1. Where does the poles of the system function of the second filter locate?
a) ej2π(k+α)M
b) ej2π(k+α)/M
c) ej2π(k-α)/M
d) ejπ(k+α)/M
Explanation: The system function of the second filter in the cascade of an FIR realization by frequency sampling method is given by
H2(z)=\(\sum_{k=0}^{M-1} \frac{H(k+α)}{1-e^{\frac{j2π(k+α)}{M}} z^{-1}}\)
We obtain the poles of the above system function by equating the denominator of the above equation to zero.
=>\(1-e^{\frac{j2π(k+α)}{M}} z^{-1}\)=0
=>z=pk=\(e^{\frac{j2π(k+α)}{M}}\), k=0,1….M-1
2.When the desired frequency response characteristic of the FIR filter is narrowband, most of the gain parameters {H(k+α)} are zero.
a) True
b) False
Explanation: When the desired frequency response characteristic of the FIR filter is narrowband, most of the gain parameters {H(k+α)} are zero. Consequently, the corresponding resonant filters can be eliminated and only the filters with nonzero gains need be retained.
3. If M and N are the orders of numerator and denominator of rational system function respectively, then how many multiplications are required in direct form-I realization of that IIR filter?
a) M+N-1
b) M+N
c) M+N+1
d) M+N+2
Explanation: From the direct form-I realization of the IIR filter, if M and N are the orders of numerator and denominator of rational system function respectively, then M+N+1 multiplications are required
4. If M and N are the orders of numerator and denominator of rational system function respectively, then how many additions are required in direct form-I realization of that IIR filter?
a) M+N-1
b) M+N
c) M+N+1
d) M+N+2
Explanation:From the direct form-I realization of the IIR filter, if M and N are the orders of numerator and denominator of rational system function respectively, then M+N additions are required.
5. If M and N are the orders of numerator and denominator of rational system function respectively, then how many memory locations are required in direct form-I realization of that IIR filter?
a) M+N+1
b) M+N
c) M+N-1
d) M+N-2
Explanation: From the direct form-I realization of the IIR filter, if M and N are the orders of numerator and denominator of rational system function respectively, then M+N+1 memory locations are required.
6. In direct form-I realization, all-pole system is placed before the all-zero system.
a) True
b) False
Explanation: In direct form-I realization, all-zero system is placed before the all-pole system.
7. If M and N are the orders of numerator and denominator of rational system function respectively, then how many memory locations are required in direct form-II realization of that IIR filter?
a) M+N+1
b) M+N
c) Min [M,N]
d) Max [M,N]
Explanation: From the direct form-II realization of the IIR filter, if M and N are the orders of numerator and denominator of rational system function respectively, then Max[M,N] memory locations are required
8. What are the nodes that replace the adders in the signal flow graphs?
a) Source node
b) Sink node
c) Branch node
d) Summing node
Explanation: Summing node is the node which is used in the signal flow graph which replaces the adder in the structure of a filter
9. The output signal of a system is extracted at a sink node.
a) True
b) False
Explanation: The input to a system originates at a source node and the output signal is extracted at a sink nod
10. If we reverse the directions of all branch transmittances and interchange the input and output in the flow graph, then the resulting structure is called as ______________
a) Direct form-I
b) Transposed form
c) Direct form-II
d) None of the mentioned
Explanation: According to the transposition or flow-graph reversal theorem, if we reverse the directions of all branch transmittances and interchange the input and output in the flow graph, then the system remains unchanged. The resulting structure is known as transposed structure or transposed form