When I adjusted the hanning window's 'symmetric' and 'periodic' parameters I got very different SNR results.

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昕毅 2023-3-10

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https://ww2.mathworks.cn/matlabcentral/answers/1926260-when-i-adjusted-the-hanning-window-s-symmetric-and-periodic-parameters-i-got-very-different-snr

评论：昕毅 2023-3-10

When I calculate sinusoidal signal to noise ratio, I add the hanning window. But when I adjusted the hanning window's 'symmetric' and 'periodic' parameters I got very different results.

When I set default or 'symmetric', SNR of the signal will be far less than when I set 'periodic'

Result of 'symmetric':

SNR of 1 signal: 126.739348

SNR of 2 signal: 114.118917

SNR of 3 signal: 102.379880

Result of 'periodic':

SNR of 1 signal: 270.135232

SNR of 2 signal: 114.363203

SNR of 3 signal: 114.463044

But the quantized signal will not be affected.

Futhermore, the length of signal will also affect SNR results? Why this wwll happen? Here are my code:

clear;
clc;
fig_num = 0;
% Generate sin signal.
Fs = 192e3;                                             % Sample frequency.(Hz)
OSR = 16;                                               % Oversample ratio.
Fs_OSR = Fs * OSR;
F0 = 1e3;                                               % Sin signal frequency.(Hz)
Amp = 0.9;                                              % Sin signal amplitude.
duration = 3e-1;                                        % Sin signal duration time.(s)
N_OSR = duration*Fs_OSR;                                % Sin signal sample number.
t_OSR = (0:1/Fs_OSR:(N_OSR-1)/Fs_OSR)';                 % Sin signal sample points.
signal_OSR = Amp * sin(2*pi*F0*t_OSR);                  % Generate sin signal.
fig_num = fig_num + 1;
plot_signal(signal_OSR, Fs_OSR, F0, fig_num)
% Define bit width and fractional bits
bit_width = 16;                                         % Total number of bits
frac_bits = bit_width - 1;                              % Number of fractional bits
% Generate quantized signal.
mode = 'fixed';
round_mode = 'ceil';
overflow_mode = 'saturate';
format = [bit_width, frac_bits];
q_obj = quantizer(mode, round_mode, overflow_mode, format);
signal_OSR_quantized = quantize(q_obj, signal_OSR);
fig_num = fig_num + 1;
plot_signal(signal_OSR_quantized, Fs_OSR, F0, fig_num)
% Generate CIC signal.
cicDecim = dsp.CICDecimator('DecimationFactor', OSR);
signal_cicDecim_quantized = cicDecim(signal_OSR_quantized);
scale_factor = max(signal_OSR_quantized)/max(signal_cicDecim_quantized);
signal_cicDecim_quantized = signal_cicDecim_quantized * scale_factor;
fig_num = fig_num + 1;
plot_signal(signal_cicDecim_quantized, Fs, F0, fig_num)
Fin_bin = F0 * length(signal_cicDecim_quantized) / Fs;
function plot_signal(signal, Fs, F0, fig_num)
    N = length(signal);
    f0_normalization = F0 * N / Fs;
    f_x_axis = Fs*(0:fix(N/2)-1)/N;
    window = hanning(N, 'periodic');
    signal = signal .* window;
    signal_spectrum_hanning = abs(fft(signal)/N) * 2;
    signal_spectrum_hanning = signal_spectrum_hanning(1:fix(N/2));
    
    near_point = 1;
    f_cut = 20e3;
    cut_index = f_cut * N / Fs;
    % cut_index = fix(N/2);
    all_index = 1 + (0:cut_index-1);
    signal_index = 1 + (f0_normalization + (-near_point:near_point));
    DC_index = 1 + (0:near_point);
    noise_index = setdiff(setdiff(all_index, signal_index),DC_index);
    SNR = 10*log10(sum(signal_spectrum_hanning(signal_index).^2) / ...
                   sum(signal_spectrum_hanning(noise_index).^2));
    fprintf('SNR of %d signal: %f\n', fig_num, SNR);
    figure(fig_num);
    subplot(2,1,1)
    plot(signal);grid
    title_str = ['The ', num2str(fig_num), ' Signal'];
    title(title_str);
    xlabel('Sample points');
    ylabel('Amplitude');
    subplot(2,1,2)
    semilogx(f_x_axis, 20*log10(signal_spectrum_hanning.^2));grid
    xlabel('Frequence (Hz)');
    ylabel('Amplitude');
end

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昕毅 2023-3-10

Because I think of SINAD as SNR(treat THD as noise), I compare my SNR caculation with built-in SINAD. When I set hanning 'periodic' and the cut-off frequency is half of the sampling frequency rather than a custom value(by changing cut_index), I got a similar answer.

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