# Linear Filtering Methods Based on DFT

This set of Digital Signal Processing Interview Questions & Answers focuses on “Linear Filtering Methods Based on DFT”.

1. By means of the DFT and IDFT, determine the response of the FIR filter with impulse response h(n)={1,2,3} to the input sequence x(n)={1,2,2,1}?
a) {1,4,11,9,8,3}
b) {1,4,9,11,8,3}
c) {1,4,9,11,3,8}
d) {1,4,9,3,8,11}

2. What is the sequence y(n) that results from the use of four point DFTs if the impulse response is h(n)={1,2,3} and the input sequence x(n)={1,2,2,1}?
a) {9,9,7,11}
b) {1,4,9,11,8,3}
c) {7,9,7,11}
d) {9,7,9,11}

3. Overlap add and Overlap save are the two methods for linear FIR filtering a long sequence on a block-by-block basis using DFT.
a) True
b) False

4. In Overlap save method of long sequence filtering, what is the length of the input sequence block?
a) L+M+1
b) L+M
c) L+M-1
d) None of the mentioned

5. In Overlap save method of long sequence filtering, how many zeros are appended to the impulse response of the FIR filter?
a) L+M
b) L
c) L+1
d) L-1

6. The first M-1 values of the output sequence in every step of Overlap save method of filtering of long sequence are discarded.
a) True
b) False

7. In Overlap add method, what is the length of the input data block?
a) L-1
b) L
c) L+1
d) None of the mentioned

8. Which of the following is true in case of Overlap add method?
a) M zeros are appended at last of each data block
b) M zeros are appended at first of each data block
c) M-1 zeros are appended at last of each data block
d) M-1 zeros are appended at first of each data block

9. In which of the following methods, the input sequence is considered as shown in the below diagram?

a) Overlap save method
c) Overlap add & save method
d) None of the mentioned

10. In which of the following methods, the output sequence is considered as shown in the below diagram?

a) Overlap save method
c) Overlap add & save method
d) None of the mentioned

11. What is the value of x(n)*h(n), 0≤n≤11 for the sequences x(n)={1,2,0,-3,4,2,-1,1,-2,3,2,1,-3} and h(n)={1,1,1} if we perform using overlap add fast convolution technique?
a) {1,3,3,1,1,3,5,2,2,2,3,6}
b) {1,2,0,-3,4,2,-1,1,-2,3,2,1,-3}
c) {1,2,0,3,4,2,1,1,2,3,2,1,3}
d) {1,3,3,-1,1,3,5,2,-2,2,3,6}

12. What is the value of x(n)*h(n), 0≤n≤11 for the sequences x(n)={1,2,0,-3,4,2,-1,1,-2,3,2,1,-3} and h(n)={1,1,1} if we perform using overlap save fast convolution technique?
a) {1,3,3,-1,1,3,5,2,-2,2,3,6}
b) {1,2,0,-3,4,2,-1,1,-2,3,2,1,-3}
c) {1,2,0,3,4,2,1,1,2,3,2,1,3}
d) {1,3,3,1,1,3,5,2,2,2,3,6}