Assignment #13

ECSE-2410 Signals & Systems - Fall 2004 Fri 10/29/04

1(10). A LTI system has the frequency response, . Find the steady-state response, , to input

2(30). Indicate on all your sketches: DC gain ( in dB), break (corner) frequencies, and slopes.

(a) Sketch the straight-line Bode Magnitude and Phase plots for .

(b) Find the crossover frequency, , of the straight line magnitude plot in (a), i.e., when .

(c) Sketch the straight-line Bode Magnitude and Phase plots for .

(d) Find the crossover frequency, , of the straight-line phase plot in (c), i.e., when .

(e) Sketch the straight-line Bode Magnitude and Phase plots for .

(f) Find the crossover frequency, , of the straight-line magnitude plot in (e), i.e., when .

3.(20) Use the “Bode” function in MATLAB to generate exact magnitude and phase plots of 2(a), (c) &

(e) above. Sketch the straight-line approximations on your MATLAB plot. MATLAB requires

that the frequency response be expressed in descending powers of jw, as, the code, for example,

>> num=[50 0];

>> den=[5 51 10];

>> bode(num,den);

>> subplot(2,1,1), title(”Bode plot – your name”);

>> den=[5 51 10];

>> bode(num,den);

>> subplot(2,1,1), title(”Bode plot – your name”);

for , is

Adding w=logspace(-1,3,500), and replacing bode(num,den) with bode(num,den,w) causes MATLAB to plot 500 points from w=10^-1 to w=10³.

4(10). For the straight-line Bode magnitude plot

shown, find the approximate

magnitude cutoff frequency, w_c.

Use Bode approximation.

5(10). O&W 6.12

6(20). O&W 6.56