TimeseriesFromPSD(S​xx, fs, T, plot_on)

Create one realization of a timeseries from a given double-sided PSD, Sxx
NOTE: Since we don't have phase information, the original timeseries is
not recoverable. We can, however, create a random timeseries that has the
same statistical characteristics as the original timeseries.
Steps:
Create perfect white noise by generating random phase in the frequency
domain, and then multiply it by your PSD. Then transfer it to the time
domain...Take note that MATLAB expects the conjugate symmetric part of
the spectrum to be the second half of the array.

INPUTS
Sxx - Double-sided power spectral density in the expected MATLAB
order e.g. [wavePSD_positiveFreq wavePSD_negativeFreq]

fs - Sample rate of the output timeseries [samples/sec]

T - Desired length of the output timeseries [seconds]

OUTPUTS
timeseries - Generated timeseries

time - Time vector corresponding to timeseries generated

EXAMPLE
T = 100; % Length of timeseries
fs = 25; % Sample rate of timeseries
f0 = 2; % For this example, just do a tone

% Build PSD of a single tone in this example
rmsLevel = 1; % RMS level of tone
df = 1/T;
GxxMag = ((rmsLevel^2)/df); % Single-Sided Power spectrum magnitude
SxxMag = GxxMag/2; % Double-sided Power spectrum magnitude
PSD_DoubleSided = zeros(T*fs, 1);
PSD_DoubleSided(f0*T+1) = SxxMag;
PSD_DoubleSided(end-f0*T+1) = SxxMag;

[timeseries, time] = TimeseriesFromPSD(PSD_DoubleSided, fs, T); % Run!

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Copyright Mike Rudolph, 2014
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Last modified: July 29, 2014
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