EC4091 DSP Laboratory

National Institute of Technology Calicut

September 9, 2013

1 Background reading, explain the following:

1. DTFT

2. DFT

3. Multiplication, circular convolution

2 Implement

1. Sample the sinusoid xa = 3sin (2πFt), where F = 2kHz at samplingfrequency, Fs = 8kHz and plot the sampled signal.

(a) Plot the frequency spectrum of the above signal.

(b) The magnitude spectrum is sampled at frequencies wk = 2πkN , k =

0, 1 · · ·N − 1. Plot sampled spectrum for N = 5, N = 50 and N =100.

(c) Obtain DFT of the sampled signal usingX (k) = 1N

∑N−1n=0 x (n) e

j2πkn/N .Plot for N = 5, 50, 100 and compare to output of part b.

2. x1 (n) = [1 2 3] and x2 (n) = [2 3], Obtain their respective 5−point DFTs,

(a) Multiply the two DFTs and plot output.

(b) Show relation to circular convolution using necessary plots.

3 Results and discussion

1. What is the signi�cance of the variable N here?

1