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# besselap() - Signal Processing

### Syntax

### Example

### Output / Return Value

### Limitations

### Alternatives / See Also

### Reference

[z,p,k] = besselap(n) returns the poles and gain of an order-n Bessel analog lowpass filter prototype. n must be less than or equal to 25. 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)=k(s−p(1))(s−p(2))⋯(s−p(n))besselap normalizes the poles and gain so that at low frequency and high frequency the Bessel prototype is asymptotically equivalent to the Butterworth prototype of the same order [1]. The magnitude of the filter is less than 1/2 at the unity cutoff frequency Ωc = 1. Analog Bessel filters are characterized by a group delay that is maximally flat at zero frequency and almost constant throughout the passband. The group delay at zero frequency is((2n)!2nn!)1/n

[z,p,k] = besselap(n)

Frequency Response of an Analog Bessel FilterOpen This Example Design a 6th-order Bessel analog lowpass filter. Display its magnitude and phase responses. [z,p,k] = besselap(6); % Lowpass filter prototype [num,den] = zp2tf(z,p,k); % Convert to transfer function form freqs(num,den) % Frequency response of analog filter