Signals and Systems - Electrical Engineering

404 C H A P T E R 6: Application to Control and Communications

0

(a) (b)

(c) (d)

5 10

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LP Prototype

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Ω

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LP−HP

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LP−BP

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LP−BE

|H

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FIGURE 6.25

Frequency transformations: (a) prototype low-pass filter, (b) low-pass to high-pass transformation, (c) low-pass

to band-pass transformation, and (d) low-pass to band-eliminating transformation.

U1 = (omega0/( j∗w)).ˆn;

num1 = b∗conj(U1’); den1 = a∗conj(U1’);

H1 = num1/den1;

% low-pass to band-pass

U2 = ((−wˆ2 + omega1ˆ2)/(BW∗j∗w)).ˆn

num2 = b∗conj(U2’); den2 = a∗conj(U2’);

H2 = num2/den2;

% low-pass to band-eliminating

U3 = ((BW∗j∗w)/(−wˆ2 + omega1ˆ2)).ˆn

num3 = b∗conj(U3’); den3 = a∗conj(U3’);

H3 = num3/den3 n