## Creating Music Beat Using Pure MATLAB Code and Wave Functions

### Code:

``````clear
close
clc

% Variables for Wave Function:
magnitude = 1;
phase_shift = 0;
vertical_shift = 0;
ct_frequency_f = [4e2 3e2 2e2 3e2 1e2 1e2];

% Total Duration of the Resultant Wave:
constant = 1e2; % Nyquist's Theorem
Fs = constant*max(ct_frequency_f); % Sampling Frequency
second = 10;

% Types of Waves and Modifications:
type_wave = 1; % 0 for sine; 1 for triangle
loop_on = 0; % 0 for alternating and spacing; 1 for mixing

% Other:
power = [1 1 1 1 1 1]; % Increment speed of the wave frequency
window_frequency = 0.1;
number_space_wave = 0; % Number of space between waves
plot_zoom = 100;
sound_on = 1;

% Wave in Time Domain and Frequency Domain:
[wave_result, t] = mix_wave(magnitude, phase_shift, vertical_shift, ct_frequency_f, second, Fs, power, type_wave, loop_on, window_frequency, number_space_wave, plot_zoom);

% Sound Enable/Disable
if sound_on == 1
soundsc(wave_result, Fs)
end
``````

### Function: mix_wave

``````function [wave_result, t] = mix_wave(magnitude, phase_shift, vertical_shift, ct_frequency_f, second, Fs, power, type_wave, loop_on, window_frequency, number_space_wave, plot_zoom)
% Date: 02/28/2022 - 03/03/2022
% By: Ka Ming Lui

% Variables calculations
count_wave_type = length(ct_frequency_f);
sample_wave = second*Fs;
number_window = second*window_frequency;

% Initializing arrays
wave_function = zeros(count_wave_type, second*Fs);
X = zeros(count_wave_type, max([sample_wave,2^20])); % default minimum assign of myFFT
magnitude_X = X;

% Generating wave-type according to the inputs
if type_wave == 0 % Sine wave
for loop_count_1 = 1:count_wave_type
[wave_function(loop_count_1, :), t] = sine_wave(magnitude, phase_shift, vertical_shift, ct_frequency_f(loop_count_1), second, Fs, power(loop_count_1));
end
elseif type_wave == 1 % Triangle wave
for loop_count_1 = 1:count_wave_type
[wave_function(loop_count_1, :), t] = triangle_wave(magnitude, phase_shift, vertical_shift, ct_frequency_f(loop_count_1), second, Fs);
end
end

% Modifying the placement method of the generated waves
if loop_on == 0 % Alternating and adding space between waves
normal_wave_window = count_wave_type*number_window;
total_wave_window = normal_wave_window*(number_space_wave + 1);
length_window = floor(sample_wave/total_wave_window);

count_window = 1;
count_wave_type_loop = 1;
for loop_count_2 = 1:normal_wave_window % Adding wave
wave_result(count_window:count_window + length_window - 1) = wave_function(count_wave_type_loop, count_window:count_window + length_window - 1);
count_window = count_window + length_window;
for loop_count_3 = 1:number_space_wave % Adding space
wave_result(count_window:count_window + length_window - 1) = 0;
count_window = count_window + length_window;
end
count_wave_type_loop = count_wave_type_loop + 1;
if count_wave_type_loop == count_wave_type
count_wave_type_loop = 1;
end
end
else % Mixing waves with different frequencies into one
wave_result = zeros(1, second*Fs);
for loop_count_2 = 1:count_wave_type
wave_result = wave_result + wave_function(loop_count_2, :);
end
end

% Unify the size of the arrays
wave_result = [wave_result zeros(1, length(t) - length(wave_result))];

% Generating plots for each waves in different frequencies
% Credit: myFFT - Dr. Iyad Obeid
count_plot = 1;
for loop_count_4 = 1:count_wave_type
[X(loop_count_4, :), f] = myFFT(wave_function(loop_count_4, :), Fs);
magnitude_X(loop_count_4, :) = abs(X(loop_count_4, :));
subplot(count_wave_type + 1, 2, count_plot); plot(t(1:length(t)/plot_zoom), wave_function(loop_count_4, 1:length(t)/plot_zoom)); title('Time Domain');
count_plot = count_plot + 1;
subplot(count_wave_type + 1, 2, count_plot); plot(f, magnitude_X(loop_count_4, :)); xlim([0 max(ct_frequency_f)*2]); grid on; title('Frequency Domain');
count_plot = count_plot + 1;
end

% Generating plots for the result wave
[X_result, f] = myFFT(wave_result, Fs);
magnitude_X_result = abs(X_result);
subplot(count_wave_type + 1, 2, count_plot); plot(t, wave_result); title('Time Domain, Resultant');
count_plot = count_plot + 1;
subplot(count_wave_type + 1, 2, count_plot); plot(f, magnitude_X_result); xlim([0 max(ct_frequency_f)*2]); grid on; title('Frequency Domain, Resultant');
end``````

### Function: triangle_wave

``````function [wave_function, t] = triangle_wave(magnitude, phase_shift, vertical_shift, ct_frequency_f, second, Fs)
tick = second*Fs;
t = linspace(0, second, tick);
wave_function = magnitude*(2/pi)*asin(sin(2*pi*ct_frequency_f.*t + phase_shift)) + vertical_shift;
end``````

### Function: sine_wave

``````function [wave_function, t] = sine_wave(magnitude, phase_shift, vertical_shift, ct_frequency_f, second, Fs, power)
tick = second*Fs;
t = linspace(0, second, tick);
wave_function = magnitude*sin(2*pi*ct_frequency_f.*t.^power + phase_shift) + vertical_shift;
end``````

Published inMATLAB