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# cheb1ap

Chebyshev Type I analog lowpass filter prototype

## Syntax

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

## Description

[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 is

$H\left(s\right)=\frac{z\left(s\right)}{p\left(s\right)}=\frac{k}{\left(s-p\left(1\right)\right)\left(s-p\left(2\right)\right)\dots \left(s-p\left(n\right)\right)}$

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.

## Examples

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### Frequency Response of an Analog Chebyshev Type I Filter

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
```

## References

[1] Parks, Thomas W., and C. Sidney Burrus. Digital Filter Design. New York: John Wiley & Sons, 1987, chap. 7.