Phase Modulation (PM): In phase modulation, the phase of the carrier signal varies linearly in accordance with the message signal voltage.        Where, s(t) is the carrier signal and m(t) is the message signal. Here in the above equation Kp is the phase sensitivity; the phase of the carrier signal signal is varied in accordance to the amplitude of the message signal where the amplitude of the carrier remain same in the modulation process. In the phase modulation process,  the modulation index = ΔΦ / fm.T where, ΔΦ is the peak frequency deviation representing the maximum change in carrier frequency due to modulation fm and T are the frequency and the period of the message signal respectively   MATLAB Code for Phase Modulation and Demodulation  % The code is written by SalimWireless.Com % Phase Modulation (PM) and Demodulation clc; clear all; close all; function PhaseModulationExample % Parameters fs = 1000; % Sampling freq...

Frequency Modulation (FM): The carrier signal's frequency varies linearly in response to the voltage variation in the message signal.             Here, modulation index = Δf / fm Where Δf is the peak frequency deviation and fm = frequency of the message signal. Here frequency deviation means how much the the frequency of the carrier signal deviates from its carrier's original frequency after frequency modulation. When performing frequency modulation (FM) with a carrier frequency of 100 Hz and a message frequency of 10 Hz, the resulting peak frequencies are as follows: 80 Hz (100 - 2*10 Hz), 90 Hz (100 - 10 Hz), 100 Hz, 110 Hz (100 + 10 Hz), 120 Hz (100 +  2*10 Hz). Figure: Frequency Spectrums of FM Signal     MATLAB Code for Frequency Modulation and Demodulation % The code is written by SalimWireless.Com % Frequency Modulation (FM) and Demodulation clc; clear all; close all; function Frequency_Modulation_Paraphrased % Parame...

  This plot shows the power distribution of an OFDM signal in frequency domain. The central flat region corresponds to the 64 subcarriers each spaced 15 kHz apart, giving a total bandwidth of 64 X 15 = 960 kHz . The PSD decreases outside this band due to the spectral shape of each subcarrier.  MATLAB Code  % The code is developed by SalimWireless.com clear; close all; clc; % PARAMETERS N = 64; % subcarriers Delta_f = 15e3; % subcarrier spacing Fs_base = 1e6; % base sampling rate M = 16; % 16-QAM fc = 2e6; % carrier BW = N * Delta_f; % approximate occupied BW desired_Fs = 10e6; % high sampling rate for oversampling % OVERSAMPLING L = ceil(desired_Fs / Fs_base); Fs_high = L * Fs_base; fprintf('Fs_base = %.1f kHz, Fs_high = %.1f kHz, L=%d\n', Fs_base/1e3, Fs_high/1e3, L); % GENERATE 16-QAM SYMBOLS data = randi([0 M-1], N, 1); qamSymbols = qammod(data, M, 'UnitAveragePower', true); % MAP TO IFFT B...

  Implementation Steps 1. FFT Computes the Frequency Content of a Signal FFT converts a time-domain signal to the frequency domain. If: The signal is sampled at rate $f_s$ You compute an $N_{\text{FFT}}$-point FFT Then each FFT bin corresponds to a frequency resolution of: $$\Delta f = \frac{f_s}{N_{\text{FFT}}}$$ So the FFT gives you accurate frequency content, assuming the signal is stationary and adequately sampled (Nyquist criterion met).  2. Magnitude Squared Gives Power (Not Amplitude) $$P[k] = |X[k]|^2$$ This gives power at each frequency bin, not just amplitude. It represents how much energy is present at each frequency. It's a key step for PSD.  3. Normalization Makes the PSD Physically Meaningful The equation: $$\text{PSD}[k] = \frac{|X[k]|^2}{N_{\text{FFT}} \cdot f_s \cdot U}$$ is derived from first principles and ensures that the u...

  This article is about how to create your first mobile app using React Native and Expo. For the development, I used the online platform expo.dev . It accelerates your work by suggesting dependencies very well (which npm packages you need to install). React Native is a JavaScript framework that helps you to launch your mobile app, similar to how React.js is used for building web applications. Like React.js, here also you create and call different components. Expo is basically a toolset for React Native — it provides pre-configured tools, libraries, and services so you don’t need to set up everything manually. Expo helps you make it easier and faster to build mobile apps (iOS and Android).   Steps Go to the expo.dev website. Opening this website you will find an interface like this, which is your first/main/directory root screen App.js . If this interface does not open, then search for and go to the ‘Snacks’ section of expo.dev, where you can create a new Snack for your mo...

   The block diagram illustrates the process of synchronous (coherent) demodulation , a method used to recover the original message signal from an Amplitude Modulated (AM) waveform.    Modulated AM Signal Input: The input signal is given by: \( s(t) = A_c \left[1 + K_a m(t)\right] \cos(2\pi f_c t) \) Where: \( A_c \): Carrier amplitude \( f_c \): Carrier frequency \( m(t) \): Message (modulating) signal \( K_a \): Amplitude sensitivity constant The Product Modulator (Multiplier) The core of synchronous demodulation is multiplying the incoming AM signal \( s(t) \) with a locally generated carrier signal \( c(t) \). For ideal demodulation, this local carrier must be a perfect replica of the original transmitter's carrier in both **frequency and phase**: \( c(t) = \cos(2\pi f_c t + \phi) \) Here, for perfect synchronization, the phase offset \( \phi \) must ideally be zero. Any deviation from th...

    The diagram shows a Phase-Locked Loop (PLL) based PM demodulator . Here's how each component functions together to retrieve the original message signal: Input signal \( a(t) \): This is the received PM signal \( S(t) \), typically in the form: \( S(t) = A_c \cos\left[ 2\pi f_c t + K_p m(t) \right] \) PD (Phase Detector): Compares the phase of the received PM signal with the phase of the signal from the VCO (Voltage Controlled Oscillator). Outputs a voltage proportional to the phase difference, which directly relates to the modulating signal \( m(t) \). The primary function of the PLL in this context is to continuously track the instantaneous phase variations of the input signal. F(s): The loop filter smooths the phase detector output, improving the dynamic response and reducing high-frequency noise. For PM demodulation, a high-pass or differentiating filter may not be needed, unlike in FM, because the phase detector directly provides the demodu...

The diagram illustrates a Phase-Locked Loop (PLL) used for demodulating Frequency Modulated (FM) signals. The working of each block is described below:   Input signal: This is the received FM signal, typically denoted as s(t) , which carries the frequency variations corresponding to the original message m(t) .   PD (Phase Detector): Compares the phase of the input signal with that of the feedback signal generated by the VCO . The output is a signal proportional to the phase difference or error. F(s) (Loop Filter): Processes the phase error signal from the PD. It smooths the signal to eliminate high-frequency components and to ensure loop stability. This filter also helps determine the **capture range** (the frequency range over which the PLL can acquire lock) and the **lock range** (the frequency range over which the PLL can maintain lock). VCO (Voltage Controlled Oscillat...