Discrete Power Spectral Density
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<pre> | <pre> | ||
| - | %Demonstrate receding noise floor in digital domain for fixed analog power spectral density | + | %Demonstrate receding noise floor in digital domain for fixed analog power spectral density. |
| + | %For COA paper. powerSpectralDensity.m | ||
clearvars; clc; close all | clearvars; clc; close all | ||
disp('This script demonstrates how thermal noise spectral level') | disp('This script demonstrates how thermal noise spectral level') | ||
| Line 8: | Line 9: | ||
k = 1.380649e-23; % Boltzmann constant [J/K] | k = 1.380649e-23; % Boltzmann constant [J/K] | ||
T_R = 300; % Resistor Temperature 300°K roughly equivalent to 27°C | T_R = 300; % Resistor Temperature 300°K roughly equivalent to 27°C | ||
| - | Vn_rms = sqrt(4 * k * T_R * R * | + | Vn_rms = sqrt(4 * k * T_R * R * 22400); % RMS thermal noise voltage from one-sided spectrum |
% Record lengths | % Record lengths | ||
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['Avg Spectral Level: ', num2str(Avg_Spectral_Level(i),'%4.0f'), 'dB' ... | ['Avg Spectral Level: ', num2str(Avg_Spectral_Level(i),'%4.0f'), 'dB' ... | ||
', Absolute Noise Level: ', num2str(Noise_Level(i), '%4.0f'), 'dB' ... | ', Absolute Noise Level: ', num2str(Noise_Level(i), '%4.0f'), 'dB' ... | ||
| - | ', N: ', num2str(N)]); | + | ', N: ', num2str(N/1000), 'k']); |
end | end | ||
% Labels & legend | % Labels & legend | ||
xlabel('Frequency [Hz]'); | xlabel('Frequency [Hz]'); | ||
| - | ylabel('Discrete Power Spectral Density [ | + | ylabel('1k\Omega Discrete Power Spectral Density [dBFS]'); |
title ('Thermal Noise Spectral Density for Decade Record Lengths'); | title ('Thermal Noise Spectral Density for Decade Record Lengths'); | ||
| - | legend('show', 'Location', 'southwest'); | + | % Create legend and retrieve its icon handles |
| + | [lgd,icons] = legend('show','Location','southwest'); | ||
| + | % icons is an array―lines for curves, patches for fills, etc. | ||
| + | % Thicken only the line icons; leave markers and patches alone | ||
| + | for ii = 1:numel(icons) | ||
| + | if strcmp(icons(ii).Type,'line') % icon is a line sample | ||
| + | icons(ii).LineWidth = 2.5; % make it thicker | ||
| + | end | ||
| + | end | ||
| + | lgd.Units = 'normalized'; % figure-relative coordinates | ||
| + | lgd.Position = [0.4275 0.18 0.18 0.12]; % [left bottom width height] | ||
xticks(0:9600:Fs); | xticks(0:9600:Fs); | ||
ax = gca; | ax = gca; | ||
Current revision
%Demonstrate receding noise floor in digital domain for fixed analog power spectral density.
%For COA paper. powerSpectralDensity.m
clearvars; clc; close all
disp('This script demonstrates how thermal noise spectral level')
disp('appears to fall in the frequency domain as record length increases.');
Fs = 48000; % Sample rate
R = 1000; % Resistance [Ohms]
k = 1.380649e-23; % Boltzmann constant [J/K]
T_R = 300; % Resistor Temperature 300°K roughly equivalent to 27°C
Vn_rms = sqrt(4 * k * T_R * R * 22400); % RMS thermal noise voltage from one-sided spectrum
% Record lengths
N_values = [Fs, 10*Fs, 100*Fs, 1000*Fs];
figure; hold on;
% Loop over different record lengths
for i = 1:numel(N_values)
N = N_values(i); %Number of samples for current record.
freq = Fs*(0:N-1)'/N; %frequency vector
% Generate thermal noise signal (standard Gaussian white noise)
noise = Vn_rms * randn(N, 1);
Y = fft(noise)/N; %no window
%Compute average spectral level
DFT_square = real(Y.*conj(Y));
Avg_Spectral_Level(i) = 10*log10(sum(DFT_square)/N); %Average Spectral Level recedes by 10dB at each pass.
Noise_Level(i) = 10*log10(sum(DFT_square)); %Absolute Noise Level is fixed and independent of N.
plot(freq, 10*log10( DFT_square), 'DisplayName', ...
['Avg Spectral Level: ', num2str(Avg_Spectral_Level(i),'%4.0f'), 'dB' ...
', Absolute Noise Level: ', num2str(Noise_Level(i), '%4.0f'), 'dB' ...
', N: ', num2str(N/1000), 'k']);
end
% Labels & legend
xlabel('Frequency [Hz]');
ylabel('1k\Omega Discrete Power Spectral Density [dBFS]');
title ('Thermal Noise Spectral Density for Decade Record Lengths');
% Create legend and retrieve its icon handles
[lgd,icons] = legend('show','Location','southwest');
% icons is an array―lines for curves, patches for fills, etc.
% Thicken only the line icons; leave markers and patches alone
for ii = 1:numel(icons)
if strcmp(icons(ii).Type,'line') % icon is a line sample
icons(ii).LineWidth = 2.5; % make it thicker
end
end
lgd.Units = 'normalized'; % figure-relative coordinates
lgd.Position = [0.4275 0.18 0.18 0.12]; % [left bottom width height]
xticks(0:9600:Fs);
ax = gca;
ax.XAxis.Exponent = 0; %disable scientific notation along x axis
ax.XTickLabel = arrayfun(@num2str, ax.XTick, 'UniformOutput', false);
xlim([0, Fs]);
ylim([-210,-160]);
grid on; hold off;
disp(' ')
disp('Sample rate is fixed at 48 kHz.')
disp('Record lengths are Fs, 10Fs, 100Fs, and 1000Fs.');
disp(' ')
disp(['Noise level w.r.t unit amplitude sinusoid: ' num2str(20*log10(10^(Noise_Level(i)/20)/(1/sqrt(2))),'%4.0f') 'dB'])