Linear filter for echo effect

Hello all!

A discrete-time causal filter is described by the following difference equation.

A simple linear filter for simulation of echo-effect can be described by the following equation

How can I represent the above equation in code?

% I'm not sure about that
syms x(n) y(n)  
eq = y(n) == c*x(n)+(1-c)*x(n-P)

Can I use syms function for n x and y.

P and c are known

Also I want to transform from difference equation to tranfer function. Can I use the function ztrans() for that?

Thanks in advance

Answer 1

[Mathieu NOE]

hello

there is a very simple way to implement echo effects - see demo code below

infile='DirectGuitar.wav';
outfile='out_echo.wav';

% read the sample waveform
[x,Fs] = audioread(infile);

% normalize x to +/- 1 amplitude
x = x ./ (max(abs(x)));

% parameters 
N_delay=20; % delay in samples
C = 0.7; % amplitude of direct sound

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

y = zeros(length(x),1);       % create empty out vector
y(1:N_delay)=x(1:N_delay); % to avoid referencing of negative samples

% for each sample > N_delay
for i = (N_delay+1):length(x)
    y(i) = C*x(i) + (1-C)*(x(i-N_delay));   % add delayed sample
    
end

% write output
% normalize y to +/- 1 amplitude
y = y ./ (max(abs(y)));
audiowrite(outfile, y, Fs);

figure(1)
hold on
plot(x,'r');
plot(y,'b');
title('Echoed and original Signal');
sound(y,Fs);