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Add minimum phase to frequency response magnitude

Since R2022b


datac = addMinPhase(data) adds phase information to the magnitude-only frequency-response signals stored in data.

Use addMinPhase to generate phase information for any complex vector H(w) for which the measured magnitude |H| is available but not the phase. addMinPhase assumes that H(w) represents the frequency response of a minimum-phase stable linear system.

When data is numeric, the sample time is assumed to be one second and the frequency is assumed to be linspace(0,pi,size(data,1)).


datac = addMinPhase(data,ts) replaces the default sample time with the sample time specified in ts. Units are in seconds.


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Load time-domain input-output data and store the frequency response in an idfrd object. Remove the phase information by taking the absolute value of the response. Plot the response.

load iddata1 z1
m0 = arx(z1,[2 3 0]);
ts = z1.Ts;
w = linspace(0,pi,128)/ts;
response = idfrd(m0,w);
response.ResponseData = abs(response.ResponseData);

Add the minimum phase information to the response. Plot the response.

responseMinPhase = addMinPhase(response,ts);

Input Arguments

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Input frequency response signals, specified as one of these values:

  • A matrix of positive real values

  • An idfrd object containing positive real values in its ResponseData property.

Sample time of signals, in seconds, specified as a nonnegative real scalar.

Output Arguments

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Frequency response signals with minimum phase added, returned as a complex matrix or as an idfrd object.

  • When data is a matrix, then datac is a complex matrix of the same size as data. If the vector data(:,i) has all real and nonnegative values, then datac(:,i) is the complex version of data(:,i) with added phase. Otherwise, datac(:,i) is identical to data(:,i).

  • When data is an idfrd object, then datac is also an idfrd object. If the matrix data.ResponseData(i,j,:) has real and nonnegative values for each input-output pair (i,j), then datac.ResponseData(i,j,:) is the complex version of that vector with added phase. Otherwise, datac.ResponseData(i,j,:) is identical to data.ResponseData(i,j,:).

Version History

Introduced in R2022b

See Also