added half circles function

src/generate_halfCircles.m

@@ -0,0 +1,44 @@
+function x = generate_halfCircles(amplitude, frequency, phase, fs, duration, duty)
+    % Generates half circles.
+
+    % By Conner Hsu
+
+    % DOCUMENTATION:
+    % amplitude scales how tall the half circle is.
+    % phase shift is in number of periods
+    % fs is the sampling frequency: how many sample points per second
+    % duration is time in seconds
+    % duty cycle should be a number between 0 and 1.
+        % duty of 0 or less would return 0 for all sample points
+        % duty of 0.25 would return a half circle for first quarter of each cycle
+        % then return 0 for the remaining 3/4ths
+    % duty of 1 would return all +amplitude
+
+    % 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
+        
+        % periodic ramp from 0 to 1
+        % progression through a cycle
+        st = mod(frequency * t - phase, 1);
+        
+        if(st < duty)
+            x(i) = sqrt((duty/2)^2-(st-duty/2)^2)/2*amplitude;
+        else
+            x(i) = 0;
+        end
+    end
+    %Testing code.
+    %t = 0:dt:duration;
+    %t(n) = [];
+    %plot(t, x);
+    sound(x, fs);
+end