Discrete Power Spectral Density - Revision history

Ranjelin at 02:38, 13 August 2025

Ranjelin — Wed, 13 Aug 2025 02:38:02 GMT

←Older revision		Revision as of 02:38, 13 August 2025
Line 9:		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 * ~~Fs/2~~); % RMS thermal noise voltage	+	Vn_rms = sqrt(4 * k * T_R * R * 22400); % RMS thermal noise voltage from one-sided spectrum

	% Record lengths		% Record lengths
Line 31:		Line 31:
	['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('1k\Omega Discrete Power Spectral Density [dB]');	+	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;

Ranjelin at 20:53, 1 November 2024

Ranjelin — Fri, 01 Nov 2024 20:53:19 GMT

←Older revision		Revision as of 20:53, 1 November 2024
Line 1:		Line 1:
	<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')

Ranjelin at 00:24, 1 November 2024

Ranjelin — Fri, 01 Nov 2024 00:24:48 GMT

←Older revision		Revision as of 00:24, 1 November 2024
Line 34:		Line 34:
	% Labels & legend		% Labels & legend
	xlabel('Frequency [Hz]');		xlabel('Frequency [Hz]');
-	ylabel('1k\Omega Discrete Power Spectral Density');	+	ylabel('1k\Omega Discrete Power Spectral Density [dB]');
	title ('Thermal Noise Spectral Density for Decade Record Lengths');		title ('Thermal Noise Spectral Density for Decade Record Lengths');
	legend('show', 'Location', 'southwest');		legend('show', 'Location', 'southwest');

Ranjelin at 06:35, 31 October 2024

Ranjelin — Thu, 31 Oct 2024 06:35:27 GMT

←Older revision		Revision as of 06:35, 31 October 2024
Line 34:		Line 34:
	% Labels & legend		% Labels & legend
	xlabel('Frequency [Hz]');		xlabel('Frequency [Hz]');
-	ylabel('1k\Omega Discrete Power Spectral Density ~~[dB/Hz]~~');	+	ylabel('1k\Omega Discrete Power Spectral Density');
	title ('Thermal Noise Spectral Density for Decade Record Lengths');		title ('Thermal Noise Spectral Density for Decade Record Lengths');
	legend('show', 'Location', 'southwest');		legend('show', 'Location', 'southwest');

Ranjelin at 02:10, 25 August 2024

Ranjelin — Sun, 25 Aug 2024 02:10:56 GMT

←Older revision		Revision as of 02:10, 25 August 2024
Line 34:		Line 34:
	% Labels & legend		% Labels & legend
	xlabel('Frequency [Hz]');		xlabel('Frequency [Hz]');
-	ylabel('Discrete Power Spectral Density [dB/Hz]');	+	ylabel('1k\Omega Discrete Power Spectral Density [dB/Hz]');
	title ('Thermal Noise Spectral Density for Decade Record Lengths');		title ('Thermal Noise Spectral Density for Decade Record Lengths');
	legend('show', 'Location', 'southwest');		legend('show', 'Location', 'southwest');

Ranjelin at 00:14, 25 August 2024

Ranjelin — Sun, 25 Aug 2024 00:14:06 GMT

←Older revision		Revision as of 00:14, 25 August 2024
Line 5:		Line 5:
	disp('appears to fall in the frequency domain as record length increases.');		disp('appears to fall in the frequency domain as record length increases.');
	Fs = 48000; % Sample rate		Fs = 48000; % Sample rate
-	R = 1000; % Resistance (Ohms)	+	R = 1000; % Resistance [Ohms]
-	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 * Fs/2); % RMS thermal noise voltage		Vn_rms = sqrt(4 * k * T_R * R * Fs/2); % RMS thermal noise voltage
Line 50:		Line 50:
	disp(' ')		disp(' ')
	disp(['Noise level w.r.t unit amplitude sinusoid: ' num2str(20*log10(10^(Noise_Level(i)/20)/(1/sqrt(2))),'%4.0f') 'dB'])		disp(['Noise level w.r.t unit amplitude sinusoid: ' num2str(20*log10(10^(Noise_Level(i)/20)/(1/sqrt(2))),'%4.0f') 'dB'])
-
	</pre>		</pre>

Ranjelin: New page:

 %Demonstrate receding noise floor in digital domain for fixed analog power spectral density clearvars; clc; close all disp('This script demonstrates how thermal noise spectral level'...

Ranjelin — Sun, 25 Aug 2024 00:12:14 GMT

New page: <pre> %Demonstrate receding noise floor in digital domain for fixed analog power spectral density clearvars; clc; close all disp('This script demonstrates how thermal noise spectral level'...

New page

<pre>
%Demonstrate receding noise floor in digital domain for fixed analog power spectral density
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 * Fs/2); % RMS thermal noise voltage

% 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)]);
end
% Labels & legend
xlabel('Frequency [Hz]');
ylabel('Discrete Power Spectral Density [dB/Hz]');
title ('Thermal Noise Spectral Density for Decade Record Lengths');
legend('show', 'Location', 'southwest');
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'])

</pre>