# Least Squares Design Method MCQ [Free PDF] – Objective Question Answer for Least Squares Design Method Quiz

1. Which of the following filter we use in least-square design methods?

A. All zero
B. All pole
C. Pole-zero
D. Any of the mentioned

Let us assume that hd(n) is specified for n > 0, and the digital filter is an all-pole filter.

2. Which of the following are cascaded in this method?

A. Hd(z), H(z)
B. 1/Hd(z), 1/H(z)
C. 1/Hd(z), H(z)
D. Hd(z), 1/H(z)

In this method, we consider the cascade connection of the desired filter Hd(z) with the reciprocal, all zero filter 1/H(z).

3. If δ(n) is the input, then what is the ideal output of yd(n)?

A. δ(n)
B. 0
C. u(n)
D. None of the mentioned

We excite the cascade configuration by the unit sample sequence δ(n). Thus the input to the inverse system 1/H(z) is hd(n) and the output is y(n). Ideally, yd(n)= δ(n).

4. What should be the value of y(n) at n=0?

A. 0
B. -1
C. 1
D. None of the mentioned

The condition that yd(0)=y(0)=1 is satisfied by selecting b0=hd(0).

5. The error between the desired output and actual output is represented by y(n).
A. True
B. False

For n > 0, y(n) represents the error between the desired output yd(n)=0 and the actual output.

6. Which of the following parameters are selected to minimize the sum of squares of the error sequence?

A. {bk}
B. {ak}
C. {bk} & {ak}
D. None of the mentioned

The parameters {ak} are selected to minimize the sum of squares of the error sequence.

7. By integrating the error equation with respect to the parameters {ak}, we obtain a set of linear equations.

A. True
B. False

By differentiating the square of the error sequence with respect to the parameters {ak}, it is easily established that we obtain the set of linear equations.

8. Which of the following operation is done on the sequence in the least-square design method?

A. Convolution
B. DFT
C. Circular convolution
D. Correlation

In a practical design problem, the desired impulse response hd(n) is specified for a finite set of points, say 0 < n d(n).

9. The least squares method can also be used in a pole-zero approximation for Hd(z).

A. True
B. False

We know that we can perform pole-zero approximation for Hd(z) by using the least-squares method.

10. In which of the following condition we can use the desired response hd(n)?

A. n < M
B. n=M
C. n > M
D. none of the mentioned

Nevertheless, we can use the desired response hd(n) for n < M to construct an estimate of hd(n).

11. Which of the following parameters are used to determine zeros of the filter?

A. {bk}
B. {ak}
C. {bk} & {ak}
D. None of the mentioned

The parameters {bk} are selected to determine the zeros of the filter that can be obtained where h(n)=hd(n).

12. The foregoing approach for determining the poles and zeros of H(z) is sometimes called Prony’s method.

A. True
B. False

We find the coefficients {bk} by pade approximation and find the coefficients {ak} by the least-squares method. Thus the foregoing approach for determining the poles and zeros of H(z) is sometimes called Prony’s method.

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

A. True
B. False

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

14. 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).

15. 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.

16. 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.

17. 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).

18. 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.

19. 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.

20. 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.

21. 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).

22. 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).

23. 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.

24. 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).

25. 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.

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

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