Skip to main content

Calculation of SNR from FFT bins in MATLAB


📘Overview 💻FFT Bin Method 💻Kaiser Window 📚Further Reading

SNR Estimation Overview

In digital signal processing, estimating the Signal-to-Noise Ratio (SNR) accurately is crucial. Below, we demonstrate how to calculate SNR from periodogram and FFT bins using the Kaiser Window. The beta (β) parameter is the key—it allows you to control the trade-off between main-lobe width and side-lobe levels for precise spectral analysis.

1 Define Sampling rate and Time vector
2 Compute FFT and Periodogram PSD
3 Identify Signal Bin and Frequency resolution
4 Segment Signal Power from Noise floor
5 Logarithmic calculation of SNR in dB

Method 1: Estimation from FFT Bins

This approach uses a Hamming window to estimate SNR directly from the spectral bins.

MATLAB Source Code 
clc; clear; close all;
% Parameters
fs = 8000; f_tone = 1000; N = 8192; 
t = (0:N-1)/fs;

% Generate signal + noise
signal = sin(2*pi*f_tone*t);
SNR_true_dB = 20; 
signal_power = mean(signal.^2);
noise_power = signal_power / (10^(SNR_true_dB/10));
noisy_signal = signal + sqrt(noise_power) * randn(1, N);

% Apply window
w = hamming(N)';
windowed_signal = noisy_signal .* w;
U = sum(w.^2)/N; 

% FFT and PSD
X = fft(windowed_signal);
f = (0:N-1)*fs/N;
Pxx = abs(X).^2 / (fs * N * U); 

% Find signal bin
[~, signal_bin] = min(abs(f - f_tone));
signal_bins = signal_bin-1 : signal_bin+1;
signal_power_est = sum(Pxx(signal_bins));

% Noise estimation
noise_bins = setdiff(1:N/2, signal_bins); 
noise_power_est = sum(Pxx(noise_bins));

% Estimate SNR
SNR_est_dB = 10 * log10(signal_power_est / noise_power_est);
fprintf('Estimated SNR from FFT: %.2f dB\n', SNR_est_dB);

Method 2: Using Kaiser Window

Optimized spectral estimation using the Kaiser window (Beta=38) for better side-lobe suppression.

MATLAB Source Code 
clc; clear; close all;
fs = 32000;
t = 0:1/fs:1-1/fs;
x = sin(2*pi*3000*t) + 0.05*randn(size(t)); % Example Signal

N = length(x);
w = kaiser(N, 38);
[Pxx, F] = periodogram(x, w, N, fs);

% SNR Estimation
freq_resolution = abs(F(2)-F(1));
[~, target_idx] = min(abs(F - 3000)); % Find 3kHz index

% Signal Power (using bins around peak)
sig_idx = target_idx-2 : target_idx+2;
Sig_power_val = sum(Pxx(sig_idx)) * freq_resolution;
Sig_power_dB = 10*log10(Sig_power_val);

% Noise Power (excluding signal)
Noise_Pxx = Pxx;
Noise_Pxx(sig_idx) = 0; 
N_avg = sum(Noise_Pxx) / (length(Pxx) - length(sig_idx));
N_power_dB = 10*log10(N_avg * fs/2);

SNR = Sig_power_dB - N_power_dB;
fprintf('SNR = %.4f dB\n', SNR);
BER vs SNR Main Page >
Fourier Transform Main Page >
Online Signal Processing Simulations Main Page >

Power Spectral Density Calculation Using FFT

Power Spectral Density (PSD) is a fundamental metric used to characterize how the power of a signal is distributed across the frequency spectrum. While a standard Fourier Transform provides the amplitude and phase of frequency components, the PSD focuses on the intensity of power, making it an essential tool for analyzing noise, stochastic processes, and signal-to-noise ratios in communication systems.

Mathematical Logic

PSD = |FFT|2 / (fs · N)

The calculation follows a strict sequence:

  • Compute the FFT of the time-domain signal.
  • Take the Absolute Magnitude.
  • Square the magnitude to find raw power.
  • Normalize by sampling rate and sample count.

Frequency Resolution (Δf)

Δf = fs / N

fs (Sampling Frequency): Higher rates increase the total range but require more samples to maintain resolution.

N (Sample Count): Increasing N provides finer frequency "bins," allowing for higher precision in identifying signal peaks.

Core Principles of Spectral Estimation

Understanding PSD requires balancing the trade-offs between frequency range and clarity:

  1. 1
    Amplitude vs. Power: Fourier Magnitude represents the "strength" of a frequency, whereas PSD represents its energy density. Squaring the magnitude is what shifts the analysis from voltage/amplitude levels to power levels.
  2. 2
    Nyquist Limits: The sampling frequency (fs) dictates the maximum detectable frequency. To avoid aliasing, the PSD can only accurately describe components up to fs / 2.
  3. 3
    Statistical Reliability: In real-world applications, raw PSD calculations (periodograms) can be "noisy." Techniques like Welch's Method or Bartlett's Method improve accuracy by averaging multiple segments of the signal to smooth out random fluctuations.

Why PSD is Crucial

PSD is the primary tool for identifying hidden periodicities in noisy data. By observing the "floor" of a PSD plot, engineers can determine the Noise Power, while the "peaks" reveal the presence of dominant signals, enabling the calculation of the Signal-to-Noise Ratio (SNR).

Read More: about Power Spectral Density Calculation Using FFT (in MATLAB)

📊 MATLAB & ONLINE SIMULATIONS (Web-Based)
🎓 GATE & UGC - NET SOLUTIONS
📡 WIRELESS & SIGNAL PROCESSING


Contact Us

Name

Email *

Message *

Popular Posts

MIMO Channel Matrix | Rank and Condition Number

MIMO / Massive MIMO MIMO Channel Matrix | Rank and Condition...   The channel matrix in wireless communication is a matrix that describes the impact of the channel on the transmitted signal. The channel matrix can be used to model the effects of the atmospheric or underwater environment on the signal, such as the absorption, reflection or scattering of the signal by surrounding objects. When addressing multi-antenna communication, the term "channel matrix" is used. Let's assume that only one TX and one RX are in communication and there's no surrounding object. Here, in our case, we can apply the proper threshold condition to a received signal and get the original transmitted signal at the RX side. However, in real-world situations, we see signal path blockage, reflections, etc.,  (NLOS paths [↗]) more frequently. The obstruction is typically caused by building walls, etc. Multi-antenna communication was introduced to address this issue. It makes diversity app...
Read more

BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...(MATLAB Code + Simulator)

Bit Error Rate (BER) & SNR Guide Analyze communication system performance with our interactive simulators and MATLAB tools. 📘 Theory 🧮 Simulators 💻 MATLAB Code 📚 Resources BER Definition SNR Formula BER Calculator MATLAB Comparison 📂 Explore M-ary QAM, PSK, and QPSK Topics ▼ 🧮 Constellation Simulator: M-ary QAM 🧮 Constellation Simulator: M-ary PSK 🧮 BER calculation for ASK, FSK, and PSK 🧮 Approaches to BER vs SNR Calculation What is Bit Error Rate (BER)? The BER indicates how many corrupted bits are received compared to the total number of bits sent. It is the primary figur...
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

How to Mount Google Drive in Google Colab

How to Mount Google Drive in Google Colab Google Colab provides temporary storage during a session. Any files stored in the /content directory will be deleted when the runtime disconnects. To store datasets, trained models, and results permanently, it is recommended to mount your Google Drive in Colab. Mounting Google Drive allows your notebook to access files directly from your Drive and save outputs there so they remain available even after the Colab session ends. Step 1: Import the Drive Module First import the Google Colab drive module. from google.colab import drive Step 2: Mount Google Drive Run the following command to mount your Google Drive. from google.colab import drive drive.mount('/content/drive') After running the command: A link will appear in the output. Click the link and log in to your Google account. Copy the authentication code provided. Paste the code back into the notebook. Or, a Google authentication page will a...
Read more

Constellation Diagrams of ASK, PSK, and FSK (with MATLAB Code + Simulator)

Constellation Diagrams: ASK, FSK, and PSK Comprehensive guide to signal space representation, including interactive simulators and MATLAB implementations. 📘 Overview 🧮 Simulator ⚖️ Theory 📈 Q-function 📚 Resources BASK Modulation Transmits one of two signals: 0 or $\sqrt{E_b}$, representing binary 0 and 1. Simple but sensitive to noise. BFSK Modulation Transmits one of two signals: $\sqrt{E_b}$ on the Y-axis or $\sqrt{E_b}$ on the X-axis. These are orthogonal signals. BPSK Modulation Transmits $+\sqrt{E_b}$ or $-\sqrt{E_b}$ (antipodal signaling). Most efficient binary scheme. ...
Read more

Wiener Filter in MATLAB

  MATLAB Code  % Wiener Filter Based on Wiener-Hopf Equation % This script demonstrates how to apply the Wiener filter to recover % a reference signal from a noisy signal using the Wiener-Hopf equation. % The filter minimizes the mean squared error between the noisy signal and the reference signal. clear; close all; clc; % Signal Parameters fs = 4000; % Sampling frequency (Hz) T = 1; % Total recording time (seconds) L = T * fs; % Signal length (samples) tt = (0:L-1) / fs; % Time vector ff = (0:L-1) * fs / L; % Frequency vector % Generate Reference Signal (a sinusoid) y = sin(2 * pi * 120 * tt); % Reference sinusoidal signal y = y(:); % Ensure column vector % Create Noisy Signal by Adding Gaussian Noise x = 0.50 * randn(L, 1) + y; % Noisy signal x = x(:); % Ensure column vector % Define Filter Order (Number of Coefficients) N = 200; % Apply Wiener Filter using custom function [xest, b, MSE] = wienerFilt(x, y, N); % Plot Results figure; subplot(411); plot(tt, x, 'k'), hold on, p...
Read more

Overmodulation & Distortion in AM

Overmodulation in AM and How It Causes Distortion 1. AM Signal Equation s(t) = A c [1 + μ m(t)] cos(2Ï€ f c t) A c = carrier amplitude m(t) = normalized modulating signal (|m(t)| ≤ 1) μ = modulation index 2. Modulation Index μ = A m / A c - Normal AM: 0 < μ ≤ 1 → no distortion - Overmodulation: μ > 1 → distortion occurs 3. Envelope and Overmodulation A(t) = A c [1 + μ m(t)] - For undistorted AM: 1 + μ m(t) ≥ 0 at all times - If μ > 1: 1 + μ m(t) < 0 at negative peaks → carrier flips Example: Let m(t) = cos(2Ï€ f m t), A c = 1 V, μ = 1.2 Minimum envelope: A min = A c [1 - 1.2] = -0.2 V Negative amplitude → envelope crosses zero → 180° phase flip 4. Mathematical Consequence -A c cos(θ) = A c cos(θ + Ï€) This phase reversal is what causes distortion in the demodulated signal. 5. Instantaneous AM Signal s...
Read more

Spectral Estimation Methods - Periodogram, Correlogram, Welch, Bartlett ...

Comparison of Periodogram Techniques Overview of spectral estimation methods and their characteristics. Periodogram Fast but high variance. Take the raw time-domain signal x[n]x[n] of length NN. Optionally apply a window (e.g., Hann, Hamming) to reduce spectral leakage. Compute the DFT or FFT of the (optionally windowed) signal. Estimate the power spectral density (PSD) from the squared magnitude of the FFT. Welch’s Method Averaged periodogram with reduced variance. Divide the signal into overlapping segments. Apply a window function to each segment. Compute the FFT and PSD of each windowed segment. Average the PSDs across all segments. Correlogram ...
Read more