create a triangle wave using only the zeros and fft functions in matlab

A triangle wave can be created by performing the inverse Fast Fourier Transform (FFT) on a series of zeros and ones. Here's a step-by-step guide to creating a triangle wave using only the zeros and FFT functions in MATLAB:

1. Initialize the parameters:

main.m
fs = 1000; % Sample rate
T = 1/fs; % Sample period
duration = 1; % Duration of the waveform (in seconds)
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2. Create a time vector:

main.m
t = 0:T:duration-T;
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3. Create a zeros vector of the same length as t:

main.m
x = zeros(size(t));
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4. Set the values of x to create the desired triangle wave:

main.m
x(t<duration/2) = 4*(t(t<duration/2)-(duration/4))/(duration/2);
x(t>=duration/2) = 4*((duration/4)-t(t>=duration/2))/(duration/2);
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5. Apply the FFT on x:

main.m
X = fft(x);
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6. Create the triangle wave by performing the inverse FFT on X:

main.m
triangle_wave = ifft(X);
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7. Plot the resulting triangle wave:

main.m
plot(t, triangle_wave);
xlabel('Time (s)');
ylabel('Amplitude');
title('Triangle Waveform');
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This code will generate a triangle wave using only the zeros and FFT functions in MATLAB.