑lobe, minimum stopband attenuation and transition width — from m7-l2.html, which follows Harris (1978); the Kaiser order estimate M ≈ (A − 8) / (2.285 Δω) from the same lesson; and the Butterworth minimum-order formula from m8-l2.html. Each sits beside the measured number so you can compare the rule of thumb with the filter you actually got.

The audio half of the lab is deferred, not dropped. The syllabus asks for “apply to audio in real time”. Audio generation and playback are parked across this repository by an owner decision, so the filter is applied to a visualised test signal instead — real filtering, shown in time and in frequency. There is no sound on this page.

FIR / IIR filter designer

Design a filter two ways at once and watch the trade-off that Modules 7 and 8 describe in words: FIR buys exactly linear phase with taps, IIR buys a sharp transition with feedback and pays for it in phase. Every readout marked measured was found by searching the computed response. Frequencies are given in Hz and, in brackets, as ω in rad/sample where ω = π is fs/2 — the normalisation the lessons use.

The chain, end to end

 

1 

 

 

2 FIR — window × ideal sinc
63

 

3 IIR — prototype + bilinear transform
6

 

4 Finite precision & test signal
10 bits

 

Magnitude response — |H(ejω)| in dB

computed by evaluating the designed coefficients at 1024 frequencies
FIR (solid, round markers) IIR (dashed, square markers) △ measured passband edge ▽ measured stopband edge

 

Phase — the headline difference

Phase (unwrapped)

radians

Group delay

samples, from Re(P/H) on the real coefficients

 

Impulse response — finite vs infinite

FIR h[n]

the coefficients themselves

IIR h[n]

the cascade driven by a unit impulse

 

Apply it — the filter doing something

 

Test signal, before and after

FIR by real convolution, IIR by the recursive difference equation

 

Cost — matching one spec with both families

60 dB
0.040
0.50 dB
Cost of meeting the same specification with an FIR and an IIR design

 

Windows — the published table beside the measured one

Window functions: published figures beside figures measured from the response designed on this page

 

What each stage does

The arithmetic, in full