15.01.2013 Views

U. Glaeser

U. Glaeser

U. Glaeser

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

|H |<br />

1<br />

FIGURE 26.1 Frequency selective (bandpass) filter: (a) shows the ideal magnitude response (thick dashed line) and<br />

an example of an elliptic (with 6 poles, 6 zeros) bandpass filter (thin solid line.) The ideal filter has two cutoff frequencies,<br />

ω cl and ω c2, that separate the two stop bands from the pass band; (b) shows the ideal group delay response (thick<br />

dashed line) and the group delay of the elliptic bandpass filter. Note that elliptic filters usually have severe phase<br />

distortion (i.e., a highly nonlinear group delay) in the passband.<br />

|H |<br />

1<br />

FIGURE 26.2 The phase equalizer is designed to equalize the passband of the elliptic filter in Fig. 26.1 so that the<br />

group delay is flat in the pass band: (a) shows the ideal equalizer response (thick dashed line) and a FIR (order 25)<br />

equalizer; (b) shows the group delay, D g{�}, where D g{I Equal. (ω)} = D g{I(ω)} − D g {H Elliptic(ω)} is the ideal group delay<br />

(thick dashed line).<br />

|H |<br />

1<br />

FIGURE 26.3 Equalized filter. The figures show the magnitude and the group delay of the elliptic filter (with 6 poles,<br />

6 zeros) after being equalized by the FIR (order 25) equalizer. The ideal filter for the example is a flat group delay<br />

frequency selective filter.<br />

Equalizer: Equalizers are applied to existing systems in order to remove distortion, or to improve the<br />

overall filter characteristic. Therefore, if the desired response of the system is D(ω), the ideal<br />

frequency response of the equalizer depends on the distortion filter H D(ω), such that<br />

One example is shown in Fig. 26.2 where the equalizer is used to reduce the phase distortion of<br />

the filter in Fig. 26.1. The phase equalized filter is shown in Fig. 26.3.<br />

Filter bank: A filter bank is a set of filters that sum to 1, the identity system:<br />

© 2001 by CRC Press LLC<br />

Transition Band<br />

Pass Band<br />

Transition Band<br />

Stop Band Stop Band<br />

0 ω<br />

c1<br />

ω<br />

c2 π<br />

(a)<br />

ω<br />

D g<br />

_ N<br />

2<br />

0 ω ω<br />

c1<br />

c2 π<br />

(b)<br />

0 ω<br />

c1<br />

ω<br />

c2 π<br />

ω 0 ω<br />

c1<br />

ω<br />

c2 π<br />

(a) (b)<br />

0 ω ω<br />

c1<br />

c2 π<br />

ω<br />

IEq( ω)<br />

=<br />

D<br />

g<br />

D<br />

I<br />

D<br />

g<br />

D<br />

I<br />

0 ω ω<br />

c1<br />

c2 π<br />

D(ω)<br />

---------------<br />

HD(ω )<br />

Ik(ω), for k = 1,…,P such that Ik(ω) =<br />

1<br />

p<br />

∑<br />

k=1<br />

ω<br />

ω<br />

ω

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!