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# besselap() - Signal Processing

```[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```

### Syntax

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

### Example

```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```