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Calculation of SNR from FFT bins in MATLAB


 

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 in the frequency domain. For that you should know the sampling rate of the signal. 

The Kaiser window is a type of window function commonly used in signal processing, particularly for designing finite impulse response (FIR) filters and performing spectral analysis. It is a general-purpose window that allows for control over the trade-off between the main lobe width (frequency resolution) and side lobe levels (suppression of spectral leakage). The Kaiser window is defined using a modified Bessel function of the first kind.

 

 Steps

  1. Set up the sampling rate and time vector
  2. Compute the FFT and periodogram
  3. Plot the periodogram using FFT
  4. Specify parameters for Kaiser window and periodogram
  5. Calculate the frequency resolution and signal power
  6. Exclude the signal power from noise calculation
  7. Compute the noise power
  8. Calculate the SNR
 

MATLAB Code for Estimation of SNR from FFT bins of a Noisy Signal

clc;
clear;
close all;

% Parameters
fs = 8000; % Sampling frequency (Hz)
f_tone = 1000; % Tone frequency (Hz)
N = 8192; % Use large N so 1000 Hz aligns with an FFT bin
t = (0:N-1)/fs; % Time vector

% Generate 1 kHz sine wave
signal = sin(2*pi*f_tone*t);

% Add white Gaussian noise
SNR_true_dB = 20; % Desired true SNR in dB
signal_power = mean(signal.^2);
noise_power = signal_power / (10^(SNR_true_dB/10));
noise = sqrt(noise_power) * randn(1, N);
noisy_signal = signal + noise;

% Apply window to reduce leakage
w = hamming(N)';
windowed_signal = noisy_signal .* w;
U = sum(w.^2)/N; % Window power normalization factor

% FFT
X = fft(windowed_signal);
f = (0:N-1)*fs/N;

% Power spectrum
Pxx = abs(X).^2 / (fs * N * U); % Proper normalization for PSD

% Find signal bin (closest to 1 kHz)
[~, signal_bin] = min(abs(f - f_tone));

% Estimate signal power from ±1 bins around 1 kHz
signal_bins = signal_bin-1 : signal_bin+1;
signal_power_est = sum(Pxx(signal_bins));

% Estimate noise power from all other bins
noise_bins = setdiff(1:N/2, signal_bins); % Use only one-sided spectrum
noise_power_est = sum(Pxx(noise_bins));

% Estimate SNR
SNR_est = signal_power_est / noise_power_est;
SNR_est_dB = 10 * log10(SNR_est);

% Print results
fprintf('True SNR: %.2f dB\n', SNR_true_dB);
fprintf('Estimated SNR from FFT: %.2f dB\n', SNR_est_dB);

% Plot
figure;
plot(f(1:N/2), 10*log10(Pxx(1:N/2)));
xlim([0 fs/2]);
xlabel('Frequency (Hz)');
ylabel('Power/Frequency (dB/Hz)');
title('Power Spectrum of Noisy Signal with Hamming Window');
grid on;

Output

True SNR: 20.00 dB
Estimated SNR from FFT: 19.77 dB
 

 
 
 
 
 
 
 

MATLAB Code for Estimation of Signal-to-Noise Ratio from Power Spectral Density Using FFT and Kaiser Window Periodogram from real signal data

clc; clear ; close all;
fs = 32000;
t = 0:1/fs:1-1/fs;

 x=load("x2.mat");
 x = x.x2;

N = length(x);
xdft = fft(x);
xdft = xdft(1:N/2+1);
psdx = (1/(fs*N)) * abs(xdft).^2;
psdx(2:end-1) = 2*psdx(2:end-1);
freq = 0:fs/length(x):fs/2;

figure; plot(freq,pow2db(psdx))
grid on
title("Periodogram Using FFT")
xlabel("Frequency (Hz)")
ylabel("Power/Frequency (dB/Hz)")

%rng default
Fi = 3000;
Fs = 32e3;
N = 1024;%2048;


w = kaiser(numel(x),38);
[Pxx, F] = periodogram(x,w,numel(x),Fs);
SNR_periodogram = snr(Pxx,F,'psd')

freq_resolution= abs(F(2)-F(3));
Signal_power= Pxx(3000); % p

s=sum((Signal_power), 1); s=s/length(Signal_power); s=abs(s);
Sig_power=pow2db(freq_resolution*s)

exclude_range = pxx(3000);
Noise_power = Pxx;
Noise_power(exclude_range) = 0; % Set the values in the specified range to zero

% Noise_power= Pxx(20001:24001); %x,y,z
n=sum((Noise_power), 1)/length(Noise_power); n=abs(n);
N_power=pow2db(freq_resolution*n)

SNR=Sig_power-N_power 

Output

 
 
 
 
 
 SNR =  25.8906 (in dB)


 

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