Digital Signal Processing

Structures for FIR Systems

Question 1
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 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%
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 4
Marks : +2 | -2
Pass Ratio : 100%
Which of the following is an method for implementing an FIR system?
Direct form
Cascade form
Lattice structure
All of the mentioned
Explanation:
There are several structures for implementing an FIR system, beginning with the simplest structure, called the direct form. There are several other methods like cascade form realization, frequency sampling realization and lattice realization which are used for implementing and FIR system.
Question 5
Marks : +2 | -2
Pass Ratio : 100%
What is the system function of all-zero filter or comb filter?
\\(\\frac{1}{M}(1+z^{-M} e^{j2πα})\\)
\\(\\frac{1}{M}(1+z^M e^{j2πα})\\)
\\(\\frac{1}{M}(1-z^M e^{j2πα})\\)
\\(\\frac{1}{M}(1-z^{-M} e^{j2πα})\\)
Explanation:
The system function H(z) which is characterized by the set of frequency samples is obtained as
Question 6
Marks : +2 | -2
Pass Ratio : 100%
The realization of FIR filter by frequency sampling realization can be viewed as cascade of how many filters?
Two
Three
Four
None of the mentioned
Explanation:
In frequency sampling realization, the system function H(z) is characterized by the set of frequency samples {H(k+ α)} instead of {h(n)}. We view this FIR filter realization as a cascade of two filters. One is an all-zero or a comb filter and the other consists of parallel bank of single pole filters with resonant frequencies.
Question 7
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.
Question 8
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 9
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 10
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%.