Skip to main content

FFT Magnitude and Phase Spectrum using MATLAB


 

MATLAB Code 

% Developed by SalimWireless.Com

clc;
clear;
close all;

% Configuration parameters
fs = 10000; % Sampling rate (Hz)
t = 0:1/fs:1-1/fs; % Time vector creation

% Signal definition
x = sin(2 * pi * 100 * t) + cos(2 * pi * 1000 * t);

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

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

% Calculate phase while avoiding numerical precision issues
tol = 1e-6; % Tolerance threshold for zeroing small values
z(abs(z) < tol) = 0;
phase = angle(z);

% Plot the original Signal
figure;
subplot(3, 1, 1);
plot(t, x, 'b');
xlabel('Time (s)');
ylabel('|y|');
title('Original Messge Signal');
grid on;

% Plot the magnitude of the Fourier Transform
subplot(3, 1, 2);
stem(f, abs(z), 'b');
xlabel('Frequency (Hz)');
ylabel('|y|');
title('Magnitude of the Fourier Transform');
grid on;

% Plot the phase of the Fourier Transform
subplot(3, 1, 3);
stem(f, phase / pi, 'b');
xlabel('Frequency (Hz)');
ylabel('Phase (radians)');
title('Phase of the Fourier Transform');
grid on;
web('https://www.salimwireless.com/search?q=fourier%20transform', '-browser');


Output 


 

 

 

Copy the MATLAB Code above from here

 

Another MATLAB Code

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

z(abs(z) < 1e-6) = 0;
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;

web('https://www.salimwireless.com/search?q=fourier%20transform', '-browser');


 

Output 







Copy the MATLAB Code above from here

 

Why use fftshift? In MATLAB, the fft function returns the DC component at the beginning of the array. To visualize a standard double-sided spectrum where 0 Hz is in the center, we use fftshift. This is essential for analyzing signal symmetry in wireless communications and signal processing.

Handling Phase Noise: Notice the tol = 1e-6 line. This is a pro-tip! We zero out very small magnitude values before calculating the phase to avoid "random" phase noise caused by floating-point errors.

Real-World Applications of FFT in MATLAB

  • Wireless Communications: Used in OFDM (5G/Wi-Fi) to split data across multiple sub-carriers.
  • Audio Engineering: Analyzing frequency response for noise cancellation and equalization.
  • Medical Imaging: Processing MRI and Ultrasound data using Fast Fourier Transforms.
  • Radar Systems: Determining the velocity of objects via Doppler shift analysis.
Return to Fourier Transform Main Page →


Interactive Online Simulators

Frequently Asked Questions

Q: Why is my magnitude plot showing peaks at the wrong frequency?
A: Ensure your sampling frequency (fs) is at least twice the highest frequency of your signal (Nyquist Theorem).

Q: How do I increase frequency resolution?
A: Increase the number of samples (N) or the time duration of your signal vector.


Further Reading

  1. Fourier Transform of Sine or Cosine
  2. Definition of the Fourier Series
  3. Continuous and Discrete Time Fourier Transform
  4. Cooley-Tukey algorithm for Fast Fourier Transform (FFT) in MATLAB
  5. Fourier Spectral Analysis
  6. Power Spectral Density Calculation Using FFT in MATLAB
  7. Autocorrelation and Periodicity of a Signal


Power Spectral Density (PSD)

Analyzing Signal Power in the Frequency Domain

In fading channels, **Power Spectral Density (PSD)** is critical because it describes how the power of your signal (or noise) is distributed across frequencies. Unlike a standard Fourier Magnitude, PSD provides a normalized view of power relative to the sampling rate.

Calculation Steps:

  1. Compute the FFT of the signal \(x(t)\).
  2. Calculate the Absolute Magnitude.
  3. Square the magnitude to get the Power Spectrum.
  4. Divide by \((fs \cdot N)\) to find the Density.

The Mathematical Model

\[ PSD = \frac{|FFT(x)|^2}{fs \cdot N} \]
\(fs\): Sampling Frequency
(Determines frequency range)
\(N\): Total Samples
(Determines resolution)
Frequency Resolution (\(\Delta f\)):
\[ \Delta f = \frac{fs}{N} \]

Note: Increasing \(N\) improves frequency resolution, while increasing \(fs\) expands the frequency range (Nyquist limit).

Read More & Access Interactive PSD Simulator
📊 MATLAB & ONLINE SIMULATIONS (Web-Based)
🎓 GATE & UGC - NET SOLUTIONS
📡 WIRELESS & SIGNAL PROCESSING


Contact Us

Name

Email *

Message *

Popular Posts

Hybrid Beamforming | Page 1

Beamforming Techniques Hybrid Beamforming... Page 1 | Page 2 | Hybrid Beamforming: Hybrid beam formation was developed to address some of the limitations of digital pre-coding approaches. Every antenna element is connected to an RF chain in digital pre-coding (beam forming) method. We also know that each RF chain is in charge of providing a separate data stream between the transmitter and the receiver. We know that a larger number of independent data streams leads to higher data rates. It has a spatial multiplexing feature for MIMO. As a result, we may assume that switching from MIMO to massive MIMO will benefit us more in terms of spatial multiplexing in massive MIMO, where each antenna is coupled to a single RF chain. We'll proceed with a definition of hybrid beam forming. Overview of hybrid beam forming with example: Unlike digital beam forming, more than one antenna element is connected to a single RF chain in hybr...
Read more

UGC NET Electronic Science Previous Year Question Papers with Solutions

Home / Engineering & Other Exams / UGC NET 2026 PYQ ⬇️ Download Papers and Solutions 📋 Exam Pattern 💡 Preparation Tips ❓ FAQs 📊 Exam Highlights: Electronic Science (88) Feature Details Junior Research Fellowship (JRF) ₹37,000 + HRA per month Eligibility M.Sc/M.Tech in Electronics (55%) Validity of Certificate JRF (3 Years) | Lectureship (Lifetime) 📥 Download UGC NET Electronics PDFs Complete collection of previous year question papers, answer keys and explanations for Subject Code 88. Start Downloading 📂 View All Question Papers June 2025 - Question Paper Download PDF June 2025 - Solved Paper + Explanation ...
Read more

MATLAB Code for Rms Delay Spread

RMS delay spread is crucial when you need to know how much the signal is dispersed in time due to multipath propagation, the spread (variance) around the average. In high-data-rate systems like LTE, 5G, or Wi-Fi, even small time dispersions can cause ISI. RMS delay spread is directly related to the amount of ISI in such systems. RMS Delay Spread [↗] Delay Spread Calculator Enter delays (ns) separated by commas: Enter powers (dB) separated by commas: Calculate   The above calculator Converts Power to Linear Scale: It correctly converts the power values from decibels (dB) to a linear scale. Calculates Mean Delay: It accurately computes the mean excess delay, which is the first moment of the power delay profile. Calculates RMS Delay Spread: It correctly calculates the RMS delay spread, defined as the square root of the second central moment of the power delay profile.   MATLAB Code  clc...
Read more

Comparisons among ASK, PSK, and FSK (with MATLAB + Simulator)

Modulation ASK, FSK & PSK Constellation MATLAB Simulink MATLAB Code Comparisons among ASK, PSK, and FSK 📘 Comparisons among ASK, FSK, and PSK 🧮 Online Simulator Bandwidth 🧮 MATLAB Code BER Analysis 📚 Further Reading 📂 View Other Topics on Comparisons among ASK, PSK, and FSK ... 🧮 Comparisons of Noise Sensitivity, Bandwidth, Complexity, etc. 🧮 MATLAB Code for Constellation Diagrams of ASK, FSK, and PSK 🧮 Online Simulator for ASK, FSK, and PSK Generation 🧮 Online Simulator for ASK, FSK, and PSK Constellation 🧮 Some Questions and Answers Comparisons among ASK, PSK, and FSK Comparison among ASK, FSK, and PSK Parameters ASK FSK PSK Variable Characteristics Amplitude ...
Read more

Advanced M-ary Modulation Simulator: Constellation, min dist, Efficiency, SER, EVM (RMS)

Advanced M-ary Communication Lab Analytical & Statistical Performance of Digital Modulation Theoretical Probability of Error (\(P_s\)) \[ P_s = Q\left(\sqrt{\frac{2 E_b}{N_0}}\right) \] Modulation (M-ary) BPSK (M=2) QPSK (M=4) 8-PSK (M=8) 16-QAM (M=16) 64-QAM (M=64) 256-QAM (M=256) SNR (\(E_b/N_0\)): 12 dB Efficiency 2 bps/Hz Min Dist (\(d_{min}\)) 1.41 Symbol Error 1.2e-5 EVM (RMS) 0.0% Constellation Diagram Noise PDF & Decision Tail 1. Geometric Mapping ...
Read more

Channel Impulse Response (CIR) (with MATLAB + Simulator)

📘 Overview & Theory 📘 How CIR Affects the Signal 🧮 Online Channel Impulse Response Simulator 🧮 MATLAB Codes 📚 Further Reading What is the Channel Impulse Response (CIR)? 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. 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. Fig: Dirac Delta Function The result of this calculation is that all frequencies are responded to equally by δ(t) . This is crucial since we never know which frequenci...
Read more

MATLAB Code for 8-PSK, 16-PSK, ...

📘 Overview & Theory 🧮 MATLAB Code for BPSK, QPSK, 8-PSK, 16-PSK, 32-PSK 🧮 Simulator for m-ary PSK 📚 Further Reading   MATLAB Code for BPSK, QPSK, 8-PSK, 16-PSK, 32-PSK clc; clear all; close all; rng(10) M = 8; % M = 2, 4, 8, 16, 32, etc. N_Bits = 2520; Phase = 0; data_info_bit = randi([0,1],N_Bits,1); data_temp = bi2de(reshape(data_info_bit,N_Bits/log2(M),log2(M))); modData = pskmod(data_temp,M,Phase); figure(1); scatterplot(modData); channelAWGN = 15; rxData2 = awgn(modData, channelAWGN); figure(2); scatterplot(rxData2); demodData = pskdemod(rxData2,M,Phase);   for BPSK, Constellation Size, M = 2 for QPSK, M = 4 for 8-PSK, M = 8, and so on    Output Figure: 8-PSK Modulation Figure: 8-PSK Demodulation after adding AWGN Noise Using the above MATLAB code you'll able be to modulate and demodulate 2-PSK, 4-PSK, 8-PSK, 16-PSK, 32-PSK and so on.  16-PSK   Fig: 16-PSK In this above code ' M ' is the number of the conste...
Read more