Franklin noise-generator


The following sections gives an introduction to the generation of model noise using the noise generator implemented in LTPDA.

Franklin's noise generator

Franklin's noise generator is a method to generate arbitrarily long time series with a prescribed spectral density. The algorithm is based on the paper 'Numerical simulation of stationary and non-stationary gaussian random processes' by Franklin, Joel N. (SIAM review, Volume 7, Issue 1, page 68-80, 1956)

See Generating model noise for more general information on this.

Franklin's method does not require any 'warm up' period. It starts with a transfer function given as ratio of two polynomials.
The generator operates on a real state vector y of length n which is maintained between invocations. It produces samples of the time series in equidistant steps T = 1/fs, where fs is the sampling frequency.

r is a vector of independent normal Gaussian random numbers Tinit, E, Tprop which are real matrices and a which is a real vector are determined once by the algorithm.

Description

When an analysis object is constructed from a pole zero model Franklin's noise generator is called (compare Creating AOs from pole zero models).

Inputs

for the function call the parameter list has to contain at least:

Outputs

Usage

The analysis object constructor ao calls the following four functions when the input is a pzmodel.

First a parameter list of the input parameters is to be done. For further information on this look at Creating parameter lists from parameters.

Starting from a given pole/zero model

The parameter list should contain the number of seconds the resulting time series should have nsecs and the sampling frequency fs.
The constructor call should look like this:

f1 = 5;
f2 = 10;
f3 = 1;
gain = 1;
fs = 10;  %sampling frequency
nsecs = 100; %number of seconds to be generated
   p = [pz(f1) pz(f2)];
   z = [pz(f3)];
   pzm = pzmodel(gain, p, z);
   a = ao(pzm, plist('nsecs', nsecs, 'fs',fs)

The output will be an analysis object a containing the time series




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