% Simplest Plucked String model: Karplus Strong Algorithm
% This matlab function does a simple implemation of the Karplus Strong
% Plucked String model. It uses the following difference equation.
% y[n] = x[n] + y[n-N] + y[n-(N+1)]
%
% pluck(freqHz, iterations, fs)
%
% freqHz       : frequency in Hz (rouding occurs when computing delay line!)
% iterations   : # of loops (duration of sound file)
% fs           : sampling frequency
%
% eg. signal = pluckedStringKS(200, 5000, 22050);
%
% Tae Hong Park, Jan 2001
%
% Princeton Univ.
% Music Department
% park@silvertone.princeton.edu

function signal = pluckedStringKS(freqHz, iterations, fs)

% Echo some useful information
% ---------------------------------------------------------------------------
N = fs/freqHz;
disp(sprintf('\nActual delay   : \t%0.5g', N))

N = floor(N);
disp(sprintf('Floored delay  : \t%0.5g', N))
disp(sprintf('Frequency      : \t%0.5g', freqHz))

disp(sprintf('duration (msec): \t%0.5g', 1000*iterations/fs))
disp(sprintf('fs             : \t%0.5g', fs))
disp(sprintf('\n'))

% make random signal -1 ~ 1 with DC Compensation
% ---------------------------------------------------------------------------
x = 2*rand(1,N);
x = x - mean(x);

% generate noise and init. delay line
% make sure burst and delay line agree: burst >= delay line
% ---------------------------------------------------------------------------
y  = [zeros(1,N+1)];

if iterations > length(x)	   
   diff = iterations - length(x);
   x  = [x zeros(1,diff)];
end

% Filtering
% y[n] = x[n] + y[n-N] + y[n-(N+1)]
% ---------------------------------------------------------------------------
% init.
out    = 0;
signal = 0;
lengthYOffset = length(y)-1;

for i=1:iterations
   out = x(i) + 0.5*(y(N) + y(N+1));   	% filter signal
   y = [out, y(1:lengthYOffset)];			% update delay line
   signal = [signal out];
end

% Play sound and plot
% ---------------------------------------------------------------------------
plot(signal), grid on, title('Simple 2 point KS Plucked String Algorithm')
sound(signal, fs)