Functions
end	numPoles ()

Get residues for these	final (stable) poles[r

Plot modelled vs actual data	plot (freqBins, abs(freqData),'-x')

	plot (freqBins, abs(Asim *res(:)), 'o')

Variables
	function [poles, residues, remainder, proportional]

Scale incoming frequencies	maxFreq = max(freqBins)

	freqBins = freqBins/maxFreq

	wPoleFreqs = 2pipoleFreqs

	sigma = -0.1

	sPoleFreqs = sigma + 1j*wPoleFreqs

Create vector of simulation frequencies	wFreqBins = 2pifreqBins

Turn this into a	matrix

Turn this into a with identical frequencies along the rows	s = repmat(1j*wFreqBins(:),1,numPoles)

for	ii

Extract zeros Form matrix with poles on diagonal	Az = diag(sPoleFreqs)

	Bz = ones(size(sPoleFreqs,2),1)

Get residues for these	Asim

Get residues for these	residual = getResidues(sPoleFreqs,freqData,wFreqBins)

Extract	resiudes

	r = Asim\freqDataFull

Count number of useful output variables	numVar = numPoles + 2

Extract these output variables	res = r(1:numVar)

hold	on

hold	off

Undo scaling of outgoing	residues = res(1:numVar-2,:)*maxFreq

Undo scaling of outgoing	poles = sPoleFreqs*maxFreq

	remainder = res(numVar-1,:)

	proportional = res(numVar,:)/maxFreq

Function Documentation

◆ final()

Get residues for these final ( stable )

◆ numPoles()

end numPoles ( )

virtual

Definition at line 14 of file getResidues.m.

Here is the caller graph for this function:

◆ plot() [1/2]

plot	(	freqBins	,
		abs(Asim *res(:))	,
		'o'
	)

◆ plot() [2/2]

Plot modelled vs actual data plot	(	freqBins	,
		abs(freqData)	,
		'-x'
	)

Variable Documentation

◆ Asim

Get residues for these Asim

Definition at line 51 of file findComplexRationalApproximation.m.

◆ Az

Extract zeros Form matrix with poles on diagonal Az = diag(sPoleFreqs)

Definition at line 36 of file findComplexRationalApproximation.m.

◆ Bz

Bz = ones(size(sPoleFreqs,2),1)

Definition at line 38 of file findComplexRationalApproximation.m.

◆ freqBins

freqBins = freqBins/maxFreq

Definition at line 11 of file findComplexRationalApproximation.m.

◆ function

function[poles, residues, remainder, proportional]

Initial value:

= findComplexRationalApproximation(freqBins,freqData)
% This function takes in frequency data and fits a rational approximation
% using Vector Fitting
% freqBins is in Hz
 
% Number of poles to use in fit
numPoles = 12

Definition at line 1 of file findComplexRationalApproximation.m.

◆ ii

for ii

Initial value:

= 1:250
    % Ensure poles are stable
    sPoleFreqs = flipReal(sPoleFreqs)

Definition at line 28 of file findComplexRationalApproximation.m.

◆ matrix

Turn this into a matrix

Definition at line 25 of file findComplexRationalApproximation.m.

◆ maxFreq

Scale incoming frequencies maxFreq = max(freqBins)

Definition at line 10 of file findComplexRationalApproximation.m.

◆ numVar

Count number of useful output variables numVar = numPoles + 2

Definition at line 61 of file findComplexRationalApproximation.m.

◆ off

hold off

Definition at line 68 of file findComplexRationalApproximation.m.

◆ on

hold on

Definition at line 67 of file findComplexRationalApproximation.m.

◆ poles

Undo scaling of outgoing remainder term and proportional terms poles = sPoleFreqs*maxFreq

Definition at line 70 of file findComplexRationalApproximation.m.

◆ proportional

proportional = res(numVar,:)/maxFreq

Definition at line 75 of file findComplexRationalApproximation.m.

◆ r

r = Asim\freqDataFull

Definition at line 55 of file findComplexRationalApproximation.m.

◆ remainder

remainder = res(numVar-1,:)

Definition at line 74 of file findComplexRationalApproximation.m.

◆ res

Extract these output variables res = r(1:numVar)

Definition at line 64 of file findComplexRationalApproximation.m.

◆ residual

Compute residual error and print to screen residual = getResidues(sPoleFreqs,freqData,wFreqBins)

Definition at line 51 of file findComplexRationalApproximation.m.

◆ residues

residues = res(1:numVar-2,:)*maxFreq

Definition at line 70 of file findComplexRationalApproximation.m.

◆ resiudes

Extract resiudes

Definition at line 53 of file findComplexRationalApproximation.m.

◆ s

Turn this into a with identical frequencies along the rows s = repmat(1j*wFreqBins(:),1,numPoles)

Definition at line 26 of file findComplexRationalApproximation.m.

◆ sigma

sigma = -0.1

Definition at line 16 of file findComplexRationalApproximation.m.

◆ sPoleFreqs

end Ensure poles are stable sPoleFreqs = sigma + 1j*wPoleFreqs

Definition at line 17 of file findComplexRationalApproximation.m.

◆ wFreqBins

Create vector of simulation frequencies wFreqBins = 2*pi*freqBins

Definition at line 23 of file findComplexRationalApproximation.m.

◆ wPoleFreqs

wPoleFreqs = 2*pi*poleFreqs

Definition at line 15 of file findComplexRationalApproximation.m.

Functions

Variables