This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Structures for FIR Systems-1”.

1. In general, an FIR system is described by the difference equation

a) True

b) False

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2. What is the general system function of an FIR system?

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3. Which of the following is an method for implementing an FIR system?

a) Direct form

b) Cascade form

c) Lattice structure

d) All of the mentioned

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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.

4. How many memory locations are used for storage of the output point of a sequence of length M in direct form realization?

a) M+1

b) M

c) M-1

d) None of the mentioned

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Explanation: The direct form realization follows immediately from the non-recursive difference equation given by

We observe that this structure requires M-1 memory locations for storing the M-1 previous inputs.

5. The direct form realization is often called a transversal or tapped-delay-line filter.

a) True

b) False

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Explanation: The structure of the direct form realization, resembles a tapped delay line or a transversal system.

a) M even

b) M odd

c) All values of M

d) Doesn’t depend on value of M

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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)

For such a system the number of multiplications is reduced from M to M/2 for M even and to (M-1)/2 for M odd. Thus for the structure given in the question, M is odd.

7. By combining two pairs of poles to form a fourth order filter section, by what factor we have reduced the number of multiplications?

a) 25%

b) 30%

c) 40%

d) 50%

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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%.

8. The desired frequency response is specified at a set of equally spaced frequencies defined by the equation:

a) π/2M(k+α)

b) π/M(k+α)

c) 2π/M(k+α)

d) None of the mentioned

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Explanation: To derive the frequency sampling structure, we specify the desired frequency response at a set of equally spaced frequencies, namely ωk=2π/M(k+α) ,k=0,1…(M-1)/2 for M odd

k=0,1….(M/2)-1 for M even

α=0 or 0.5

9. The realization of FIR filter by frequency sampling realization can be viewed as cascade of how many filters?

a) Two

b) Three

c) Four

d) None of the mentioned

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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.

10. What is the system function of all-zero filter or comb filter?

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Explanation: The system function H(z) which is characterized by the set of frequency samples is obtained as

11. The zeros of the system function of comb filter are located:

a) Inside unit circle

b) On unit circle

c) Outside unit circle

d) None of the mentioned

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Explanation: The system function H(z) which is characterized by the set of frequency samples is obtained as

13. Where does the poles of the system function of the second filter locate?

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Explanation: The system function of the second filter in the cascade of an FIR realization by frequency sampling method is given by

14. When the desired frequency response characteristic of the FIR filter is narrowband, most of the gain parameters {H(k+α)} are zero.

a) True

b) False

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Explanation: When the desired frequency response characteristic of the FIR filter is narrowband, most of the gain parameters {H(k+α)} are zero. Consequently, the corresponding resonant filters can be eliminated and only the filters with nonzero gains need be retained.

15. Which of the following filters have a cascade realization as shown below?

a) IIR filter

b) Comb filter

c) High pass filter

d) FIR filter

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Explanation: The system function of the FIR filter according to the frequency sampling realization is given by the equation

The above system function can be represented in the cascade form as shown in the above block diagram.

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