additive sine wave synthesis

same as a previous pull request i made (i just gave it a better name instead of "addSynth")

add_sine.m

@@ -0,0 +1,34 @@
+function x = add_sine(amplitude, fundamental, harmonics, fs, duration)
+% ADD_SINE: Additive sine wave synthesis
+
+%CONTRIBUTORS:
+%Benjamin Liou: Original author
+
+% DOCUMENTATION:
+% harmonics should ideally be a 1D matrix of:
+    % overtones: positive integers
+    % undertones: 1/ positive integers
+    % example: [1/2, 1, 2, 3]
+    % NOTE: pitch of the fundamental frequency will still be perceived even
+        % when the fundamental itself is missing. ex. [4,5,6]
+    
+% NOTE: it seems like when MATLAB's built in sound() takes in values,
+    % magnitudes over 1 get distorted.
+    
+    
+    
+    % initialize local variables from input arguments
+    n = fs * duration; % number of samples (length of matrix)
+    
+    % initialize a one dimensional zero matrix to be populated
+    x = zeros(1, n);
+    
+    % populate matrix by adding sine waves
+    for harmonic = harmonics
+        x = x + generate_sine(1, fundamental * harmonic, 0, fs, duration);
+    end
+    
+    % scale to amplitude
+    scalar = max(abs(x));
+    x = x / scalar * amplitude;
+end