Digital Signal Processing

Structures for FIR Systems

Question 1
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.
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%
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 4
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 5
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 6
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 7
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 8
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 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 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