User`s guide

Table Of Contents

Time and Frequency Response

5-13

For example,

bode(sys,{0.1 , 100})

draws the Bode plot between 0.1 and 100 radians/second. You can also specify

a particular vector of frequency points as in

w = logspace(–1,2,100)

bode(sys,w)

The logspace command generates a vector w of logarithmically spaced

frequencies starting at rad/s and ending at rad/s. See

the reference page for

linspace for linearly spaced frequency vectors.

Note: In discrete time, the frequency response is evaluated on the unit circle

and the notion of “frequency” should be understood as follows. The upper half

of the unit circle is parametrized by

where is the system sample time and is ca lled the Nyquist frequency.

The variable plays the role of continuous-time freq u ency. We use t h is

“equivalent frequency” as an -axis variable in all discrete-t ime frequency

response plots. In addition, the frequency response is plotted only up to the

Nyquist frequency because it is peri odic with period ( a phenome non

known as aliasing).

Note: An easy way to implement these response-plotting functions is

through the LTI Viewer. See Chapter 6, “The LTI Viewer” for more

information.

Plotting and Comparing Multiple Systems

The LTIViewerprovides one method of plotting various responsesfor multiple

models. SeeChapter6,“TheLTI Viewer”toseehow toaccomplishthis.You can

also use the command line response-plotting functions to plot the response of

–

0.1= 10

100=

jωT

= ,0ωω

------=≤≤