- Can we connect two LTI systems, with impulse responces h1[n] and h2[n], in series ? What will be the output y[n] in such a case ?
- Extend the above understanding on how to calculate the overall response when independent LTIs are connected in a complex arrangement of series and parallel connections.
- What do you understand about Region of Convergence (RoC) ?
- Explain why the z-Transform is incomplete (without RoC) in defining the z-domain representation of a given time-domain function. Given examples.
- What are the properties of z-Transform ?
- Locate the z-Transforms and RoC for the following functions from your text book :
- Impulse function delta[n]
- Step function u[n]
- Increasing function a^n u[n]. Read a^n as a raised to the power of n.
- n (a^n) u[n]
- -a^n. u[-n-1]
- -na^n u[-n-1]
- Note : The inverse z-Transform can be computed by any one of the following methods :
- Direct evaluation
- Expansion into a series of terms in the variables z, and z^-1
- Partial-fraction expansion and table lookups.
Wednesday, February 29, 2012
Homework - 9
Answer the following questions by referring to the text book :
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Related to Q1
ReplyDeleteCan we connect two LTI systems, with impulse responces h1[n] and h2[n], in series ? What will be the output y[n] in such a case ?
Yes we can connect two LTI systems in series (cascade).
Output in such case when impulse is sent as an input signal is:
y(n) = -inf to +inf Σh1(k)h2(n-k) or equivalently
y(n) = -inf to +inf Σh2(k)h1(n-k)
Sir please let me know if my understanding is right.
x[n] ---> h1[n]--h2[n]-----> y[n]
ReplyDeletey[n] = x[n]*h1[n]*h2[n] where * indicates convolution operation.
So, what you wrote is correct except that you have not included the input x[n].
You can find y[n] in two ways.
First find h1[n]*h2[n].
Then find x[n]* {result of the above convolution operation}