2019-12-02 15:47:40 +01:00
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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2020-11-12 10:21:37 +01:00
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addpath('./mat/');
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2019-12-02 15:47:40 +01:00
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% Time Domain Signal
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% Let's first define the number of sample and the sampling time.
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N = 10000; % Number of Sample
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dt = 0.001; % Sampling Time [s]
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t = dt*(0:1:N-1)'; % Time vector [s]
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% We generate of signal that consist of:
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% - a white noise with an RMS value equal to =anoi=
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% - two sinusoidal signals
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% The parameters are defined below.
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asig = 0.1; % Amplitude of the signal [V]
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fsig = 10; % Frequency of the signal [Hz]
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ahar = 0.5; % Amplitude of the harmonic [V]
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fhar = 50; % Frequency of the harmonic [Hz]
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anoi = 1e-3; % RMS value of the noise
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% The signal $x$ is generated with the following code and is shown in figure [[fig:time_domain_x_zoom]].
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x = anoi*randn(N, 1) + asig*sin((2*pi*fsig)*t) + ahar*sin((2*pi*fhar)*t);
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figure;
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plot(t, x);
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xlabel('Time [s]');
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ylabel('Amplitude');
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xlim([0, 1]);
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% Estimation of the magnitude of a deterministic signal
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% Let's compute the PSD of the signal using the =blackmanharris= window.
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nx = length(x);
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na = 8;
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win = blackmanharris(floor(nx/na));
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[pxx, f] = pwelch(x, win, 0, [], 1/dt);
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% Normalization of the PSD.
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CG = sum(win)/(nx/na);
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NG = sum(win.^2)/(nx/na);
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fbin = f(2) - f(1);
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pxx_norm = pxx*(NG*fbin/CG^2);
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% We determine the frequency bins corresponding to the frequency of the signals.
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isig = round(fsig/fbin)+1;
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ihar = round(fhar/fbin)+1;
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% The theoretical RMS value of the signal is:
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srmt = asig/sqrt(2); % Theoretical value of signal magnitude
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% And we estimate the RMS value of the signal by either integrating the PSD around the frequency of the signal or by just taking the maximum value.
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srms = sqrt(sum(pxx(isig-5:isig+5)*fbin)); % Signal spectrum integrated
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srmsp = sqrt(pxx_norm(isig) * NG*fbin/CG^2); % Maximum read off spectrum
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% Estimation of the noise level
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% The noise level can also be computed using the integration method.
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% The theoretical RMS noise value is.
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nth = anoi/sqrt(max(f)) % Theoretical value [V/sqrt(Hz)]
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% We can estimate this RMS value by integrating the PSD at frequencies where the power of the noise signal is above the power of the other signals.
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navg = sqrt(mean(pxx_norm([ihar+10:end]))) % pwelch output averaged
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