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# cheb1ap() - Signal Processing

### Syntax

### Example

### Output / Return Value

### Limitations

### Alternatives / See Also

### Reference

[z,p,k] = cheb1ap(n,Rp) returns the poles and gain of an order n Chebyshev Type I analog lowpass filter prototype with Rp dB of ripple in the passband. The function returns the poles in the length n column vector p and the gain in scalar k. z is an empty matrix, because there are no zeros. The transfer function isH(s)=z(s)p(s)=k(s−p(1))(s−p(2))…(s−p(n))Chebyshev Type I filters are equiripple in the passband and monotonic in the stopband. The poles are evenly spaced about an ellipse in the left half plane. The Chebyshev Type I passband edge angular frequency ω0 is set to 1.0 for a normalized result. This is the frequency at which the passband ends and the filter has magnitude response of 10–Rp/20.

[z,p,k] = cheb1ap(n,Rp)

Frequency Response of an Analog Chebyshev Type I FilterOpen This Example Design a 6th-order Chebyshev Type I analog lowpass filter with 3 dB of ripple in the passband. Display its magnitude and phase responses. [z,p,k] = cheb1ap(6,3); % Lowpass filter prototype [num,den] = zp2tf(z,p,k); % Convert to transfer function form freqs(num,den) % Frequency response of analog filter