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Author: ECheynet

Documentation.mlx

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+function [t,f] = getSamplingPara(M,fs)
+%  The function getSamplingPara(M,fs) computes the time and frequency 
+% vectors based on two inputs: the sampling frequency fs and an integer M 
+% used to compute the number of time step, which is equal to 2^M.
+% 
+% Inputs:
+%   M: is a natural number used as the power of 2 and is used to compute the 
+% number of time step for the simulation.
+%   fs: Sampling frequency (Hz)
+% 
+% Outputs:
+%   t: dimensions [1 xN]: time vector (units: s)
+%   f: dimensions [1 x N/2]: frequency vector  (units: s^(-1))
+% 
+% Author: E. Cheynet - UiS - last modified : 25-08-2018 
+%% 
+if mod(M,1)~=0 || M<=0, error(' ''M'' should be a natural '); end
+N = 2^M; % number of time step
+dt = 1/fs; 
+tmax=dt.*N; 
+t = (0:N-1)*dt;
+fprintf(['Duration of target time series is ',num2str(tmax/3600,3),' hours, i.e. ',num2str(tmax,3),' sec \n\n'])
+f0 = 1/tmax;  % minimal frequency recorded
+fc = fs/2; % Nyquist freq
+f = [f0:f0:fc]; % frequency vector
+end

getSamplingPara.m

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+function [u,t] = randomProcess(f,S)
+% 
+% [u] = randomProcess(f,S) generates in the time domain a random process
+% based on a target power spectral density S, the element of which are
+% associated with the frequency vector f.
+%
+% Inputs:
+% f: double-precision array of size [1 x Nfreq] of frequency (in Hz)
+% S: double-precision array of size [1 x Nfreq] of the target PSD.
+%
+% Outputs:
+% u: double-precision array of size [N x 1] representing the random process
+% t: double-precision array of size [N x 1] representing the time
+% 
+% Author: E. Cheynet - UiB - last modified : 11-06-2020
+
+%% Definitions
+Nfreq = numel(f);
+dt = 1/(2*f(end));
+
+%% Compute the core spectral matrix A with random phases and the target PSD
+A= sqrt(S).*exp(1i*2*pi*rand(1,Nfreq));
+A = A(:);
+
+%% Apply the IFFT
+Nu = [A(1:Nfreq) ; real(A(Nfreq)); conj(flipud(A(2:Nfreq)))];
+u=real(ifft(Nu).*sqrt(Nfreq./(dt)));
+
+t = [0:numel(u)-1].*dt;
+
+end