User`s guide

Table Of Contents

bode

11-23

structure. The reduction to Hessenberg form provides a good compromise

between efficiency and reliability. See [1] for more details on this technique.

For discrete-time systems, the frequency response is obtained by evaluating

the transfer function on the unit circle. To facilitate interpretation, the

upper-half of the unit circle is parametrized as

where is the sample time. is called the Nyquist frequency.The

equivalent “continuous-time frequency” is then used as the -axis variable.

Because

is periodic with period ,

bode plots the response only up t o the Nyquist

frequency . If the sample time is unspecified, the default value is

assumed.

Diagnostics If t he system has a pole on the axis (or unit circle in the discrete case) and

w happens t o contain this frequency point, the gain is infinite, is

singular, and

bode produces t he warning message

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

See Also evalfr Response at single complex frequency

freqresp Frequency response computation

ltiview LTIsystemviewer

nichols Nichols plot

nyquist Ny quist plot

sigma Singular value plot

References [1] Laub, A.J., “Efficient Multivariable Frequency Response Computations,”

IEEE Transactions on Automatic Control, AC-26 (1981), pp. 4 07–408.

()

jωT

= ,0ωω

≤≤

------=

jωT

()

–