PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

660 Practical MATLAB® Applications for Engineers

FIGURE 6.84
Plots of Butterworth and Chebyshev BSFs of Example 6.22.

0 1 2 3 4

0

−0.5

0

0.5

1

1.5

magnitude

−0.5

0

0.5

1

1.5

magnitude

Butt. BS,center freq=2,stopband=1Butt. Butt.BSF

Cheb.BS ,cent freq=2,BW stopband=1 Cheb. BSF

0246

0246

− 200

− 100

100

200

phase (deg)

0

− 200

− 100

100

200

phase (deg)

frequency (rad/sec)

0246

frequency (rad/sec)

b. Then ht

s

()




£^11

1









h(t) = e−t for t > 0

and

c. h(nT) = e−nT for t > 0

b. H(z) = Z{e−nT } * T

H(z) = Z{e−n(0.01)} * {0.01}

H(z) = Z{e−(0.01)}n (^) {0.01}
Hz
z
ze
()


(. )
001
(^001)

6.5 Application Problems

P.6.1 Verify that the transfer function given by

Hjw

a

jw a

()
 a



for  0

is of an LPF, and evaluate by hand the following

a. The gain at H(w = 0 ) and H(w = ∞)

b. The cutoff frequency wc

c. The gain at H(w = wc) and phase at H(w = wc)

d. The fi lter’s BW