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Chebyshev Filter

Equiripple passband or stopband for sharper transitions

Order: 4
ε = 0.5 (1 dB)
ωc = 0.5π

Chebyshev vs Butterworth (Same Order)

Chebyshev Polynomial T_n(x)

Chebyshev Filter Properties

Type I: Equiripple in the passband, monotonic in the stopband. Sharper transition than Butterworth for the same order.

Type II (Inverse): Monotonic in the passband, equiripple in the stopband. Useful when passband flatness is critical.

Ripple Parameter (ε): Controls the amplitude of the ripple. Higher ε = more ripple but sharper transition.

Trade-off: Chebyshev achieves sharper cutoff than Butterworth but at the cost of passband ripple. The ripple has exactly n peaks for order n.