diff --git a/README.md b/README.md
index e2a7772..1807172 100644
--- a/README.md
+++ b/README.md
@@ -2,18 +2,56 @@
 
  Audio synthesizer project created by ECE 45 students, written using the MATLAB language and MATLAB GUI
  
+ ## Contributors
  Will add member names shortly
  
  ## Function Prototypes
- 
-function x = generate_wave(amplitude, frequency, phase, fs, duration, duty)
- 
-fuction x = envelope(input, fs, period, attack , decay, sustain, release)
+Templates to create your own functions.
+
+ ### Wave generating function
+```
+function x = generate_WAVENAME(amplitude, frequency, phase, fs, duration, duty)
+% GENERATE_WAVENAME: returns a matrix of sampled WAVENAME wave
+
+% CONTRIBUTORS:
+% Person1: how you contributed
+% Person2: how you contributed
+% etc
+
+% DOCUMENTATION:
+% phase shift is in number of periods
+% fs is the sampling frequency: how many sample points per second
+% duration is time in seconds
+% duty is a number between 0 and 1
+
+    % 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
+        YOUR CODE HERE
+    end
+end
+```
+NOTE: duty does not apply to some functions (such as sinusoids)
+
+ ### Envelope function
+```
+function x = envelope(input, fs, period, attack , decay, sustain, release)
+```
 where attack, decay, release are percentages between 0 to 1 of the period
 sustain is the percentage of the amplitude it should sustain for
 **envelope can be pitch or amplitude envelope**
 
+
+### Filter function
+```
 function  output_timedomain = Filter(input_soundin_timedomain, Fs, LOW, MED, HIGH) 
+```
 where LOW, MED, HIGH are user-selected variables of any value. 
 **output should be in time domain for all functions (new sound)**
  
diff --git a/src/.DS_Store b/src/.DS_Store
index 5008ddf..14624d2 100644
Binary files a/src/.DS_Store and b/src/.DS_Store differ
diff --git a/src/Main_test.m b/src/Main_test.m
index 9eb7060..1ebd646 100644
--- a/src/Main_test.m
+++ b/src/Main_test.m
@@ -39,5 +39,4 @@ release = 0.1;
 x = DarellAmplitudeEnvelope(x, fs, attack,decay,sustain,release); %output new sound in time domain
 %play over 5 counts, should only hear 200hz
 playtime = 5;
-play_continuous(x, fs, playtime)
-
+play_continuous(x, fs, playtime)
\ No newline at end of file
diff --git a/src/add_sine.m b/src/add_sine.m
new file mode 100644
index 0000000..e0354fe
--- /dev/null
+++ b/src/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
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diff --git a/src/amplify.m b/src/amplify.m
new file mode 100644
index 0000000..153767b
--- /dev/null
+++ b/src/amplify.m
@@ -0,0 +1,8 @@
+function output = amplify(input, multiplier)
+    %input: a 1D array representing the sound signal in the time domain
+    %multiplier: a scalar that multiplier all values in the input array to
+    %            amplify or decrease the volume.
+    %Returns: input signal scaled by the multiplier in the time domain.
+    %Author: Conner Hsu
+    output = input*multiplier;
+end
\ No newline at end of file
diff --git a/src/amplifyFreqRange.m b/src/amplifyFreqRange.m
new file mode 100644
index 0000000..88adc8d
--- /dev/null
+++ b/src/amplifyFreqRange.m
@@ -0,0 +1,23 @@
+function output = amplifyFreqRange(input, fs, low, high, multiplier)
+    %Amplifies frequencies within a specified range, leaves all other
+    %frequencies the same.
+    %By Conner Hsu
+    
+    %input: 1D array representing the sound signal in the time domain
+    %fs: sampling frequency
+    %low: a scalar representing the lower bound of frequencies to be amplified
+    %high: a scalar representing the upper bound of frequencies to be amplified
+    %multiplier: a scalar that multiplies frequencies between low and high
+    %Returns modified signal in the time domain.
+    
+    len = length(input);
+    f = fs*(-len/2:len/2-1)/len;
+    
+    outputW = fftshift(fft(input));
+    for i = 1:length(outputW)
+       if (low < abs(f(i)) && abs(f(i)) < high)
+           outputW(i) = outputW(i)*multiplier;
+       end
+    end
+    output = real(ifft(fftshift(outputW)));
+end
\ No newline at end of file
diff --git a/src/generate_sawtooth.m b/src/generate_sawtooth.m
new file mode 100644
index 0000000..76e1726
--- /dev/null
+++ b/src/generate_sawtooth.m
@@ -0,0 +1,40 @@
+function x = generate_sawtooth(amplitude, frequency, phase, fs, duration, duty)
+% generate_sawtooth: returns a matrix of sampled sawtooth wave
+
+% CONTRIBUTORS:
+% Ben Zhang: Function author
+
+% DOCUMENTATION:
+% phase shift is in number of periods
+% fs is the sampling frequency: how many sample points per second
+% duration is time in seconds
+% duty is a number between 0 and 1 
+    %duty does not apply for sawtooth wave
+
+    % 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
+    period = 1 / frequency; % period of the wave
+    
+    % initialize a one dimensional zero matrix to be populated
+    x = zeros(1, n);
+    
+    
+    % populate the matrix
+    for i = 1:n
+        t = i * dt; % time of the i'th sample
+        st = mod(frequency * t - phase, 1); % Progression through cycle
+        
+        slope = 2 * amplitude / period; % the incline slope from start to amplitude
+        mid = period / 2;
+        
+        %part before the straght vertical line
+        if(st < mid)
+            x(i) = slope * st; % amplitude from start to +amplitude
+        
+        %part after the straght vertical line
+        else
+            x(i) = slope * (st - 0.5) - amplitude; %amplitude from -amplitude to start
+        
+    end
+end
diff --git a/src/generate_sine.m b/src/generate_sine.m
index 4add313..86a86fc 100644
--- a/src/generate_sine.m
+++ b/src/generate_sine.m
@@ -1,15 +1,28 @@
 function x = generate_sine(amplitude, frequency, phase, fs, duration, duty)
-%GENERATE_SINE:Arthur Lu returns a matrix of sampled sine wave, where the
-%phase shift is in number of periods
-    x = zeros(1, fs * duration);
-    A = amplitude;
-    f = frequency;
-    p = phase;
-    n = fs * duration;
-    dt = 1 / fs;
+% GENERATE_SINE: returns a matrix of sampled sine wave
+
+% CONTRIBUTORS:
+% Arthur Lu: Original author
+% Benjamin Liou: refactoring and annotations
+
+% DOCUMENTATION:
+% phase shift is in number of periods
+% fs is the sampling frequency: how many sample points per second
+% duration is time in seconds
+% duty does not apply for sinusoids
+   
+
+    % 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;
-        x(i) = A * sin(2 * pi * f * t - p);
+        t = i * dt; % time at the i'th sample
+        x(i) = amplitude * sin(2 * pi * frequency * t - phase);
     end
 end
 
diff --git a/src/generate_square.m b/src/generate_square.m
index bf3134e..1abc6f3 100644
--- a/src/generate_square.m
+++ b/src/generate_square.m
@@ -1,19 +1,40 @@
 function x = generate_square(amplitude, frequency, phase, fs, duration, duty)
-%GENERATE_SINE:Arthur Lu returns a matrix of sampled sine wave, where the
-%phase shift is in number of periods
-    x = zeros(1, fs * duration);
-    A = amplitude;
-    f = frequency;
-    p = phase;
-    n = fs * duration;
-    dt = 1 / fs;
+% GENERATE_SQUARE: returns a matrix of sampled square wave
+
+% CONTRIBUTORS:
+% Arthur Lu: Original author
+% Benjamin Liou: refactoring and annotations
+
+% DOCUMENTATION:
+% 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 -amplitude for all sample points
+    % duty of 0.25 would return +amplitude for first quarter of each cycle
+        % then return -amplitude for the remaining three-fourths
+    % 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;
-        st = mod(f * t - p, 1);
+        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) = A;
+            x(i) = amplitude;
         else
-            x(i) = -A;
+            x(i) = -amplitude;
         end
     end
 end
diff --git a/src/generate_triangle.m b/src/generate_triangle.m
index 94b78ad..f1a50ca 100644
--- a/src/generate_triangle.m
+++ b/src/generate_triangle.m
@@ -1,19 +1,43 @@
 function x = generate_triangle(amplitude, frequency, phase, fs, duration, duty)
-%GENERATE_SINE:Arthur Lu returns a matrix of sampled sine wave, where the
-%phase shift is in number of periods
-    x = zeros(1, fs * duration);
-    A = amplitude;
-    f = frequency;
-    p = phase;
-    n = fs * duration;
-    dt = 1 / fs;
+% GENERATE_TRIANGLE: returns a matrix of sampled square wave
+
+% CONTRIBUTORS:
+% Arthur Lu: Original author
+% Benjamin Liou: refactoring and annotations
+
+% DOCUMENTATION:
+% 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 0.25 would have positive slope for first quarter of each cycle
+        % then have negative slope for the remaining three-fourths
+
+
+
+% 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;
-        st = mod(f * t - p, 1);
+        
+        % periodic ramp from 0 to 1
+        % progression through a cycle
+        st = mod(frequency * t - phase, 1);
+        
         if(st < duty)
-            x(i) = A*(1/duty * st - 0.5);
+            slope = amplitude / duty;
+            intercept = -0.5 * amplitude;
+            x(i) = slope * st + intercept;
         else
-            x(i) = A*(-(1/(1-duty))*st + (duty/(1-duty)) + 1 - 0.5);
+            slope = -amplitude / (1 - duty);
+            intercept = amplitude*( duty/(1-duty) + 0.5);
+            x(i) = slope * st + intercept;
         end
     end
 end
\ No newline at end of file
diff --git a/src/generate_white.m b/src/generate_white.m
new file mode 100644
index 0000000..ce3fb2d
--- /dev/null
+++ b/src/generate_white.m
@@ -0,0 +1,13 @@
+function x = generate_white(amplitude, fs, duration)
+%GENERATE_WHITE: returns a matrix of sampled white noise
+
+%CONTRIBUTORS:
+%Benjamin Liou: Original author
+
+%DOCUMENTATION:
+% white noise can then be filtered to produce different hues of noises
+
+
+%time domain matrix of random sample points between +-amplitude
+x = amplitude * 2 * (rand(1, fs * duration) - 0.5);
+end
\ No newline at end of file
diff --git a/src/lfo_sine.m b/src/lfo_sine.m
new file mode 100644
index 0000000..a9acbdb
--- /dev/null
+++ b/src/lfo_sine.m
@@ -0,0 +1,29 @@
+function x = lfo_sine(amplitude, frequency, phase, fs, duration, input)
+% LFO_SINE: modulates an input matrix
+
+% CONTRIBUTORS:
+% Benjamin Liou: Original author
+
+% DOCUMENTATION:
+% frequency is typically below 20Hz (according to wikipedia)
+% fs and duration should be same as input
+
+
+
+    % 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 lfo, which will be used to modulate the input
+    lfo = zeros(1, n);
+    
+    % populate lfo matrix
+    for i = 1:n
+        t = i * dt; % time at the i'th sample
+        lfo(i) = amplitude * sin(2 * pi * frequency * t - phase);
+    end
+    
+    % modulate input
+    x = lfo .* input;
+    
+end
\ No newline at end of file
diff --git a/src/reverse.m b/src/reverse.m
new file mode 100644
index 0000000..586c606
--- /dev/null
+++ b/src/reverse.m
@@ -0,0 +1,6 @@
+function output = reverse(input)
+    %input: a 1D array representing the sound signal in the time domain
+    %returns: the input signal with its elements in reverse order.
+    %By Conner Hsu
+    output = flip(input);
+end
\ No newline at end of file