# FIR Least Squares Filters

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “FIR Least Squares Inverse Filters”.

1. Wiener filter is an FIR least-squares inverse filter.
a) True
b) False

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)

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)

4. It is not desirable to restrict the inverse filter to be FIR.
a) True
b) False

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

6. What should be the length of the truncated filter?
a) M
b) M-1
c) M+1
d) Infinite

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

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

9. The auto correlation of the sequence is required to minimize ε.
a) True
b) False

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

11. FIR filter that satisfies ∑Mk=0bkrhh(k−l)=rdh(l), l=0,1,…M is known as wiener filter.
a) True
b) False

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

13. If the set of linear equations from the equation ∑Mk=0bkrhh(k−l)=rdh(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

14. What is the number of computations proportional to, in Levinson-Durbin algorithm?
a) M
b) M2
c) M3
d) M1/2