DSP (FFT & DFT)

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

• True

• False

For a decimation-in-frequency FFT algorithm, which of the following is true?

• Both input and output are in order

• Both input and output are shuffled

• Input is shuffled and output is in order

• Input is in order and output is shuffled

FFT may be used to calculate

1) DFT

2) IDFT

3) Direct Z transform

4) In direct Z transform

• a. 1, 2 and 3 are correct

• b. 1 and 2 are correct

• c. 1 and 3 are correct

• d. All the four are correct

W_N^k+N/2=?

• a) W_N^k

• b) -W_N^k

• c) W_N^-k

• d) None of the mentioned

What is the circular convolution of the sequences X1(n)={2,1,2,1} and x2(n)={1,2,3,4}?

• a) {14,14,16,16}

• b) {16,16,14,14}

• c) {2,3,6,4}

• d) {14,16,14,16}

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

• a) Overlap save method

• b) Overlap add method

• c) Overlap add & save method

• d) None of the mentioned

What are the twiddle factors associated with stage-2 of DIT FFT algorithm.

• W₈⁰

• W₈⁰, W₈²

• W₈⁰,W₈¹,W₈²,W₈³

• None of these

Compute the 4 point DFT of [1,0,1,0] using radix-2 DIT FFT algorithm

• [2,0,2,0 ]

• [4,0,4,0]

• [8,0,8,0]

• [1,0,1,0]

If X(k) discrete Fourier transform of x(n), then the inverse discrete Fourier transform of X(k) is:

• $\frac{1}{N}\sum_{k=0}^{N-1}X\left[k\right]e^{\frac{j\ 2\ \pi\ n\ k}{N}}$

• $\frac{1}{N}\sum_{k=0}^{N-1}X\left[k\right]e^{\frac{-\ j\ 2\ \pi\ n\ k}{N}}$

• $\sum_{k=0}^{N-1}X\left[k\right]e^{\frac{j\ 2\ \pi\ n\ k}{N}}$

• $\sum_{k=0}^{N-1}X\left[k\right]e^{\frac{-\ j\ 2\ \pi\ n\ k}{N}}$

DFT is applied to

• Infinite sequences

• Finite discrete sequences

• Continuous infinite signals

• Continuous finite sequences