Digital Signal Processing

Structures for FIR Systems

Question 1
Marks : +2 | -2
Pass Ratio : 100%
What is the unit sample response of the mth filter?
hm(0)=0 and hm(k)=αm(k), k=1,2…m
hm(k)=αm(k), k=0,1,2…m(αm(0)≠1)
hm(0)=1 and hm(k)=αm(k), k=1,2…m
none of the mentioned
Explanation:
We know that Hm(z)=Am(z) and Am(z) is a polynomial whose equation is given as Am(z)=\\(1+\\sum_{k=1}^m α_m (k)z^{-k}\\), m≤1 and A0(z)=1
Question 2
Marks : +2 | -2
Pass Ratio : 100%
How many memory locations are used for storage of the output point of a sequence of length M in direct form realization?
M+1
M
M-1
None of the mentioned
Explanation:
The direct form realization follows immediately from the non-recursive difference equation given by y(n)=\\(\\sum_{k=0}^{M-1}b_k x(n-k)\\).
Question 3
Marks : +2 | -2
Pass Ratio : 100%
What is the general system function of an FIR system?
\\(\\sum_{k=0}^{M-1}b_k x(n-k)\\)
\\(\\sum_{k=0}^M b_k z^{-k}\\)
\\(\\sum_{k=0}^{M-1}b_k z^{-k}\\)
None of the mentioned
Explanation:
We know that the difference equation of an FIR system is given by y(n)=\\(\\sum_{k=0}^{M-1}b_k x(n-k)\\).
Question 4
Marks : +2 | -2
Pass Ratio : 100%
What are the lattice coefficients corresponding to the FIR filter with system function H(z)= 1+(13/24)z-1+(5/8)z-2+(1/3)z-3?
(1/2,1/4,1/3)
(1,1/2,1/3)
(1/4,1/2,1/3)
None of the mentioned
Explanation:
Given the system function of the FIR filter is
Question 5
Marks : +2 | -2
Pass Ratio : 100%
If we consider a sequence of FIR filer with system function Hm(z)=Am(z), then what is the definition of the polynomial Am(z)?
\\(1+\\sum_{k=0}^m α_m (k)z^{-k}\\)
\\(1+\\sum_{k=1}^m α_m (k)z^{-k}\\)
\\(1+\\sum_{k=1}^m α_m (k)z^k \\)
\\(\\sum_{k=0}^m α_m (k)z^{-k}\\)
Explanation:
Consider a sequence of FIR filer with system function Hm(z)=Am(z), m=0,1,2…M-1
Question 6
Marks : +2 | -2
Pass Ratio : 100%
In general, an FIR system is described by the difference equation y(n)=\\(\\sum_{k=0}^{M-1}b_k x(n-k)\\).
True
False
Explanation:
The difference equation y(n)=\\(\\sum_{k=0}^{M-1}b_k x(n-k)\\) describes the FIR system.
Question 7
Marks : +2 | -2
Pass Ratio : 100%
What is the value of the coefficient α2(1) in the case of FIR filter represented in direct form structure with m=2 in terms of K1 and K2?
K1(K2)
K1(1-K2)
K1(1+K2)
None of the mentioned
Explanation:
The equation for the output of an FIR filter represented in the direct form structure is given as
Question 8
Marks : +2 | -2
Pass Ratio : 100%
The constants K1 and K2 of the lattice structure are called as reflection coefficients.
True
False
Explanation:
The equation of the output from the second stage lattice filter is given by
Question 9
Marks : +2 | -2
Pass Ratio : 100%
The desired frequency response is specified at a set of equally spaced frequencies defined by the equation?
\\(\\frac{\\pi}{2M}\\)(k+α)
\\(\\frac{\\pi}{M}\\)(k+α)
\\(\\frac{2\\pi}{M}\\)(k+α)
None of the mentioned
Explanation:
To derive the frequency sampling structure, we specify the desired frequency response at a set of equally spaced frequencies, namely ωk=\\(\\frac{2\\pi}{M}\\)(k+α), k=0,1…(M-1)/2 for M odd
Question 10
Marks : +2 | -2
Pass Ratio : 100%
The FIR filter whose direct form structure is as shown below is a prediction error filter.
True
False
Explanation:
The FIR structure shown in the above figure is intimately related with the topic of linear prediction. Thus the top filter structure shown in the above figure is called a prediction error filter.