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freqresp

11-86

Algorithm For transfer functions or zero-pole-gain models, freqresp evaluates the

numerator(s) and denominator(s) at the specified frequency points. For

continuous-time state-space models , t he frequency response is

Whennumerical ly safe, is diagonalized forfast evaluation of this expression

at the frequencies . Otherwise, is reduced to upper Hessenberg

formand thelinearequation issolvedateachfrequency point,

taking a dvantage of the Hessenberg structure. The reduction to Hessenberg

form provides a good compromise between efficiency and reliability. See [1] for

more details on this technique.

Diagnostics If the system has a pole on the axis (or unit circle in the discrete-time case)

and

w happens to contain this frequency point, the gain is infinite, is

singular, and

freqresp produces the following warning message.

Singularity in freq. response due to jw-axis or unit circle pole.

See Also evalfr Response at sing le complex frequency

bode Bode plot

nyquist Ny quist plot

nichols Nichols plot

sigma Singular value plot

ltiview LTIsystemviewer

References [1] L aub, A.J., “Efficien t Multivariable F requency Response Computations,”

IEEE Transactions o n Automatic Control, AC-26 (1 981), pp. 407–408.

ABCD

,,,()

DCjωA–()

–

B,+ ωω

... ω

,,=

...

–()

–