Is there a function to find the product of a transfer function array?

I have a transfer function array created, for example, by

%sample number of biquads
numBQs = 20;

%preallocate transfer function
BQtfs = tf(zeros(1,1,numBQs));

Fs = 12000; %Hz

%loop over each biquad to create discrete transfer function
for i1 = 1:numBQs
    %create discrete transfer function
    BQtfs(:,:,i1) = tf([1 -1.5 0.9], [1 -0.9 0.9], 1/Fs);
end

The biquad filter coefficients are typically coming from matrices containing the numerator (and denominator) coefficients in a row such that the transfer function array would be filled by something that looks like

BQtfs(:,:,i1) = tf(BQ_b(i1,:),BQ_a(i1,:), 1/Fs);

If I now want to combine my biquad filters into a single filter, I create the product of the transfer functions. Is there a function or a better way to combine them than a simple loop such as

BQtf = BQtfs(:,:,1);
    for i1 = 2:lenBQs
        BQtf = BQtf*BQtfs(:,:,i1);
    end
    

The end game is simply to be able to plot the individual filters and the combined filter.

    bode(BQtfs) 

can be used to efficiently plot the transfer function array, but I'm not sure if there is a better way than this to plot the combined filter.

Answer 1

[Star Strider]

See if the series (linik) function will do what you want.

[Shawn Treacy]

I saw that function, but I'm unable to get it to operate on the array. Do you have a working syntax for that?

[Star Strider]

If I understand correctly what you want to do, I would do something like this:

Fs = 12000; %Hz
sys = tf([1 -1.5 0.9], [1 -0.9 0.9], 1/Fs);
sys1 = 1;

%sample number of biquads
numBQs = 20;

%loop over each biquad to create discrete transfer function
for i1 = 1:fix(numBQs/2)-1
    %create discrete transfer function
    sys1 = series(sys1,sys);
end

figure
bode(sys1)

This produces a tf object as ‘sys1’.

You will likely have to experiment with it to get the result you want.