Butterworth / Chebyshev IIR
This interactive simulator explores Butterworth / Chebyshev IIR in Визуализация математики. Design Butterworth, Chebyshev I/II LP/HP filters: |H(f)|, phase, impulse response, and z-plane pole–zero plot via bilinear transform. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.
Для кого: For learners comfortable with heavier math or second-level detail. Typical context: Визуализация математики.
Ключевые понятия
- butterworth
- chebyshev
- iir
- iir filter design
- math
Как это работает
**IIR digital filter design**: pick an analog prototype (**Butterworth** flat passband, **Chebyshev I** equiripple in passband, **Chebyshev II** equiripple in stopband), apply the **bilinear transform** with **pre-warping** and watch the magnitude response, optional phase, and the **z-plane pole / zero map** update live. Crank up the order to sharpen the roll-off (steeper transition); pull **f_c** through the spectrum to see how poles slide along the unit circle. Chebyshev I gains roll-off at the cost of in-band ripple R_p; Chebyshev II is flat in the passband but ripples in the stopband around R_s.
Основные формулы
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