Thapar University 2006 B.Tech Electronics and Communications Engineering DIGITAL SIGNAL PROCESSING - Question Paper

1

a)

Determine the response of the LTI system y(n)=5 y(n-l) - y(n-2) + 6 x(n) to the input signal x(n)= 5 (n) - 0.2 S (n-1).

6

b)

Comment upon the linearity, causality, stability and time invariance propert of the discrete time system and jutify your answer

i) y(n) - x(2n) ii) y(n) = x(-n+2) iii) y(n) = x(n) u(n)

6

c)

Explain the concept of frequency in continuous and discrete time domain.

2.4

2

a)

Find the Z-transform of the following:

i) x(n) = n²u(n) ii) x(n) = naⁿu(n) -1 < a <1 iii) x(n) = (l/2)ⁿ [u(n)-u(n-10)]

6

b)

Find the inverse Z-transform of the following:

,>*<- lose-;") - O.SX

Hi) X(z). ^z'+^2z" z² - z + 0.3561

6

c)

Explain the requirement of Region of Convergence (ROC) in Z-transform.

2.4

3

a)

Calculate the linear convolution, circular convolution, auto correlation and cross correlation of the sequences x(n) = [1,2,3,4] and h(n) = [ 1,2,1,1].

6

b)

Compute the 8-point DFT of Hanning window using radix-2 DIT algorithm with the help of neat sketch.

6

c)

List the properties of Discrete Fourier transform.

2.4

4

a)

A filter function h(n)= [2 ,1 ,0,1] is given and it is desired to filter a long data sequence

x(n)= [ 1,2, 4, 6, 5, 3,4, 2, 1, 3, 5, 7, 5, 3, 2, 1, 3, 4, 5, 6, 5, 4.......]. Calculate the output of the

filter for the given filter function using a method of filtering oflong data sequences.

6

b)

Using Divide and conquer approach calculate the discrete Fourier transform of signal x(n)=[ 1,2, 1,2, 1,1, 1,1, 0,1, 0,1, 1,2, 3,4]

6

c)

What is alias frequency? Explain with suitable example.

2.4

5

0

Obtain the coefficients of a linear phase FIR filter to meet the specifications given below using the window method.

Stopband attenuation 41 dB Passband ripple 0.01 dB Transition width 5 kHz Sampling frcqucncy 100 kHz Ideal cutoff frequency 12 kHz

6

b)

Using pole-zero placement method, obtain the transfer function, realization and the difference equation of a digital notch filter that meets the following specifications:

Notch frequency 50 IIz 3 dB width of notch 5 Hz Sampling Frequency 500 Hz

6

c)

Differentiate FIR and HR filters.

2.4

6

a)

A requirement exists to simulate in a digital computer an analog system with the following normalized characteristics:

ms)=-

S +S+ 1

Obtain a suitable transfer function using the impulse invariant method. Assume a sampling frequency of 10 kHz and a 3 dB cutoff frequency of 1.5 kHz.

*>)

Determine, using BZT method the transfer function and difference equation for the digital equivalent of resistance- capacitance (RC) filter shown in figure below. Assume a sampling frequency of 150 Hz and cut off of 30 Hz.

O

o----WV--J-------)(i)

T^c

6

c)

Discuss the design of an FIR filter using Kaiser window. Also give the required equations.

2.4

7

a)

Explain in detail the process of conversion of an analog signal to digital signal.

6

b)

Discuss Butterworth, Chebyshev and Elliptical Filter approximations in detail.

6

c)

List various applications of DSP and discuss any one of them in detail with neat sketch.

2.4