Anna University Regulation 2013 Information Technology (IT) IT6502 DSP 2marks & 16marks for all 5 units are provided below. Download link for IT 5th SEM IT6502 Digital Signal Processing Short answers, Question Bank are listed down for students to make perfect utilization and score maximum marks with our study materials.

FREQUENCY TRANSFORMATIONS

Part A – 2 Marks

1. Define DFT and IDFT (or) what are the analysis and synthesis equations of DFT

DFT (Analysis Equation)

IDFT (Synthesis Equation)

2. State the properties of DFT

- Periodicity
- Linearity and symmetry
- Multiplication of two DFTs
- Circular convolution
- Time reversal
- Circular time shift and frequency shift
- Complex conjugate
- Circular correlation

3. Define circular convolution

Let x1(n) and x2(n) are finite duration sequences both of length N with DFTs X1 (k) and X2 (k). If X3(k) = X1(k) X2(k) then the sequence x3(n) can be obtained by circular convolution defined as.

4. How to obtain the output sequence of linear convolution through circular convolution

Consider two finite duration sequences x (n) and h (n) of duration L samples and M samples. The linear convolution of these two sequences produces an output sequence of duration L+M-1 samples. Whereas, the circular convolution of x(n) and h(n) give N samples where N=max(L,M).In order to obtain the number of samples in circular convolution equal to L+M-1, both x(n) and h(n) must be appended with appropriate number of zero valued samples. In other words by increasing the length of the sequences x (n) and h(n) to L+M-1 points and then circularly convolving the resulting sequences we obtain the same result as that of linear convolution.

5. What is zero padding? What are its uses?

Let the sequence x (n) has a length L. If we want to find the N-point DFT (N>L) of the sequence x (n), we have to add (N-L) zeros to the sequence x (n). This is known as zero padding. The uses of zero padding are We can get better display of the frequency spectrum. With zero padding, the DFT can be used in linear filtering.

6. Define sectional convolution.

If the data sequence x (n) is of long duration it is very difficult to obtain the output sequence y(n) due to limited memory of a digital computer. Therefore, the data sequence is divided up into smaller sections. These sections are processed separately one at a time and controlled later to get the output.

7. What are the two methods used for the sectional convolution?

The two methods used for the sectional convolution are 1) The overlap-add method and 2) overlap-save method.

8. What is overlap-add method?

In this method the size of the input data block xi (n) is L. To each data block we append M-1 zeros and perform N point circular convolution of xi (n) and h(n). Since each data block is terminated with M-1 zeros the last M-1 points from each output block must be overlapped and added to first M- 1 points of the succeeding blocks.This method is called overlap-add method.

9. What is overlap-save method?

In this method, the data sequence is divided into N point sections xi (n). Each section contains the last M-1 data points of the previous section, followed by L new data points to form a data sequence of length N=L+M-1. In circular convolution of xi (n) with h (n) the first M-1 points will not agree with the linear convolution of xi(n) and h(n) because of aliasing, the remaining points will agree with linear convolution. Hence we discard the first (M-1) points of filtered section xi (n) N h (n). This process is repeated for all sections and the filtered sections are abutted together.

10. Why FFT is needed?

The direct evaluation DFT requires N2 complex multiplications and N2 –N complex additions. Thus for large values of N direct evaluation of the DFT is difficult. By using FFT algorithm, the number of complex computations can be reduced. Therefore, we use FFT.

11. What is FFT?

The Fast Fourier Transform is an algorithm used to compute the DFT. It makes use of the symmetry and periodicity properties of twiddle factor to effectively reduce the DFT computation time. It is based on the fundamental principle of decomposing the computation of DFT of a sequence of length N into successively smaller DFTs.

12. How many multiplications and additions are required to compute N point DFT using radix- 2 FFT?

The number of multiplications and additions required to compute N point DFT using radix-2 FFT are N log2 N and N/2 log2 N respectively.

13. What is meant by radix-2 FFT?

The FFT algorithm is most efficient in calculating N point DFT. If the number of output points N can be expressed as a power of 2 that is N = 2M, where M is an integer, then this algorithm is known as radix-2 algorithm.

14. What is DIT algorithm?

Decimation-In-Time algorithm is used to calculate the DFT of an N point sequence. The idea is to break the N point sequence into two sequences, the DFTs of which can be combined to give the DFT of the original N point sequence. This algorithm is called DIT because the sequence x (n) is often splitted into smaller sub- sequences.

15. What is DIF algorithm?

It is a popular form of the FFT algorithm. In this the output sequence X (k) is divided into smaller and smaller sub-sequences, that is why the name Decimation – In – Frequency.

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