Calculation of SNR from FFT bins in MATLAB

• 📘 Overview
• 🧮 MATLAB Code for Estimation of SNR from FFT bins
• 🧮 MATLAB Code for SNR from PSD using Kaiser Window
• 📚 Further Reading

Here, you can find the SNR of a received signal from periodogram / FFT bins using the Kaiser operator. The beta (β) parameter characterizes the Kaiser window, which controls the trade-off between the main lobe width and the side lobe level.

Steps

1. Set up the sampling rate and time vector
2. Compute the FFT and periodogram
3. Calculate the frequency resolution and signal power
4. Exclude the signal power from noise calculation
5. Compute the noise power and SNR

MATLAB Code for Estimation of SNR from FFT bins

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);

MATLAB Code for SNR from PSD using Kaiser Window

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);

Further Reading

• Add AWGN noise directly to PSD in MATLAB