MATLAB Code clc; clear; close all ; % ========================================================================= % === DEFINE A TIME INDEX 'n' CENTERED AROUND ZERO === % ========================================================================= N = 64; % Number of samples (keep it even for symmetry) n = -N/2 : N/2-1; % MODIFIED: Time index now includes negative values % --- Other Parameters --- Fs = N; % Define Sampling Frequency in Hz f0 = 8; % "Hardcore" frequency in Hz (e.g., 8 cycles in 1 sec) omega0 = 2 * pi * f0 / Fs; % Convert Hz to rad/sample % --- Frequency Axis for Plotting --- f_norm = -0.5:0.001:0.5; % Normalized frequency freq_hz = f_norm * Fs; % Frequency axis in Hz w = 2 * pi * f_norm; % Angular frequency for DTFT calculation % ====================================================================...

APPARATUS : 1. TIMS-301 Modelling System 2. C.R.O (20MHz) 3. Spectrum Analyzer 4. Connecting chords & probes. AM Signal, S(t) = E(1 + m·cos(μt)) · cos(ωt) Where, E is the amplitude of the AM signal μ is the frequency of the message signal (in rad/s) ω is the frequency of the carrier signal (in rad/s) m is the modulation index (varies from 0 to 1) = {A(1 + m·cos(μt))} × {B·cos(ωt)} = {low frequency term a(t)} × {high frequency term c(t)} The low frequency term can be considered as: a(t) = DC + m(t) Using an adder, we try to keep the modulation index or modulation depth exactly 100%. Figure: AM, with m = 1 For example, if we set DC voltage to A volts and the amplitude of the AC part as A·m, then the ratio is 1 at the adder output, indicating 100% amplitude modulation. Circuit Diagram Figure: AM Circuit PROCEDURE : 1. Generate a message signal from the AUDIO OSCILLATOR module. The oscillator ...

Power Distribution In practice, the AM wave s(t) is a voltage or current signal. In either case, the average power delivered to a 1-ohm load resistor by s(t) is comprised of three components: Carrier power = (1/2) A c 2 Upper side-frequency power = (1/8)μ 2 A c 2 Lower side-frequency power = (1/8)μ 2 A c 2 The ratio of the total sideband power to the total power in the modulated wave is therefore equal to μ 2 / (2 + μ 2 ), which depends only on the modulation factor μ. If μ = 1, that is, 100% modulation is used, the total power in the two side-frequencies of the resulting AM wave is only one-third of the total power in the modulated wave. A major topic in Amplitude Modula...

  MATLAB Script  clc; clear; close all; % Time domain setup Fs = 1000;               % Sampling frequency T = 1/Fs;                % Sampling interval L = 2048;                % Number of samples t = (-L/2 : L/2 -1)*T;   % Symmetric time vector % Unit step function u(t) ≈ heaviside(t) x = double(t >= 0);      % Discrete unit step % FFT and frequency axis X = fftshift(fft(x));    % Shift zero freq to center f = (-Fs/2):(Fs/L):(Fs/2 - Fs/L);   % Frequency vector % Normalize FFT output X = X / L; % Plot time-domain signal figure(); plot(t, x, 'LineWidth', 1.5); title('Unit Step Function u(t)'); xlabel('Time (s)'); ylabel('Amplitude'); grid on; xlim([-0.01 0.01]); % Plot frequency-domain magnitude figure(); plot(f, abs(X), 'LineWidth', 1.5); title('Fourier Transform of a Rectangular Function'); xlabel('Frequency (Hz...

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  MATLAB Script  clc; clear; close all; % Parameters N = 1024;              % Number of points delta = zeros(1, N);   % Create zero array delta(N/2) = 1;        % Discrete delta at center % Time and frequency vectors Fs = 1000;                             % Sampling frequency t = (-N/2:N/2-1)/Fs;                   % Time vector f = (-N/2:N/2-1)*(Fs/N);               % Frequency vector % Fourier Transform using FFT X = fftshift(fft(delta)); % Plot figure; plot(f, abs(X)); xlabel('Frequency (Hz)'); ylabel('|X(ω)|'); title('Fourier Transform of a Delta Function'); grid on; web('https://www.salimwireless.com/search?q=fourier%20transform', '-browser');   Output      Further Reading 

Summary Based on  Yeung, 2025:  Yeung, C.K.A., Lo, B.F. and Torborg, S. Drone detection via low complexity zadoff-chu sequence root estimation. In 2020 IEEE 17th Annual Consumer Communications & Networking Conference (CCNC) (pp. 1-4). IEEE, 2020, January.   The rise in drone usage—from agriculture and delivery to surveillance and racing—has introduced major privacy and security challenges. Modern drones often use OFDM (Orthogonal Frequency Division Multiplexing) with Zadoff-Chu (ZC) sequences for synchronization. While powerful, detecting these sequences blindly (without knowing their parameters) remains a challenge. Aim This article presents a low-complexity solution to blindly detect ZC sequences used by unknown drones. The approach uses a novel double differential method that works without large correlation banks, making it efficient and real-time capable. ZC Sequence Fundamentals A ZC sequence of prime length P and roo...

DFT-spread OFDM (DFTs-OFDM) has lower Peak-to-Average Power Ratio (PAPR) because it "spreads" the data in the frequency domain before applying IFFT, making the time-domain signal behave more like a single-carrier signal rather than a multi-carrier one like OFDM. Deeper Explanation: Aspect OFDM DFTs-OFDM Signal Type Multi-carrier Single-carrier-like Process IFFT of QAM directly QAM → DFT → IFFT PAPR Level High (due to many carriers adding up constructively) Low (less fluctuation in amplitude) Why PAPR is High Subcarriers can add in phase, causing spikes DFT "pre-spreads" data, smoothing it Used in Wi-Fi, LTE downlink LTE uplink (as SC-FDMA) In OFDM, all subcarriers can...