# FIR Least Squares Inverse Filter MCQ [Free PDF] – Objective Question Answer for FIR Least Squares Inverse Filter Quiz

1. Wiener filter is an FIR least-squares inverse filter.

A. True
B. False

FIR least-square filters are also called as Wiener filters.

2. If h(n) is the impulse response of an LTI system and hI(n) is the impulse response of the inverse LTI system, then which of the following is true?

A. h(n).hI(n)=1
B. h(n).hI(n)=δ(n)
C. h(n)*hI(n)=1
D. h(n)*hI(n)=δ(n)

The inverse to a linear time-invariant system with impulse response h(n) is defined as the system whose impulse response is hI(n), satisfying the following condition h(n)*hI(n)=δ(n).

3. If H(z) is the system function of an LTI system and HI(z) is the system function of the inverse LTI system, then which of the following is true?

A. H(z)*HI(z)=1
B. H(z)*HI(z)=δ(n)
C. H(z).HI(z)=1
D. H(z).HI(z)=δ(n)

The inverse to a linear time-invariant system with impulse response h(n) and system function H(z) is defined as the system whose impulse response is hI(n) and system function HI(z), satisfies the following condition

H(z).HI(z)=1.

4. It is not desirable to restrict the inverse filter to FIR.

A. True
B. False

In most practical applications, it is desirable to restrict the inverse filter to be an FIR filter.

5. Which of the following method is used to restrict the inverse filter to be FIR?

A. Truncating hI(n)
B. Expanding hI(n)
C. Truncating HI(z)
D. None of the mentioned

In many practical applications, it is desirable to restrict the inverse filter to FIR. One of the simple methods to get this requirement is to truncate hI(n).

6. What should be the length of the truncated filter?
A. M
B. M-1
C. M+1
D. Infinite

In the process of truncating, we incur a total squared approximation error where M+1 is the length of the truncated filter.

7. Which of the following criterion can be used to optimize the M+1 filter coefficients?

B. Least squares error criterion
C. Least squares error criterion & Pade approximation method
D. None of the mentioned

We can use the least-squares error criterion to optimize the M+1 coefficients of the FIR filter.

8. Which of the following filters have a block diagram as shown in the figure?

C. Least squares FIR filter
D. Least squares wiener filter

Since from the block diagram, the coefficients of the FIR filter coefficients are optimized by the least-squares error criterion, it belongs to the least-squares FIR inverse filter or wiener filter.

9. The autocorrelation of the sequence is required to minimize ε.

A. True
B. False

When ε is minimized with respect to the filter coefficients, we obtain the set of linear equations which are dependent on the autocorrelation sequence of the signal h(n).

10. Which of the following are required to minimize the value of ε?

A. rhh(l)
B. rdh(l)
C. d(n)
D. all of the mentioned

When ε is minimized with respect to the filter coefficients, we obtain the set of linear equations
$$\sum_{k=0}^M b_k r_{hh} (k-l)=r_{dh} (l)$$, l=0,1,…M

and we know that rdh(l) depends on the desired output d(n).

11. FIR filter that satisfies $$\sum_{k=0}^M b_k r_{hh} (k-l)=r_{dh} (l)$$, l=0,1,…M is known as wiener filter.

A. True
B. False

The optimum, in the least square sense, FIR filter that satisfies the linear equations in $$\sum_{k=0}^M b_k r_{hh} (k-l)=r_{dh} (l)$$ =r_{dh} (l)), l=0,1,…M is called the wiener filter.

12. What should be the desired response for an optimum wiener filter to be an approximate inverse filter?

A. u(n)
B. δ(n)
C. u(-n)
D. none of the mentioned

If the optimum least-squares FIR filter is to be an approximate inverse filter, the desired response is
d(n)=δ(n).

13. If the set of linear equations from the equation $$\sum_{k=0}^M b_k r_{hh} (k-l)=r_{dh} (l)$$, l=0,1,…M are expressed in matrix form, then what is the type of matrix obtained?

A. Symmetric matrix
B. Skew symmetric matrix
C. Toeplitz matrix
D. Triangular matrix

We observe that the matrix is not only symmetric but it also has the special property that all the elements along any diagonal are equal. Such a matrix is called a Toeplitz matrix and lends itself to efficient inversion by means of an algorithm.

14. What is the number of computations proportional to, in the Levinson-Durbin algorithm?

A. M
B. M2
C. M3
D. M1/2

The Levinson-Durbin algorithm is the algorithm that is used for the efficient inversion of the Toeplitz matrix which requires a number of computations proportional to M2 instead of the usual M3.

15. Filter parameter optimization technique is used for designing which of the following?

A. FIR in time domain
B. FIR in frequency domain
C. IIR in time domain
D. IIR in the frequency domain

We describe a filter parameter optimization technique carried out in the frequency domain that is representative of frequency domain design methods.

16. In this type of design, the system function of the IIR filter is expressed in which form?

A. Parallel form
C. Mixed form
D. Any of the mentioned

The design is most easily carried out with the system function for the IIR filter expressed in the cascade form as
H(z)=G.A(z).

17. It is more convenient to deal with the envelope delay as a function of frequency.
A. True
B. False

Instead of dealing with the phase response ϴ(ω), it is more convenient to deal with the envelope delay as a function of frequency.

18. Which of the following gives the equation for envelope delay?

A. dϴ(ω)/dω
B. ϴ(ω)
C. -dϴ(ω)/dω
D. -ϴ(ω)

Instead of dealing with the phase response ϴ(ω), it is more convenient to deal with the envelope delay as a function of frequency, which is

Tg(ω)= -dϴ(ω)/dω.

19. What is the error in magnitude at the frequency ωk?

C. G.A(ωk) – A(ωk)
D. None of the mentioned

The error in magnitude at the frequency ωk is G.A(ωk) – Adk) for 0 ≤ |ω| ≤ π, where Adk) is the desired magnitude response at ωk.

20. What is the error in delay at the frequency ωk?

A. Tgk)-Tdk)
B. Tgk)+Tdk)
C. Tdk)
D. None of the mentioned

Similarly, as in the previous question, the error in delay at ωk is defined as Tgk)-Tdk), where Tdk) is the desired delay response.

21. The choice of Tdk) for error in the delay is complicated.

A. True
B. False

We know that the error in the delay is defined as Tgk) – Tdk). However, the choice of Tdk) for error in the delay is complicated by the difficulty in assigning a nominal delay of the filter.

22. If the error in the delay is defined as Tgk) – Tg0) – Td(ωkk), then what is Tg0)?

A. Filter delay at nominal frequency in stopband
B. Filter delay at nominal frequency in the transition band
C. Filter delay at nominal frequency
D. Filter delay at the nominal frequency in passband

We are led to define the error in delay as Tgk) – Tg0) – Tdk), where Tg0) is the filter delay at some nominal center frequency in the passband of the filter.

23. We cannot choose any arbitrary function for the errors in magnitude and delay.
A. True
B. False

As a performance index for determining the filter parameters, one can choose any arbitrary function of the errors in magnitude and delay.

24. What does ‘p’ represents in the arbitrary function of error?

A. 2K-dimension vector
B. 3K-dimension vector
C. 4K-dimension vector
D. None of the mentioned

In the error function, ‘p’ denotes the 4K dimension vector of the filter coefficients.

25. What should be the value of λ for the error to be placed entirely on delay?

A. 1
B. 1/2
C. 0
D. None of the mentioned

The emphasis on the errors affecting the design may be placed entirely on the delay by taking the value of λ as 1.

26. What should be the value of λ for the error to be placed equally on magnitude and delay?
A. 1
B. 1/2
C. 0
D. None of the mentioned

The emphasis on the errors affecting the design may be equally weighted between magnitude and delay by taking the value of λ as 1/2.

27. Which of the following is true about the squared-error function E(p,G)?

A. Linear function of 4K parameters
B. Linear function of 4K+1 parameters
C. Non-Linear function of 4K parameters
D. Non-Linear function of 4K+1 parameters

The squared error function E(p,G) is a non-linear function of 4K+1 parameters.

28. Minimization of the error function over the remaining 4K parameters is performed by an iterative method.

A. True
B. False

Due to the non-linear nature of E(p,G), its minimization over the remaining 4K parameters is performed by an iterative numerical optimization method.

29. The iterative process may converge to a global minimum.
A. True
B. False