Fourier series and its spectrum in continuous time signals

Fourier series in continuous time signals represents a periodic signal as a sum of sinusoidal components

The project scope includes explaining the concept of Fourier series, its mathematical formulation, and its significance in signal processing and communication. It involves illustrating how to compute Fourier coefficients, visualize signal reconstruction using various sinusoidal components, and demonstrate applications in signal analysis and synthesis. Additionally, practical examples and interactive simulations may be utilized to enhance understanding and engagement. The project emphasizes intuitive understanding while delving into the mathematical intricacies of Fourier series

% Define the continuous-time signal x(t)
t = -2:0.001:2; % Time vector
x = exp(-2*t).*cos(10*pi*t); % Signal with exponential and cosine components

% Compute the Fourier transform using the Fourier transform function
X = fftshift(fft(x));

% Compute the frequency axis for plotting
fs = 1/(t(2)-t(1)); % Sampling frequency
f = linspace(-fs/2, fs/2, length(X));

% Plot the magnitude spectrum of the Fourier transform
figure;
plot(f, abs(X), 'LineWidth', 1.5);
xlabel('Frequency (Hz)');
ylabel('|X(f)|');
title('Magnitude Spectrum of Fourier Transform');

% Plot the phase spectrum of the Fourier transform
figure;
plot(f, angle(X), 'LineWidth', 1.5);
xlabel('Frequency (Hz)');
ylabel('Phase of X(f)');
title('Phase Spectrum of Fourier Transform');