Digital Signal Processing

Structures for FIR Systems

Question 1
Marks : +2 | -2
Pass Ratio : 100%
If a three stage lattice filter with coefficients K1=1/4, K2=1/2 K3=1/3, then what are the FIR filter coefficients for the direct form structure?
(1,8/24,5/8,1/3)
(1,5/8,13/24,1/3)
(1/4,13/24,5/8,1/3)
(1,13/24,5/8,1/3)
Explanation:
We get the output from the third stage lattice filter as
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%
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 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%
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 6
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 7
Marks : +2 | -2
Pass Ratio : 100%
Which of the following is the application of lattice filter?
Digital speech processing
Adaptive filter
Electroencephalogram
All of the mentioned
Explanation:
Lattice filters are used extensively in digital signal processing and in the implementation of adaptive filters.
Question 8
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 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 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.