Pulse-width modulation (PWM), or pulse-duration modulation (PDM), is a method of controlling the average power delivered by an electrical signal.   Fig: An example of PWM in an idealized inductor driven by a blue line voltage source modulated as a series of sawtooth pulses, resulting in a red line current in the inductor.    Duty cycle A low duty cycle equates to low power because the power is off for most of the time; the word duty cycle reflects the ratio of "on" time to the regular interval or "period" of time. The duty cycle is measured in percent, with 100% representing full on. A digital signal has a duty cycle of 50% and looks like a "square" wave when it is on 50% of the time and off the other 50%. A digital signal has a duty cycle of greater than 50% when it spends more time in the on state than the off state. A digital signal has a duty cycle of 50% when it alternates between the on and off states more often than not.         Mathematical...

The windowed periodogram is a widely used technique for estimating the Power Spectral Density (PSD) of a signal. It enhances the classical periodogram by mitigating spectral leakage through the application of a windowing function. This technique is essential in signal processing for accurate frequency-domain analysis.   Power Spectral Density (PSD) The PSD characterizes how the power of a signal is distributed across different frequency components. For a discrete-time signal, the PSD is defined as the Fourier Transform of the signal’s autocorrelation function: S x (f) = FT{R x (τ)} Here, R x (τ)}is the autocorrelation function. FT : Fourier Transform   Classical Periodogram The periodogram is a non-parametric PSD estimation method based on the Discrete Fourier Transform (DFT): P x (f) = \(\frac{1}{N}\) X(f) 2 Here: X(f): DFT of the signal x(n) N: Signal length However, the classical periodogram suffers from spectral leakage due to abrupt truncation of the ...

MATLAB Code for Manual Eigenvalue Decomposition clc; clear; close all; A = [1,2]; R = A' * A; array_length = length(A); eigenvalues = manual_eigenvalue_decomposition(R, array_length); disp('Eigenvalues:'); disp(eigenvalues); eigenvectors = find_eigenvectors(R, eigenvalues); disp('Eigenvector Matrix:'); disp(eigenvectors); % Manual Eigenvalue Decomposition Function function eigenvalues = manual_eigenvalue_decomposition(A, n) eigenvalues = zeros(n, 1); % Initialize eigenvalues as a column vector for i = 1:n % Start with a random vector v = randn(n, 1); % Power iteration to find the eigenvector corresponding to the largest eigenvalue for j = 1:10 % Iteration count (power iteration steps) v = A * v; % Multiply by matrix A v = v / norm(v); % Normalize the vector end % Eigenvalue is the Rayleigh quotient eigenvalues(i) = (v' * A * v) / (v' * v); % Deflate the matrix to find the next eigenvector A = A - eigenvalues(i) * (v * v'); end end funct...

MATLAB Code % The code is developed by SalimWireless.com clc; clear; close all; % Input Signal and Parameters Fs = 1000; % Sampling frequency t = 0:1/Fs:0.3; % Time vector x = cos(2*pi*200*t) + randn(size(t)); % Signal: 200 Hz cosine + noise % Welch's Method Parameters segmentLength = 256; % Length of each segment overlapFraction = 0.5; % Fractional overlap (50%) overlapSamples = floor(segmentLength * overlapFraction); % Overlap in samples step = segmentLength - overlapSamples; % Step size N = length(x); % Length of the input signal % Define Hann Window hannWindow = 0.5 * (1 - cos(2 * pi * (0:segmentLength-1)' / (segmentLength - 1))); windowEnergy = sum(hannWindow.^2); % Normalization factor % Segment the Signal into Overlapping Windows numSegments = floor((N - overlapSamples) / step); % Number of segments segments = zeros(segmentLength, numSegments); for i = 1:numSegments startIdx = (i - 1) * step + 1; endIdx = star...

  MATLAB Script % The code is developed by SalimWireless.Com clc; clear; close all; % Parameters frequency = 10; % Message signal frequency (Hz) carrier_frequency = 100; % Carrier signal frequency (Hz) fs = 1000; % Sampling frequency % Time values t = linspace(0, 1, 10000); % Message signal message_signal = sin(2 * pi * frequency * t); % Carrier signal carrier_signal = cos(2 * pi * carrier_frequency * t); % DSB-SC Modulation dsbsc_modulated_signal = message_signal .* carrier_signal; % DSB-SC Demodulation dsbsc_demodulated_signal = dsbsc_modulated_signal .* carrier_signal; % Low-pass filter lpf_cutoff = frequency; % Low-pass filter cutoff frequency [b, a] = butter(6, lpf_cutoff / (0.5 * fs)); % 6th-order Butterworth filter dsbsc_demodulated_signal_filtered = filter(b, a, dsbsc_demodulated_signal); % Plot results figure; % Subplot 1: Message signal subplot(3, 1, 1); plot(t, message_signal, 'b'); title('Message Signal'); xlabel('Time'); yl...

Pulse-position modulation (PPM) is a form of signal modulation in which M message bits are encoded by transmitting a single pulse in one of 2M possible required time shifts. This is repeated every T seconds, such that the transmitted bit rate is M/T bits per second. Pulse position modulation is one type of analog modulation which allows variation within the position of the pulses based on the sampled modulating signal’s amplitude is called PPM or Pulse Position Modulation. In this type of modulation, the amplitude & width of the pulses are kept stable & the position of the pulses only varied. The PPM technique allows computers to transmit data by simply measuring the time taken to reach each data packet to the computer. So is frequently used within optical communication where there is small multi-pathway interference. This modulation totally transmits digital signals & cannot be utilized by analog systems. It transmits simple data which is not efficient while transferring f...