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# besself() - Signal Processing

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### Example

### Output / Return Value

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besself designs lowpass, analog Bessel filters, which are characterized by almost constant group delay across the entire passband, thus preserving the wave shape of filtered signals in the passband. besself does not support the design of digital Bessel filters.[b,a] = besself(n,Wo) designs an order n lowpass analog Bessel filter, where Wo is the frequency up to which the filter's group delay is approximately constant. Larger values of the filter order (n) produce a group delay that better approximates a constant up to frequency Wo. besself returns the filter coefficients in the length n+1 row vectors b and a, with coefficients in descending powers of s, derived from this transfer function:H(s)=B(s)A(s)=b(1) sn+b(2) sn−1+⋯+b(n+1)a(1) sn+a(2) sn−1+⋯+a(n+1).[z,p,k] = besself(...) returns the zeros and poles in length n or 2*n column vectors z and p and the gain in the scalar k. [A,B,C,D] = besself(...) returns the filter design in state-space form, where A, B, C, and D arex˙=A x+B uy=C x+D u.and u is the input, x is the state vector, and y is the output.

[b,a] = besself(n,Wo)[z,p,k] = besself(...)[A,B,C,D] = besself(...)

Frequency Response of an Analog Bessel FilterOpen This Example Design a 5th-order analog lowpass Bessel filter with approximately constant group delay up to rad/s. Plot the magnitude and phase responses of the filter using freqs. [b,a] = besself(5,10000); freqs(b,a) Frequency Response of a Digital Bessel FilterOpen This Example Design an analog Bessel filter of order 5. Convert it to a digital IIR filter using bilinear. Display its frequency response. Fs = 100; % Sampling Frequency [z,p,k] = besself(5,1000); % Bessel analog filter design [zd,pd,kd] = bilinear(z,p,k,Fs); % Analog to digital mapping sos = zp2sos(zd,pd,kd); % Convert to SOS form fvtool(sos) % Visualize the digital filter