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src/generate_keyboard.m

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+function x = generate_keyboard(amplitude, frequency, phase, fs, duration, duty)
+% GENERATE_KEYBOARD: returns a matrix of a sum of sine waves
+
+% CONTRIBUTORS:
+% Ryan Goh: author
+
+% DOCUMENTATION:
+% fs is the sampling frequency: how many sample points per second
+% duration is time in seconds
+% amplitude, phase, and duty are not used in this function
+
+% This function's purpose is to generate a wave that can simulate the sound of a digital keyboard.
+% Sound is best suited for frequencies near the middle octave of the
+% piano(261.6 - 523.2). Frequencies too high or too low do not sound
+% similar to the intended sound.
+
+% Referenced Arthur Lu and Benjamin Liou's generate sine function. Also
+% adapted wave model from https://dsp.stackexchange.com/questions/46598/mathematical-equation-for-the-sound-wave-that-a-piano-makes
+
+
+    % initialize local variables from input arguments
+    n = fs * duration; % number of samples (length of matrix)
+    dt = 1 / fs; % sampling period: time between two sample points
+    
+    % initialize a one dimensional zero matrix to be populated
+    x = zeros(1, n);
+    
+    % populate the matrix
+    for i = 1:n
+        t = i * dt; % time at the i'th sample
+        
+        %wave model of keyboard sound. 
+        %Original version from https://dsp.stackexchange.com/questions/46598/mathematical-equation-for-the-sound-wave-that-a-piano-makes
+        y = sin(2 * pi * frequency * t) * exp(-0.002 * 2 * pi * frequency * t) ...
+        + (sin(3*2*pi*frequency*t)*exp(-0.002 * 2 * pi * frequency * t)) / 2 ...
+        + (sin(4*2*pi*frequency*t)*exp(-0.002 * 2 * pi * frequency * t)) / 8 ...
+        + (sin(5 * 2 * pi * frequency * t) * exp(-0.002 * 2 * pi * frequency * t)) / 16 ...
+        + (sin(6 * 2 * pi * frequency * t) * exp(-0.002 * 2 * pi * frequency * t)) / 25 ...
+        + (sin(7 * 2 * pi * frequency * t) * exp(-0.002 * 2 * pi * frequency * t)) / 50 ...
+        + (sin(8 * 2 * pi * frequency * t) * exp(-0.002 * 2 * pi * frequency * t)) / 100 ...
+        + (sin(9 * 2 * pi * frequency * t) * exp(-0.002 * 2 * pi * frequency * t)) / 200;
+        
+        %Further adjustments to improve sound
+        y = y + y * y * y;
+        y = y * (1 + 16*t*exp(-1000*t));
+        
+        x(i) = 0.15 * y;%multiplied by fixed amplitude value of 0.15
+    end
+end