Using tfest to find a system model

Here is some example code that demonstrates how to use tfest to fit a linear model to frequency response data:

%Generate some synthetic frequency response measurement data
s = tf( [ 1 0 ], 1 );
highPass = s / ( s + 1 )

[ magnitude, phase, frequency ] = bode( highPass );

% add some random noise
noiseStandardDeviation = 0.05;
magnitude = magnitude + noiseStandardDeviation * randn( size( magnitude ) );
phase = phase + noiseStandardDeviation * randn( size( phase ) );

numeratorForm = [ 1 0 ]; % decreasing powers of s -- numerator for HPF has no constant term, so set it to zero (otherwise tfest will fit a constant value)
denominatorForm = [ 1 0 ]; % decreasing powers of s -- numerator for HPF has no constant term, so set it to zero (otherwise tfest will fit a constant value)

estimatedTransferFunction = FitTransferFunction( magnitude, phase, frequency, numeratorForm, denominatorForm )

function EstimatedTransferFunction = FitTransferFunction( MagnitudeRatio, PhaseDifferenceDegrees, FrequencyHertz, NumeratorForm, DenominatorForm )
    % convert magnitude and phase to single complex vector
    complexResponseData = MagnitudeRatio .* exp( 1i .* PhaseDifferenceDegrees .* pi ./ 180 );

    % create optional initial model for tfest so that known zero
    % coefficients can be constrained
    initalModel = idtf( NumeratorForm, DenominatorForm );
    zeroCoefficients = find( NumeratorForm == 0 );
    for ii = 1:numel( zeroCoefficients )
        initalModel.Structure.Numerator.Free(ii) = false;
    end
    zeroCoefficients = find( DenominatorForm == 0 );
    for ii = 1:numel( zeroCoefficients )
        initalModel.Structure.Denominator.Free(ii) = false;
    end

    frequencyResponseData = frd( complexResponseData, FrequencyHertz, 'FrequencyUnit', 'Hz');
    EstimatedTransferFunction = tfest( frequencyResponseData, initalModel );
end