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%
%   Hw3_Pb1.m
%   ELEC-E5610 - Acoustics and the Physics of Sound
%   November 2020
%
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%
%   Problem:
%   Given the initial displacement of a plucked undamped string (see
%   below), create the spectrum of the resulting vibration.

%% String parameters:
L = 1; % string length
d = 999; % no. of spatial steps
x = 0:L/d:L-L/d; % spatial axis, divides L into d steps
h = 0.01; % plucking amplitude
p = 4; % plucking point variable (actual plucking location is L/p)
y0 = zeros(1,d); % create string displacement vector

%% set initial string shape (triangular string, plucked at L/p):
for n = 1:d
    if x(n) <= L/p
        y0(n) = p*h/L*x(n);
    else % L/p < x <= L
        y0(n) = p*h/(p-1)*(1-x(n)/L);
    end
end

% draw string displacement:
close all;
figure(1);
plot(x,y0);
title('Initial string shape');
xlabel('String length coordinate');
ylabel('String displacement');

%% create the spectrum
Fs = 48000; % sampling frequency
Y = zeros(1,Fs/2); % initialize the spectrum
f0 = 440; % fundamental frequency (Hz)
nmax = floor((Fs/2)/f0); % highest representable mode number (Nyquist theorem)

%%%%%%%%%%% INSERT YOUR OWN CODE HERE %%%%%%%%%%%
for n = 1:nmax    
    Y(n*f0) = getNthStringModeAmplitude(n,h,p,L,x); % spectrum of the string vibration
end
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%% Plot the spectrum:
figure(2);
hold on
epsilon = 1e-20; % a small constant to be added to the spectrum so that log(0) is avoided when plotting below 
Y = Y./max(Y); % normalize spectrum to 0 dB
plot(20*log10(abs(Y+epsilon))); % plot spectrum
title('Resulting spectrum');
grid on; % plot grid for clarity
xlabel('Frequency (Hz)'); % name the x-axis
ylabel('Amplitude (dB)'); % name the y-axis
axis([0 Fs/2 -100 0]); % zoom in