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function varargout = spa(varargin)
// Use spectral analysis to estimate frequency response
//
// Calling Sequence
// frdData = spa(plantData,winSize,Freq)
// Parameters
// plantData : iddata type
// winSize : non-neative integer number
// Freq : frequency points to evaluate the response
// frdData : frd type object
// Description
// spa function does the estimation of the frequency response of iddata of a plant using the spectral analysis. Hanning window is used in spectral
// analysis. Default size of the window is minimum of the number of sample divided by 10 or 30. The default frquency point is %pi x (1:128)/(sampling time x 128).
// Examples
// a = [1 0.2];b = [0 0.2 0.3];
// sys = idpoly(a,b,'Ts',0.1)
// u = idinput(1024,'PRBS',[0 1/20],[-1 1])
// y = sim(u,sys)+rand(1024,1)
// plantData = iddata(y,u,0.1)
// frdData = spa(plantData)
// Authors
// Bhushan Manjarekar, Ashutosh Kumar Bhargava
[lhs , rhs] = argn();
if ( rhs < 1 || rhs > 3 ) then
errmsg = msprintf(gettext("%s: Wrong number of input arguments" ),"spa");
error(errmsg)
elseif typeof(varargin(1)) <> "iddata" then
error(msprintf(gettext("%s:Plant data must be ""iddata"" type.\n"),"spa"))
end
plantData = varargin(1)
windowSize = %F
inputFreq = %F
// ------------------------------------------------------------------------------
// arranging the plant data
inputData = plantData.InputData;
if ~size(inputData,"*") then
error(msprintf(gettext("%s:Input data must be non-zero vector. \n"),"spa"))
end
outputData = plantData.OutputData
if ~size(outputData,"*") then
error(msprintf(gettext("%s:Output data must be non-zero vector. \n"),"spa"))
end
// ------------------------------------------------------------------------------
N = size(inputData,'r')
nout = size(outputData,'c')
nin = size(inputData,'c')
if ~windowSize then
windowSize = min(N/10, 30)
end
if inputFreq then
else
inputFreq = (1:128)/128 * %pi/plantData.Ts
end
M = windowSize
Ryu = xcov(outputData,inputData,M,'biased')
Ruu = xcov(inputData,inputData,M,'biased')
Ryy = xcov(outputData,outputData,M,'biased')
G = [];spect = [];
for ii = 1:nout
phiY = spaCalculation(inputFreq,Ryy,M)
temp = phiY
for jj = 1:nin
phiYU = spaCalculation(inputFreq,Ryu,M)// sapply(freq, cov2spec, Ryu[i, j, ], M)
phiU = spaCalculation(inputFreq,Ruu,M)
G = [G phiYU./phiU]
// pause
temp = temp - phiYU .* conj(phiYU)./phiU
end
spect = [spect temp]
end
// disp(size(spect))
// disp(spect)
frdData = frd(G',inputFreq',plantData.Ts,spect')
varargout(1) = frdData
endfunction
function varargout = spaCalculation(varargin)
inputFreq = varargin(1)
xcovData = varargin(2)
Mnumber = varargin(3)
temp = []
win_l=window('hn',2*Mnumber+1)
for ii = 1:size(inputFreq,'c')
seq1 = exp(-(%i) * (-Mnumber:Mnumber) * inputFreq(ii))
data = (seq1.*win_l)
data2 = sum(data.*xcovData')
temp = [temp data2]
end
varargout(1) = temp
endfunction
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