B.E. Computers, IT Notes/Solved Question papers Maharashtra, Mumbai

Saturday, August 9, 2014

IMAGE PROCESSING [ELECTIVES] MAY 2012 ELECTRONICS AND TELECOMMUNICATION SEMESTER 8

Con. 4479-12. (REVISED COURSE) GN-8375
(3 Hours) [Total Marks : 100]

N. B. : (1) Question No. 1 is Compulsory.
(2) Attempt any four questions out of remaining six questions.
(3) Figures to the right indicate full marks.

1.	Justify the following statements :-	20
	(a) Poorly illuminated images cannot be easily segmented.
	(b) The median filtering perfoms well in images corrupted by impulse noise.
	(c) If kernel of an binze transform is seperable and symmetric, the transform
	can be expressed in matrix form.
	(d) The first derivate of chain code mormalize it to rotation.
	(e) the entropy of an image is maximized by histogram equalization.
2. (a)		6
	length N. Show that N2 orthogonal patterns (basic images) of size N x N
	can be generated using the sequences. Prove the orthogonality of
	these patterns.
(b)	Write first four Hass sequences of length N =4, using these sequences	6
	generate 16 orthogonal Hass patterns.
(c)	Using folloowing three orthogonal sequences show that 9 orthogonal	8
	patterns of size 3 x 3 can be generated. Give all patterns.
3. (a)	What is histogram of a digital image ? What information one can get by	8
	observing the histogram of images ?
(b)	Histogram of a digital binze with eight quantization level is given below.	12
	Perform histogram equalisation. Derive the transformation function
	and new histogram.
4. (a)	Write 8 x 8 Harr matrix and prepare butterfly diagram to compute Harr	10
	coeffcidents of a sequence of length n = 8.
(b)	Using above diagram compute Harr cofficidents of the following sequence.	10
	f(x) = {1 2 3 4 4 3 3 1}
	Evaluate the energy in each of the transform cofficidents.
5. (a)	What is 2-DDFT ? State the properties of DFT matrix applicable to	6
	images.
(b)	Write the expression for 1-D and 2-D. Discrete cosine transform.	6
	State its usefulness in image processing.
(c)	Obtain 2-D DFT of following 3 x 3 image.	8

6. (a)	What is image compression ? Explain different types of reduncies.	6
(b)	Explain the basic principle of transform coding for image compression and	7
	illustrate the save with the help of Discrete Fourier Transform (DFT) and
	Discrete Cosine Transform (DCT).
(c)	Find a set of code words and average word length using Hoff man coding	7
	scheme with symbol having different probabilities as given.
7.	Write short notes on :-	20
	(a) Texture analysis
	(b) Fourier Descriptors
	(c) Image Restoration
	(d) K-L transform
	(e) Moments.

IMAGE PROCESSING [ELECTIVES] MAY 2008 ELECTRONICS AND TELECOMMUNICATION SEMESTER 8

Con.3430-08. (REVISED COURSE) CO-3487

(3 Hours) [Total Marks:-100]

N.B:- (1) Question No.1 is compulsory.
(2) Attempt any four out of remaining six questions.
(3) Figures to the right indicate full marks.
(4) Assume suitable data wherever necessary and justify the same.

1. (a) Consider the image segment shown below:- [5 Marks]
3 1 2 1 (q)
2 2 0 2
1 2 1 1
(p) 1 0 1 2
Compute the lengths of the shortest 4, 8 and m-path between p and q.
(b) Explain Morphological thining algorithm. [5 Marks]
(c) Justify 'Quality of picture depends on no. of pixels and gray-levels. [5 Marks]
(d) Obtain the slant transformation of the image f(x,y) [5 Marks]

2. (a) Explain the separability and translation property of Discrete Fourier transform for an
image. [10 Marks]
(b) The square is represented by co-ordinates (1,1), (3,1), (1,3)and (3,3). If the square is
rotated by 45˚ clockwise and shifted by 2 units, obtain its new co-ordinates. [10 Marks]

3. (a) Gray level Histogram of an image is given below:- [10 Marks]

Compute the gray level Histogram of the output image obtained by enhancing the input
by histogram equalization technique. Draw input, output histogram along with its transfer
function.
(b)Apply prewitt and Laplacian operators on given image segment. use appropriate threshold.
Give output image before and after thresholding. [10 Marks]

4. (a) Write first four wash sequence of length N=4. Using these sequences generate sixteen
orthogonal walsh patterns. [10 Marks]
(b) Draw and explain block diagram of IPEG Encoder and Decoder. [10 Marks]

5. (a) Generate Huffman code for the given source. Calculate Entropy of the source, average

length code word and Huffman efficiency. [12 Marks]

(b) Consider an 8-pixels line of gray scale data as {12,12,13,13,10,13,57,54}. Which has
been uniformly quantized with 8 bit accuracy. Construct its IGS code. State and explain
in brief the type of redundancy which is exploited here to achieve compression. [8 Marks]

6. (a) Define opening and closing operations. perform these operations on following image
segment with given structuring element:- [10 Marks]

Image Segment Structuring Element
(b) For given boundary compute 4 path chain code find first difference, circular first
difference shape number and order of boundary. [10 Marks]

7. Write short notes on(any four):- [20 Marks]
(a) Pseudo color Image Processing
(b) Arithmetic Coding
(c) Brightness Adaption and Discrimination
(d) Region-oriented segmentation.
(e) Texture
(f) Moments

DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) May 2014

DISCRETE TIME SIGNAL PROCESSING

DISCRETE TIME SIGNAL PROCESSING (DTSP)
Semester 7
(3 Hours) May 2014

MV-19989
[Total Marks : 100]

N.B. :

(1)

Question No. 1 is compulsory.

(2)

Attempt any four questions out of remaining six questions.

(3)

Assumptions made should be clearly stated.

(4)

Figures to the right indicate full marks.

(a)

Obtain a digital filter transfer function H(ω) by applying Imputse invariance transformation on the analog TF.

H_a(s) = s/s² + 3s + 2 Use f_s = 1 K samples/sec.

(b)

Consider a filter with TF :
H(z) = (z^-1 - a) / (1 - az^-1)
Identify the type of filter and justify it.

(c)

Find the number of complex multiplications and complex additions required to find DFT for 32 point sequence. Compare them with the number of computations required if FFT algorithm is used.

(d)

Consider the sequence x(n) = δ(n) + 2δ(n - 2) + δ(n -3).
Find DFT of x(n).

(a)

A sequence is given as x(n) = {1 + 2j, 1 + 3j, 2 + 4j, 2 + 2j}
     (i) Find X(k) using DIT-FFT algorithm.
     (ii) Using the results in (i) and not otherwise find DFT of p(n) and q(n) where
             p(n) = { 1, 1, 2, 2}
             q(n) = { 2, 3, 4, 2}

(b)

X(K) = +36, -4 + j9.656, -4 + j 1.656, -4, -4 -j 1.656, -4 -j4, -4 -j9.656
Find x(n) using IFFT algorithm (use DIT IFFT).

(c)

Explain the properties of symmetricity and periodicity of phase factor.

(a)

By means of FFT-IFFT method (DIT algo) Compute Circular convolution of
x(n) = {2, 1, 2, 1} h(n) = {1, 2, 3, 4}

(b)

An 8 point sequence x(n) = {1, 2, 3, 4, 5, 6, 7, 8}

(i)	Find X(K) using DIF FFT algorithm
(ii)	Let x₁(n) = {5, 6, 7, 8, 1, 2, 3, 4} Using appropriate DFT property and answer of previous part, determine x₁(K)
(iii)	Again use DFT property and find X₂(K) where x₂(n) = x(n) + x₁(n).

(a)

Draw the Lattice filter realization for the all pole filter

H(z) = 1/1+3/4z^-1 +1/2z^-2 +1/4z^-3

(b)

Obtain DF-I, DF-II, cascade (First order sections) and parallel (First order sections) structures foe the system describe by
y(n) = -0.1 y( n -1) +0.72 y(n - 2) + 0.7 x(n) - 0.252 x(n -1).

(a)

Design a FIR low pass digital filter using Hamming window for N = 7

H_d(e^jw) = e^-3jω	-0.75Π < ω < 0.75Π
=0	0.75Π < \| ω \| < Π

(b)

A LPF has following specifications :-

0.8 < \| H (ω \| < 1	for 0 < ω < 0.2Π
\| H(ω \| < 0.2	for 0.6Π < ω < Π

Find filter order and analog cut off frequency if
(i) Bilinear transformation is used for designing
(ii) Impulse invariance is used for designing

(a)

Explain up sampling by an integer factor with neat diagram and waveforms.

(b)

Explain the need of a low pass filter with a decimator and mathematically prove that ω_y = ω_xD.

Write notes on any four of the following :-

(a)

Frequency sampling realization of FIR filters

(b)

Goertzel algorithm

(c)

Set top box for digital TV reception

(d)

Adaptive echo cancellation

(e)

Filter banks.

Friday, August 8, 2014

IMAGE PROCESSING [ELECTIVES] MAY 2011 ELECTRONICS AND TELECOMMUNICATION SEMESTER 8

1.	Answer the following question :-	20
	(a) Is the Huffman code optical ? Prove with an example.
	(b) Justify 'Quality of picture depends on the number of pixels and grey levels'.
	(c) Explain slant transform.
	(d) Justify/ contradict 'for digital Image having salt and pepper noise, median
	filter is the best'.
2. (a)	Explain the following Image Enhancement Techniques with application :-	15
	(i) Intensity level slicing
	(ii) Range Compression
	(iii) Edge detection.
(b)	Compare between contrast stretching and histogram equalization.	5
3. (a)	A 8 level image is given below :-	10
	Prepare the histogram of the given image.
	Perform Histogram equalization and draw New Histogram.
(b)	A source emits 8 symbols with the probabilities given :-	10
	Obtain Huffman code and calculate entropy, average code word length and coding
	efficiency.
4. (a)	Name different types of image segemenation techniques. Explain the splitting and	10
	merging technique with the help of an example.
(b)	Apply slant transform and DCT transform on the given image and compare the	10
	result.
5. (a)	What is Hadamard Transform ? Write a 4 x 4 Hadamard matrix and its application.	10
	Is H(4) Orthogonal and Normalized.
(b)	Apply Low and High Pass Spatial masks on the following image matrix. Prove	10
	that High Pass = Original - Lowpass. Assume virtual Rows and Columns.
6. (a)	Compare :-	10
	(i) Lossy and Lossless compression.
	(ii) Objective fidelity criteria and subjective fidelity criteria.
(b)	Explain segmentation based on discontinuty and segmentation based on	10
	similarities.
7.	Write short notes on any four of the follwoing :-	20
	(a) Haar Transform
	(b) Frequency domain filtering
	(c) Wiener Filtering
	(d) Spatial domain filtering
	(e) Connectivity of Pixels

IMAGE PROCESSING [ELECTIVES] DECEMBER 2008 ELECTRONICS AND TELECOMMUNICATION SEMESTER 8

Con.5796-08 (REVISED COURSE) RC-7328

(3 Hours) [Total Marks:-100]

N.B: (1) Question No.1 is compulsory.
(2) Attempt any four questions from remaining six.

1. (a) A CCD camerachip of dimensions 7 x 7 mm and having a resolution of 1024 x 1024
element is focused on a square flat area, located 0.5m away. How many line pairs/mm
will this camera be able to resolve. The camera is equipped with a 35 mm lens. [5 Marks]
(b) Explain the process of image averaging. [5 Marks]
(c) Explain intensity slicing technique used in pseudocolor image processing. [5 Marks]
(d) A binary image contains straight lines oriented horizontally, vertically at 45˚ and at-45˚. Give
a set of 3 x 3 masks that can used to detect 1-pixel long breaks in these lines. Assume that
gray level of the lines is 1 and gray level of background is zero. [5 Marks]

2. (a) Consider the images shown. The image on right is obtained by- [10 Marks]
(i) Multiplying image on left by (-1)
(ii) By computing DFT.
(iii) taking complex conjugate of transform
(iv) computing inverse of DFT
(v) Multiplying the real part by (-1)
Explain (mathematically) why image on right appears as it does.

(b) Suppose that you are given a set of images generated by an experiment dealing with stellar
events. Each image consists of a set of bright, widely scattered dots corresponding to
stars in sparsely occupied section of universe. The problem is that stars are barely visible,
due to superimposed illumination resulting from atmospheric dispersion. If these images
are modelled as a product of constant illumination component with a set of impulses,
give an enhancement procedure based on homomorphic filtering designed to bring out
the image components due to stars themselves.

3. (a) Find the edge corresponding to minimum cost path in subimage as shown. [15 Marks]

Assume that edge starts in first column and ends in last column.
(b) Justify: Poorly illuminated images cannot be segmented easily. [5 Marks]

4. (a) Explain the following boundary descriptors- [10 Marks]
(i) Statistical moments
(ii) Shape numbers
(b) What is limiting effect of repeatedly - [10 Marks]
(i) Dilating an image
(ii) Eroding an image
Assume that

5. (a) Explain use of LZW coding for image compression. [10 Marks]
(b) Describe JPEG 2000 image compression standard. [10 Marks]

6. (a) What would be effect of setting to zero the lower order and higher order bit planes in
general on histogram of image. [6 Marks]
(b) Show that Laplacian operation is invariant to rotation. [7 Marks]
(c) Discuss the limiting effect of repeatedly applying 3 x 3 low pass spatial filter to a digital
image. Ignore border effects. [7 Marks]

7. (a) For given orthogonal matrix A and image u. [10 Marks]
Find the transformed image and basis images.
(b) Find Euler number of following regions. [5 Marks]

Thursday, August 7, 2014

DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) December 2013

DISCRETE TIME SIGNAL PROCESSING

DISCRETE TIME SIGNAL PROCESSING (DTSP)
Semester 7
(3 Hours) December 2013

LJ-13936
[Total Marks : 100]

N.B. :

(1)

Question No. 1 is compulsory.

(2)

Attempt any four questions out of remaining six questions.

(3)

Assumptions made should be clearly stated.

(a)

Transfer functions of casual and stable digital filters are given below. State whether these filters are
Minimum . Maximum / Mixed Phased filters

(i)	H₁(Z)	(1-1/2z)(1-1/4z) ________________
		(Z-1/3)(Z-1/5)
(ii)	H₂(Z)	(1-1/2z)(1-1/4z) _________________
		(Z-1/3)(Z-1/5)
(iii)	H₃(Z)	(1-1/2z)(1-1/4z) _________________
		(Z-1/3)(Z-1/5)

(b)

Compute DFT of the sequence X_1,(n) = {1, 2, 3, 4} using property and not otherwise compute DFT of X_2,(n) = {1+j, 2+2j, 4+4j, 2+2j}

(c)

The impulse response of a system is h(n) = aⁿu(n), a ≠ 0. Determine a and sketch pole zero plot for this system to act as :-

(i) Stable low pass filter.
(ii) Stable high pass filter.

(d)

Draw direct form structure for a filter with transfer function,
H(z) = 1 + 3z^-1 +2z^-3 + 4z^-4

(a)

Consider a filter with impulse response, h(n) = {0.5, 1, 0.5}. Sketch its amplitude spectrum. Find its response to the inputs

(i) X₁(n) = cos (nΠ/2)
(ii) X₂(n) = 3 + 2 δ (n) -4 cos (nΠ/2)

(b)

Determine circular convolution of x(n) = {1,2,1,4} and h (n) = {1,2,3,2} using time domain convolution and radix-2FFT. Also find circular correlation using time domain correlation.

(a)

Explain overlap and add method for long filtering. Using this method find output of a system with impulse response, h(n) = {1,1,1} and input x(n) = {1, 2, 3, 3, 4, 5}.

(b)

Compute DFT of a sequence, x(n) = {1,2,2,2,1,0,0,0} using DIF-FFT algorithm. Sketch its magnitude spectrum.

(a)

Draw lattice filter realization for a filter with the following transfer function.
H(z) = 1/1 + 13/24Z^-1 +5/8z^-2 +1/3z^-3

(b)

Design a low pass Butter worth filter with order 4 and passband cut off frequency of 0.4Π. Sketch pole zero plot. Use Bilinear transformation. Draw direct form II structure for the designed filter.

(a)

Design an FIR Bandpass filter with the following specifications :-
     Length : 9
     stop band cut off frequency : 0.7Π
     Use Hanning window.

(b)

The transfer function of a filter has two poles at z=0, two zeroes at z=-1 and a dc gain of 8. Final transfer function and impulse response.

Is this a casual or noncasual filter?
is this a linear phase filter?
If another zero is added at z =-1 find transfer function and check whether it is a linear phase filter or not.

(a)

Transfer function of an FIR filter is given by H(z) = 1-z^-N
Sketch pole zero plots for N = 4 and N = 5
Prove that it is a comb filter.

(b)

Write about frequency sampling realizationof FIR filters.

(a)

Explain the process of decimation for reducing sampling rate of signal.

(b)

Compare various windows used for designing FIR filters.

B.E. Electronics & Telecommunication, Wireless Networks (WN), Semester 8, December 2012.

B.E. Electronics & Telecommunication,

Wireless Networks (WN), Semester 8, December 2012.

Con. 10020-12

KR- 5094

(REVISED COURSE)

(3 Hours)

[Total Mark: 100]

N.B. (1) Question No 1 is compulsory.

(2) Attempt any four questions out of remaining six questions.

(3) Draw neat sketches wherever required.

(4) Assume suitable data if required.

1. (a) What is role of General Packet Radio Services (GPRS) in the GSM. ---- (5 Marks)

(b) Why is power control used in CDMA 2000 and WCDMA? ---- (5 Marks)

(c) Explain the security aspect of Bluetooth. ----- (5 Marks)

(d) Write various uses of Wireless Sensor Network. ---- (5 Marks)

2. (a) Explain UMTS network reference architecture in detail. ----- (10 Marks)

(b) Discuss QoS attributes used in UMTS. ----- (10 Marks)

3. (a) Discuss the forward and reverse link channels in CDMA 2000.----- (10 Marks)

(b) Explain evolution of IS – 95 in detail. --- (10 Marks)

4. (a) Explain Link budget analysis and requirements of wireless network. ---- (10 Marks)

(b) Draw and explain WAP programming model in detail. ---- (10 Marks)

5. (a) Define and explain different terms used in Bluetooth. ---- (10 Marks)

(b) Explain wireless sensor network protocol stack in detail. ----- (10 Marks)

6. (a) Compare all versions of IEEE 802.11 WLAN. ----- (10 Marks)

(b) Give the advantages, disadvantages and application of WAP. ---- (10 Marks)

7. (a) Compare CDMA 2000 and WCDMA. ----- (10 Marks)

(b) Write a short note on RFID. ---- (10 Marks)

IMAGE PROCESSING [ELECTIVES] MAY 2013 ELECTRONICS AND TELECOMMUNICATION SEMESTER 8

Con. 9068-13. (REVISED COURSE) GS-3901
(3 Hours) [Total Marks : 100]

N.B. (1) Question No. 1 is Compulsory.
(2) Attempt any four questions out of remaining six questions.
(3) Assume suitable data wherever necessary.

1. (a)	Is there any advantage of frequency domian filters over special filters ? Why ?	5
(b)	Compare Canny edge detector with Laplacian of Gaussian Gaussian edge detector.	5
(c)	Why is zig-zig scanning preferred in JPEG standard.	5
(d)	Distinguish between lossy and lossless compression.	5
2. (a)	Explain image sampling and quantisation. A medical image has a size of 8 x 8 inches.	10
	The sampling resolution is 5 cycles/mm. How many pixels are required ? Will and
	image of size 256 x 256 be enough.
(b)	Let V = {0, 1}. Compute De, D4, D8 and Dm distances between two pixels p and	10
	q . Let the pixel coordinates of p and q be (3, 0) and (2, 3) respectively for the image
	shown. Find distance measures.
3. (a)	Compute 2-D DFT of 4 x 4 gray scale image given below and then compute inverse	10
	2- D DFT of transform coefficient.
(b)	Explain with example how Slant transform and DCT transform of (4 x 4) image	10
	can be used for image compression.
4. (a)	For a given image find -	10
	(i) Digital negative of an image.
	(ii) Contrast stretching r2 = 5, r1 = 3, s2 = 6, s1 = 2
	(iii) Bit plane slicing.
(b)	Explain image enhancement in frequency domain.	10
5. (a)	Perform histogram equalization for 8 x 8 image shown in table.	10
	Image gray level distribution
(b)	Explain segmentation based on discontinuity and segmentation based on similarities.	10
6. (a)	Calculate entropy and coding redundancy for the symbols given in table using Huffman	10
	codes.
(b)	What is difference between image enhancement and image restoration ?	5
(c)	Explain modeling the degradation function in image restoration.	5
7.	Write short notes on any two :-
	(a) Wiener Filtering	10
	(b) Hotellig Transform	10
	(c) Homomorphic filter.	10

B.E. Electronics & Telecommunication, Wireless Networks (WN), Semester 8, December 2013.

B.E. Electronics & Telecommunication,

Wireless Networks (WN), Semester 8, December 2013.

Con. 8981–13.

LJ - 13868

(REVISED COURSE)

(3 Hours)

[Total Mark: 100]

N.B. (1) Question No 1 is compulsory.

(2) Attempt any four questions out of remaining six questions.

(3) Draw neat sketches wherever required.

(4) Assume suitable data if required.

1. (a) List out of components of sensor nodes. ---- (5 Marks)

(b) What is adaptive multirate coding? ---- (5 Marks)

(c) Explain the concept of hidden node and exposed node with respect to WLAN.---- (5 Marks)

(d) List out services provided by 3G Networks. ---- (5 Marks)

2. (a) Explain park, hold and sniff mode of operations in Bluetooth. Draw the complete flow diagram for network connection establishment in Bluetooth. --- (10 Marks)

(b) Compare WAP and imode protocol stack. ---- (10 Marks)

3. (a) Explain sensor Network protocol stack in detail. ----- (10 Marks)

(b) Explain the concept of High Speed Downlink packet access in detail.---- (10 Marks)

4. (a) Calculate the uplink cell load factor and number of voice user for a WCDMA system using the following data. What is the pole capacity of the cell? ----- (10 Marks)

Information rate (Ri) : 12.2 kbps
Chip ratr (Rc) : 3.84 Mcps
Required Eb/Nt : 4 dB
Required interference margin : 3 dB
Interference factor due to other cells : 0.5
Channel activity factor : 0.65

(b) Explain transmit diversity present in forward link of cdma 2000.---- (10 Marks)

5. (a) Explain link budget analysis and requirements of wireless networks. ---- (10 Marks)

(b) Explain UMTS network architecture. List important features of the UMTS interface. Support your answer with neat block diagram.---- (10 Marks)

6. Write short note on : ---- (20 Marks)

(a) Zigbee Protocol

(b) Wimax

7. (a) Explain LR – WPAN device architecture with suitable diagram . ---- (10 Marks)

(b) State and explain commonly used wireless LAN topologies with diagram. ---- (10 Marks)

IMAGE PROCESSING ELECTIVES DECEMBER 2007 ELECTRONICS AND TELECOMMUNICATION SEMESTER 8

Con.5857-07. (REVISED COURSE) CD-7206

(3 Hours) [Total Marks:-100]

N.B:- (1) Question No.1 is compulsory.
(2) Answer any four out of remaining six questions.
(3) Figures to the right indicate full marks.
(4) Assume suitable data if necessary.

1) Justify/Contradict following statements(Any five):- [20 Marks]
(a) For digital image having salt and pepper noise median filter is the best.
(b) Continuous image histogram can be perfectly equalized, but it may not be so for Digital Image.
(c) Run length coding always gives data compression.
(d) Quality of picture depends on number of pixels and gray levels that represent the picture.
(e) All image compression techniques are invertible.
(f) Magnitude and determinant of unity Transform is unity.

2. (a) Gray level Histogram of an image is given below:- [10 Marks]

Gray Levels	0	1	2	3	4	5	6	7
No of pixels	0	0	26	39	16	84	20	0

Compute Gray Level Histogram of the output image obtained by enhancing the input by
histogram equalization technique.
(b) Assume that edge starts in the first row and ends in the last row for the following gray
image. [10 Marks]
5 6 1
6 7 0
7 1 3
Sketch all possible paths and determine edge corresponding to minimum cost path.

3. (a) Explain basic principles of detecting following in the images. [10 Marks]
(i) Lines (ii) Points (iii) Edges
Give 3x3 mask for each of them and explain their operation.
(b) Find Huffman code for the following six symbols. The symbols and their probabilities are
given in tabular form.

Symbol	A1	A2	A3	A4	A5	A6
Probability	0.1	0.4	0.06	0.1	0.04	0.3

4. (a) Explain the following techniques [10 Marks]
(i) Arithmetic Coding (ii) Bit plane coding
(b) Explain method of segmentation of images by region splitting and merging. [10 Marks]

5. (a) Explain Replication and Linear Interpolation method of zooming. Apply these techniques
to following image and obtain zoomed image

(b) Show that 2D-DCT of an image can be computed by row and column passes with
1D DCT algorithm. [10 Marks]

6. (a) For 2x2 transform A & Image U [10 Marks]

Calculate transformed Image V & the basic image.
(b) Prove two Dimensional Energy Conservation relation. [10 Marks]

Where f(x,y) represent 2D Image signal and F(u,v) represent transform image

7. Write short notes on (any four) [20 Marks]
(i) Uniform and Nonuniform sampling.
(ii) Fourier Descriptor
(iii) Chain Code
(iv) Descrete Fourier Transform
(v) Connectivity of pixels

DISCRETE TIME SIGNAL PROCESSING (DTSP) Semester 7 (3 Hours) May 2013

DISCRETE TIME SIGNAL PROCESSING

DISCRETE TIME SIGNAL PROCESSING (DTSP)
Semester 7
(3 Hours) May 2013

GS-5332
[Total Marks : 100]

N.B. :

(1)

Question No. 1 is compulsory.

(2)

Attempt any four questions out of remaining six questions.

(3)

Assumptions made should be clearly stated.

(4)

Assume any suitable data wherever required but justify the same.

(5)

Figures to the right indicate marks.

(6)

Illustrate the answer with sketches wherever required.

(7)

Answer to the questions should be grouped and written together

(8)

Use Blue/Black ball ink pen to write answers. Use of pencil should be done only to draw sketches and graphs.

(a)

Assume that a complex multiplier takes 1 micro sec to perform one multiplication and that the amount of time to compute a DFT is determined by the amount of time to perform all the multiplications.

(i) How much time does it take to compute a 1024 point DFT directly?
(ii) How much time is required is FFT is used?

(b)

Let h[n] be the unit impulse response of a Low Pass filter with a cutoff frequency ω_c, What type of filter has a unit sample response g[n] = (-1)^u h[n].

(c)

A two pole low pass filter has the system function H(z) = b₀/(1-pz^-1)² Determine the values of b₀ and P such that the frequency response H(ω) satisfies the condition
| H(0) | = 1 and | H(Π/4)² | = 1/2

(d)

Consider filter with transfer function. Identify the type of filter and justify it.

	H(z) =	Z^-1 - a ^{__________________}
		1 - az^-1

(a)

the unit sample response of a system is h(n)={3,2,1} use overlap-add method of linear filtering to determine output sequence for the repeating input sequence x[n] =
{2,0,-2,0,2,1,0,-2,-1,0}

(b)

For a given sequence x(n) = {2,0,0,1}, perform following operations:-

(i)	Find out the 4 point DFT of x(n)
(ii)	Plot x(n), its periodic extension X_P(n) and X_P(n-3)
(iii)	Find out 4 point DFT of X_p(n-3)
(iv)	Add phase angle in (i) with factor -[2Πrk/N] where N=4, r=3 k=0, 1, 2, 3
(v)	Comment on the result you had in point (i) and (ii)

(a)

The transfer function of discrete time casual system is given below:-

H(z) =	1-z^-1 ^{__________________}
	1 - 0.2z^-1 - 0.15z^-2
(i)	Find the difference equation
(ii)	Draw cascade and parallel realization
(iii)	Show pole-zero diagram and then find magnitude at ω = 0 and ω = Π
(iv)	Calculate the impulse the laesponse of the system.

(b)

Obtain the lattice realization for the system :

	H(z) =	1 + 3z^-1 + 3z^-2 + z^-3 ^{__________________}
		1+3/4z^-1 + 1/2z^-2 + 1/4z^-3

(a)

What is linear phase filter? What conditions are to be satisfied by the impulse response of an FIR system in order to have a linear phase? Plot and justify compulsory zero locations for symmetric even ant symmetric even and antisymmetric odd FIR filters.

(b)

Determine the zeros of be following FIR system and indicate whether the system is minimum phase, maximum phase, or mixed phase.

H₁(z)	=	6 + z^-1 - Z^-2
H₂(z)	=	1 - z^-1 - 6z^-2
H₁(z)	=	1 - 5/2z^-1 - 3/2z^-2
H₁(z)	=	1 + 5/3z^-1 - 2/3z^-2

Comment on the stability of the minimum and maximum phase system

(a)

A digital low pass filter is required to meet the following specifications :-

Pass Band ripple	:	< 1dB
Pass Band edge	:	4 KHz
Stop Band attenuation	:	> 40 dB
Stop Band edge	:	8 KHz
Sampling rate	:	24 KHz

Find order, cutoff frequency and pole locations for Butterworth filter using bilinear transformation

(b)

Design an FIR digital filter to approximate an ideal low-pass filter with passband gain of unity, cut-off frequency of 950 Hz and working at a sampling frequency of Fs = 5000 Hz. The length of the impulse response should be 5. Use a rectangular window.

(a)

Explain the need of a low pass filter with a decimator and mathematically prove that
ω_y = ω_xD

(b)

Why is the direct form FIR structure for a multirate system inefficient? Explain with neat diagrams how this inefficency is overdone in implementing a decimator and an interpolator.

Write notes on any four of the following :-

(a)

DTMF detection using Goertzel algorithms

(b)

Filter banks

(c)

Comparison of FIR and IIR filters

(d)

Split radix FFT

(e)

Optimum Equiripple Linear phase FIR filter design.