Obtain the direct form I, direct form II, and cascade realizations for the following system: 1 1 y(n) = y(n − 1) − y(n − 2) + x(n) + √3x(n − 1) Is this system stable?

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4) Obtain the direct form I, direct form II, and cascade realizations for the following system:
3
1
1
y(n) = ²1 y(n − 1) − ² y(n − 2) + x(n) + ½ x(n − 1)
Is this system stable?
Transcribed Image Text:4) Obtain the direct form I, direct form II, and cascade realizations for the following system: 3 1 1 y(n) = ²1 y(n − 1) − ² y(n − 2) + x(n) + ½ x(n − 1) Is this system stable?
Expert Solution
Step 1: what is given and what to do:

Given:

A DT system,

y open square brackets n close square brackets equals 3 over 4 y open square brackets n minus 1 close square brackets minus 1 over 8 y open square brackets n minus 2 close square brackets plus x open square brackets n close square brackets plus 1 third x open square brackets n minus 1 close square brackets

To obtain:

Direct form I, II and cascade realizations of the above system. 

we also need to determine whether the system  is stable?

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