# (Aktu Btech) Digital Signal Processing Important Unit-4 DFT and FFT

With the help of the B.Tech. AKTU Quantum Book, master the skill of digital signal processing. Gain access to important notes, frequently asked questions, and insightful knowledge in this area. Unit-4 DFT and FFT

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Important Questions For Digital Signal Processing:
*Quantum               *B.tech-Syllabus
*Circulars                *B.tech AKTU RESULT
* Btech 3rd Year    * Aktu Solved Question Paper```

## Q1. Calculate the DFT of x(n) = cos an.

Ans. Given: x(n) = cos an

To Find: DFT.

2. Putting n = 0, 1,………….N-1

## Q2. Find the 10-point DFT of the following sequence:

Ans. 1. For 10 point DFT, N= 10

## Q3. Determine the 4-point discrete time sequence from its DFT X(k) = {4, 1 – j, -2, 1 + j}.

Ans. 1. IDFT is defined as

6. Therefore, the IDFT of the given DFT produces the following four point discrete time sequence.

x(n) = {1, 2, 0, 1}

## Q4. Derive the relation between DFT and z-transform of a discrete time sequence x(n).

Ans. 1. The z-transform of x(n) is given as

2. If X(z) is sampled at the N equally spaced points on the unit circle, these points will be

3. The R.H.S. of eq. (4.10.1) is DFT X(k), thus the relationship between DFT and z-transform

## Q5. Compute the circular convolution of two discrete time sequences x1 (n) = {1,2, 1,2} and x2 (n) = {3, 2, 1, 4}.

Ans. Given: x1 (n) = {1,2, 1,2}, x2 (n) = {3, 2, 1, 4}

To Find: Circular convolution.

## Q6. Find the linear convolution using circular convolution of the following sequence:

x(n) = {1,2, 1}, h(n) = {1, 2}.

Ans. Given: x(n) = {1,2, 1}, h(n) = {1, 2}

To Find: Linear convolution.

3. Let us make length of x(n) and h(n) equal to 4 by adding zeros at end.

5. Substituting the values of W4 and xn in eq. (4.17.1), we get