How to create a second order bandpass filter. (Sallen-key bandpass filter)

I need to code a bandpass filter using the given transfer function:

H(s)=((h(w/Q)*s)/((s^2) + (w/Q)*s+w^2))
w=2*pi*5000
Q factor is 2
h=5

The aim is to plot the magnitude of the transfer function.

I have tried to use the syntax fdesign.bandpass but do not know how to compile the specstring. Thanks in advance for your assistance!

Answer 1

[Star Strider]

First, use the Symbolic Math Toolbox to do the (error-free) algebra and substitutions and create the polynomial vectors, then use the Signal Processing Toolbox freqs function to plot the transfer function (Bode plot):

syms s
w = sym(2*pi*5000);
Q  = sym(2);
h = sym(5);
H(s) = ((h*(w/Q)*s)/((s^2) + (w/Q)*s+w^2));             % Substitute Values
H = simplify(H, 'steps',10);                            % Simplify
[Hn,Hd] = numden(H);                                    % Separate Numerator & Denominator Polynomials
Hnp = sym2poly(Hn)                                      % Convert To Double Polynomial
Hdp = sym2poly(Hd)                                      % Convert To Double Polynomial

figure(1)
freqs(Hnp, Hdp)                                         % Bode Plot

If you want to create a discrete filter, you need to specify a sampling frequency. Then use the bilinear function to convert from continuous to discrete.

My apologies for the delay. Life and software updates intrude.