Butterworth bandpassfilter transfer function

Hi,

I have second order butterworth bandpassfilter with central frequency 800Hz. Damping ratio is 0.707. Sampling frequency 20k. How can derive continuous time transfer function and discreate transfer function from it in Matlab?

[Mathieu NOE]

hello Janne

see butter help

by default , it generates the discrete time filter

but if you add argument 's' you get an anlog design

[Janne Hamalainen]

Hi,

Sorry can you specify, how to generate the discreate fcn?

[Mathieu NOE]

everything is explained in the help :

help butter

butter Butterworth digital and analog filter design.

[B,A] = butter(N,Wn) designs an Nth order lowpass digital

Butterworth filter and returns the filter coefficients in length

N+1 vectors B (numerator) and A (denominator). The coefficients

are listed in descending powers of z. The cutoff frequency

Wn must be 0.0 < Wn < 1.0, with 1.0 corresponding to

half the sample rate.

If Wn is a two-element vector, Wn = [W1 W2], butter returns an

order 2N bandpass filter with passband W1 < W < W2.

[B,A] = butter(N,Wn,'high') designs a highpass filter.

[B,A] = butter(N,Wn,'low') designs a lowpass filter.

[B,A] = butter(N,Wn,'stop') is a bandstop filter if Wn = [W1 W2].

When used with three left-hand arguments, as in

[Z,P,K] = butter(...), the zeros and poles are returned in

length N column vectors Z and P, and the gain in scalar K.

When used with four left-hand arguments, as in

[A,B,C,D] = butter(...), state-space matrices are returned.

butter(N,Wn,'s'), butter(N,Wn,'high','s') and butter(N,Wn,'stop','s')

design analog Butterworth filters. In this case, Wn is in [rad/s]

and it can be greater than 1.0.

% Example 1:

% For data sampled at 1000 Hz, design a 9th-order highpass

% Butterworth filter with cutoff frequency of 300Hz.

Wn = 300/500; % Normalized cutoff frequency

[z,p,k] = butter(9,Wn,'high'); % Butterworth filter

[sos] = zp2sos(z,p,k); % Convert to SOS form

h = fvtool(sos); % Plot magnitude response

% Example 2:

% Design a 4th-order butterworth band-pass filter which passes

% frequencies between 0.15 and 0.3.

[b,a]=butter(2,[.15,.3]); % Bandpass digital filter design

h = fvtool(b,a); % Visualize filter

See also buttord, besself, cheby1, cheby2, ellip, freqz,

filter, designfilt.

Documentation for butter