Digital Signal Processing

Structures for FIR Systems

Question 1
Marks : +2 | -2
Pass Ratio : 100%
By combining two pairs of poles to form a fourth order filter section, by what factor we have reduced the number of multiplications?
25%
30%
40%
50%
Explanation:
We have to do 3 multiplications for every second order equation. So, we have to do 6 multiplications if we combine two second order equations and we have to perform 3 multiplications by directly calculating the fourth order equation. Thus the number of multiplications are reduced by a factor of 50%.
Question 2
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 3
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 4
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 5
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 6
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 7
Marks : +2 | -2
Pass Ratio : 100%
What is the output of the single stage lattice filter if x(n) is the input?
x(n)+Kx(n+1)
x(n)+Kx(n-1)
x(n)+Kx(n-1)+Kx(n+1)
Kx(n-1)
Explanation:
The single stage lattice filter is as shown below.
Question 8
Marks : +2 | -2
Pass Ratio : 100%
What is the condition of M, if the structure according to the direct form is as follows?
M even
M odd
All values of M
Doesn’t depend on value of M
Explanation:
When the FIR system has linear phase, the unit sample response of the system satisfies either the symmetry or asymmetry condition, h(n)=±h(M-1-n)
Question 9
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 10
Marks : +2 | -2
Pass Ratio : 100%
The direct form realization is often called a transversal or tapped-delay-line filter.
True
False
Explanation:
The structure of the direct form realization, resembles a tapped delay line or a transversal system.