Ways to Apply filter for Signal

I have a matrix of signals, with each row representing a signal, and a corresponding matrix of filters, where each row represents the filter for a specific signal. How can I efficiently apply the convolution of each signal with its corresponding filter?

Answer 1

[Star Strider]

A loop may be appropriiate. Put the fiilters in a cell array, and then call each filter with its appropriate signal.

Example —

Fs = 1000;
Fn = Fs/2;
Wp = [1 100]/Fn;                                                    % Passband Frequency (Normalised)
Ws = [0.5 105]/Fn;                                                % Stopband Frequency (Normalised)
Rp =  1;                                                            % Passband Ripple
Rs = 60;                                                            % Passband Ripple (Attenuation)
[n,Wp] = ellipord(Wp,Ws,Rp,Rs);                                     % Elliptic Order Calculation
[z,p,k] = ellip(n,Rp,Rs,Wp);                                        % Elliptic Filter Design: Zero-Pole-Gain 
[sos{1},g{1}] = zp2sos(z,p,k);                                      % Second-Order Section For Stability

Wp = [100 200]/Fn;                                                  % Passband Frequency (Normalised)
Ws = [95 205]/Fn;                                               % Stopband Frequency (Normalised)[n,Wp] = ellipord(Wp,Ws,Rp,Rs);                                     % Elliptic Order Calculation
[z,p,k] = ellip(n,Rp,Rs,Wp);                                        % Elliptic Filter Design: Zero-Pole-Gain 
[sos{2},g{2}] = zp2sos(z,p,k);                                      % Second-Order Section For Stability

t = linspace(0, 5, 10000);
s = randn(2, 10000);                                                % Signal Matrix

for k = 1:size(s,1)
    out{k} = filtfilt(sos{k},g{k},s(k,:));
end

figure
tiledlayout(size(s,1), 1)
for k = 1:size(s,1)
    nexttile
    plot(t, out{k})
    grid
    title("Signal "+k)
end

.

Answer 2

[Gayatri]

Hi Nikhil,

If you have a matrix of signals where each row represents a distinct signal and another matrix of filters with each row corresponding to a filter, you can apply the associated filters to the signals simultaneously.

• Convert the matrices into cell arrays and leverage the 'cellfun' function to apply convolution row by row as follows:

     A = [1 0 1; 1 0 1]; % Matrix A: Contains signals as rows.
     B = [2 7; 2 7];     % Matrix B: Contains filters as rows.

• Transform each matrix into a cell array, where each cell holds a single row of the original matrix. This enables efficient row-wise operations:

     cellA = num2cell(A, 2);
     cellB = num2cell(B, 2);

• Use 'cellfun' to perform convolution between each signal and its corresponding filter:

     result = cellfun(@(x, y) conv(x, y), cellA, cellB, 'UniformOutput', false);

Here, 'cellfun' applies the convolution function to each pair of corresponding rows from the two cell arrays (cellA and cellB). The 'UniformOutput', false option allows the output to be stored as a cell array because convolution can produce results of varying lengths.

For additional information on the 'cellfun' function, refer to the MATLAB documentation: https://www.mathworks.com/help/releases/R2022a/matlab/ref/cellfun.html

I hope it helps!