FFT Magnitude and Phase Spectrum using MATLAB (2024)

clc;
clear;
close all;

% Parameters
fs = 100; % Sampling frequency
t = 0:1/fs:1-1/fs; % Time vector

% Signal definition
x = cos(2*pi*15*t - pi/4) - sin(2*pi*40*t);

% Compute Fourier Transform
y = fft(x);
z = fftshift(y);

% Frequency vector
ly = length(y);
f = (-ly/2:ly/2-1)/ly*fs;

% Compute phase
phase = angle(z);

% Plot magnitude of the Fourier Transform
figure;
subplot(2, 1, 1);
stem(f, abs(z), 'b');
xlabel('Frequency (Hz)');
ylabel('|y|');
title('Magnitude of Fourier Transform');
grid on;

% Plot phase of the Fourier Transform
subplot(2, 1, 2);
stem(f, phase, 'b');
xlabel('Frequency (Hz)');
ylabel('Phase (radians)');
title('Phase of Fourier Transform');
grid on;

Parent Topics

Fourier Series and Fourier TransformFourier TransformMATLAB

Fourier Series and Fourier TransformFourier TransformMATLAB

Wireless Signal Processing CIR, Doppler Shift & Gaussian Random Variable The Channel Impulse Response (CIR) is a concept primarily used in the field of telecommunications and signal processing. It provides information about how a communication channel responds to an impulse signal. What is the Channel Impulse Response (CIR) ? It describes the behavior of a communication channel in response to an impulse signal. In signal processing, an impulse signal has zero amplitude at all other times and amplitude ∞ at time 0 for the signal. Using a Dirac Delta function, we can approximate this. ...(i) δ( t) now has a very intriguing characteristic. The answer is 1 when the Fourier Transform of δ( t) is calculated. As a result, all frequencies are responded to equally by δ (t). This is crucial since we never know which frequencies a system will affect when examining an unidentified one. Since it can test the system for all frequencies, δ( t) bec

Read more

Modulation Constellation Diagrams BER vs. SNR BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ... 1. What is Bit Error Rate (BER)? The abbreviation BER stands for bit error rate, which indicates how many corrupted bits are received (after the demodulation process) compared to the total number of bits sent in a communication process. It is defined as, In mathematics, BER = (number of bits received in error / total number of transmitted bits) On the other hand, SNR refers to the signal-to-noise power ratio. For ease of calculation, we commonly convert it to dB or decibels. 2. What is Signal to Noise Ratio (SNR)? SNR = signal power/noise power (SNR is a ratio of signal power to noise power) SNR (in dB) = 10*log(signal power / noise power) [base 10] For instance, the SNR for a given communication system is 3dB. So, SNR (in ratio) = 10^{SNR (in dB) / 10} = 2 Therefore, in this instance, the signal power is twice as

Read more

The array response vectors for uniform linear arrays (ULA) with elements, N are represented as Similarly, for Uniform Planer arrays (UPA), the array response vectors can be represented as, Where 0 ≤ x ≤ W 1 -1 and 0 ≤ y ≤ W 2 -1 Fig : Directional cosine vectors at each antenna element In figure above, it is illustrated that when transmitted signal reaches at receiver it creates different path lengths at different antenna element. Here in figure the second ray creates path-length difference of dcosθ with the first element. As there will be phase difference for same angle of departure (AOD) rays transmitted from Tx side. The corresponding calculation of phase difference is shown in figure.

Read more

Wireless Signal Processing Gaussian and Rayleigh distributions ... 1. Gaussian Distribution The Gaussian distribution has a lot of applications in wireless communication. Since noise in wireless communication systems is unpredictable, we frequently assume that it has a Gaussian distribution. Any wireless communication diagram will show the addition of AWGN noise as the signal travels through the channel. Due to its independence from operating frequency, it is known as AWGN, or additive white Gaussian noise. To determine the noise in a signal, we compute noise power density, or noise power / Hz (here, bandwidth in Hz). It mostly serves to represent real-valued random variables whose distributions are unknown in the scientific and social sciences. It has a bell shape. According to the theory of a Gaussian random variable, under certain circ*mstances, the average of numerous samples (observations) of a random variable with a finite mean and variance is itse

Read more

(Search any topic) Search any topic on the whole website Modulation Signal Processing Beamforming MATLAB 5G Wireless GATE-ESE-NET Programming Telecommunication Channel Impulse Response Computer Networks MIMO - Multiple Input Multiple Output Filters Millimeter wave Python Constellation Diagrams BER vs SNR Electronics Industry Fourier Series and Fourier Transform Frequency bands Wireless Communication Q & A ASK FSK PSK Channel Model IoTs UWB pskmod Antenna Applications and Games C Programming Channel Estimation Equalizers Gaussian Random Variable Projects Q & A QAM Transform Fading Microwave News about 5G PAM Python Matrix Operations SSC Exam Web Design WordPress Ionospheric Communication JavaScript MATLAB Simulink Mobile & Accessories OFDM Signal Processing for 5G Analog Circuits Cell Towers Computer Digital Circuits Fourier Series HomePage Information and Coding Theory Laplace Transform MySQL Node.js Search ShareLinkF / Generate QR Z Transform It's

Read more

Home / Engineering & Other Exams /UGC NET 2022: Previous Year Question Papers ... NET | GATE | ESE | UGC-NET (Electronics Science, Subject code: 88 ) UGC Net Electronic Science Questions Paper With Answer Key Download Pdf [December 2024] UGC Net Electronic Science Questions Paper With Answer Key Download Pdf [June 2024] UGC Net Electronic Science Questions Paper With Answer Key Download Pdf [December 2023] UGC Net Electronic Science Questions Paper With Answer Key Download Pdf [June 2023] UGC Net Electronic Science Questions Paper With Answer Key Download Pdf [December 2022] UGC Net Electronic Science Questions Paper With Answer Key Download Pdf [June 2022] UGC Net Electronic Science Questions Paper With Answer Key Download Pdf [December 2021] UGC Net Electronic Science Questions With Answer Key Download Pdf [June 2020] UGC Net Electronic Science Questions With Answer Key Download Pdf [December 2019] UGC Net Electronic Science Questions With Answer Key Download Pdf [

Read more

Signal Processing RMS Delay Spread, Excess Delay Spread, and Multipath... RMS Delay Spread, Excess Delay Spread, and Multipath (MPCs) The fundamental distinction between wireless and wired connections is that in wireless connections signal reaches at receiver thru multipath signal propagation rather than directed transmission like co-axial cable. Wireless Communication has no set communication path between the transmitter and the receiver. The line of sight path, also known as the LOS path, is the shortest and most direct communication link between TX and RX. The other communication pathways are called non-line of sight (NLOS) paths. Reflection and refraction of transmitted signals with building walls, foliage, and other objects create NLOS paths. [ Read More about LOS and NLOS Paths] Multipath Components or MPCs: The linear nature of the multipath component signals is evident. This signifies that one multipath component signal is a scalar multiple of

Read more

Decision Feedback Equalizer is the abbreviation for this. We know that in a typical wireless communication scenario, different multipath cause the signal to arrive at the receiver at different times after transmitting it from the transmitter. Our signal may show a slight spatial frequency shift as a result.By using several taps to receive signals with varying time delays or signals with a slight frequency shift, equalizers solve this problem by changing their tap weights. Decision feedback equalizers continuously update their tap coefficient vectors by reducing the error between the desired signal and adaptive filter output. Inter-symbol interference (ISI) happens in a typical wireless communication system when the modulation bandwidth exceeds the radio channel's coherence bandwidth. Equalization reduces the ISI produced by multipath within a time-dispersive channel. ** Coherence bandwidth is the bandwidth (range of frequencies) over which the channel is constant is called coher

Read more