Fourier Transform

Using sines and cosines to reconstruct a signal
the Fourier transform
Frequency domain for a signal
Three properties of convolution relating to Fourier Transform

Reconstructing a signal
Repeating impulse function
Target Signal f^T(t)

Basic building block
f(t) = A cos(nwt)
a amplitude, w, frequency

% Cosines of different frequencies
n = 4; % no. of periods (say, seconds)
t = linspace(0, n, n * 90); % time samples
A = 2; % amplitude

f1 = A * cos(1 * (2 * pi) * t);
plot(t, f1);

f2 = A * cos(2 * (2 * pi) * t);
plot(t, f1);

f3 = A * cos(3 * (2 * pi) * t);
plot(t, f1);

f4 = A * cos(4 * (2 * pi) * t);
plot(t, f1);