PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

576 Practical MATLAB® Applications for Engineers

ripple in the stop band and a smooth gain with maximum fl atness in the pass band

(see Figure 6.15).

The stop band does not approach zero as fast as type 1.

The ripple effect becomes more evident as the order of the fi lter increases.

R.6.60 The magnitude square of the transfer function H(jw) of a Chebyshev type-1 fi lter is
given by

Hw

a Cwwnp

()

()

2

22

1

1



where Cn(x) is referred to as the Chebyshev polynomial of order n, in the region

defi ned by

1

1

1

2

Hwap()
() 205. for w w

where ε denotes the maximum stop band deviation.

The Chebyshev polynomial coeffi cients Cn(x) of order n are defi ned by

Cx

nx x

n nxx

()

cos( cos ( ))

cos( cosh ( ))





1

1

01

1

for

for









FIGURE 6.15
(See color insert following page 374.) Magnitude plots of normalized analog Chebyshev type-2 LPFs of orders
n = 1, 2, 3, 4, and 10.

0 1 2 3 4 5 6

0

0.2

0.4

0.6

0.8

1

Normalized frequency

Gain

Chebyshev type-2 LPF/order n = 1, 2, 3, 4, 10

n = 1

n = 3

n = 2 n = 4

n = 10