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Specimen Question Papers Specimen Question Papers: Important Note: The questions in these papers are meant to illustrate the general format, style, distribution, weight, degree of difficulty, time factor etc. (as there are no papers from previous years to refer to.) Students are advised to prepare for ALL topics covered in the class, and not to neglect those topics which may not have been included in the following papers. This section carries 50 marks and is meant to be completed in 1½ hours. Paper I Q1 a) Discuss the classification of sequences, giving one example of each type (8) b) Comment with proof on the linearity, causality, stability and time invariance of the system y[n] = nx[n] (8) or Q1 a) Explain the relationship between single and double pole locations in the z-plane and the impulse response. (8) b) If g[n] is an even sequence and h[n] is an odd sequence state with proof which of the following is odd and which is even 1) v[n] = h[n]h[n] 2) x[n] = g[n]h[n] (8) Q2 a) Explain the differences between FIR and IIR Filters and mention their advantages and disadvantages. (8) b) A FIR LPF is required with specifications pass-band edge frequency = 1.5 kHz transition width =0.5 kHz, and f c is centred on the transition band. Stop-band attenuation >50 dB sampling frequency = 8 kHz Select a suitable window and find N. .If the window is w(n) = 0.54 + 0.46 Cos(2 π n/N) find filter impulse response coefficients h ( −2) and h (2) (8) or Q2 a) How will you perform the geometric evaluation of the frequency response of a LTI system? (8) b) What are window functions? How are they useful? Give the properties of the Hamming window.(8) Q3 Any Three: (18) a) Notch and comb filters b) Sampling c) Concept of pipelining in DSP processors d) TMC320C25 processor architecture. Paper II Q1 a) What are the differences in the concept of frequency for continuous and discrete signal? explain. (8) b) State with proof whether y[n] = x 2[n] – x[n-1]x[n+1] is linear or not. (8) or Q1 a) Explain classification of discrete time systems with reference to their output/input relationships (8) b) A system has its impulse response h(n) defined over 0 ≤ n ≤ N-1. If N =7 and h[n] = h[N-n-1] prove that the system has a linear phase characteristic and find the phase delay. (8) Q2 a) Write a note on the frequency sampling method of filter design (8) b) A filter is required to meet the following specifications : complete signal rejection at DC and 250 Hz, narrow pass-band centred at 125 Hz, 3 – dB bandwidth of 10 Hz. If sampling frequency is 500 Hz, obtain the transfer function and difference equation by pole-zero placement. (8) or Q2 a) Discuss the conversion of a low-pass filter H(z) and h(n) to a high-pass filter system function and impulse response. Give example/s and proof (8) b) Explain the reason for pre-warping in IIR filter design using Bilinear transformation. (8) Q3 Answer any THREE (18) a) Types and properties of Linear phase FIR functions. b) Band transformations in IIR filter design. c) Differences between conventional and DSP processors d) The ADSP2100 processor architecture Paper III Q1 a) Discuss the classification of different types of signals, giving an example of each type (8) b) If y[n] = x[n +1] – 2x[n] +x[n −1], is the system linear? Time invariant? causal? (8) or Q1 a) Discuss the concepts of linearity, time invariance, stability and causality of systems (8) b) If y[n] = ay[n −1] + bx[n] n ≥ 0 and a and b are constants, find the expression for the output y[n] in terms of the input samples and initial condition y[-1]. Is the system linear if y[-1] = 1? (8) Q2 a) Discuss the computer-aided design of FIR filter using the Remez algorithm. (8) b) A RC (analogue) filter has a normalised transfer function 1/(s+1). It is to be used to design a digital filter with a cut-off 30 Hz, and sampling frequency is 150 Hz Use the BZT to find the transfer function and difference equation of the digital filter. (8) or Q2 a) Discuss the digital resonator. (8) b) Explain the sources of errors in implementation of IIR digital filters. (8) Q3 a) Analogue filter prototypes used for IIR digital filter design (18) b) Harvard architecture c) Simple FIR Filter design by pole-zero placement d) Architecture of DSP56000 THE MAHARAJA SAYAJIRAO UNIVERSITY OF BARODA First Semester of BE IV (Electronics) examination 2000 Wednesday, November 29 3 PM to 6 PM Digital Signal Processing N.B.: i) Answer the two sections in separate answer-books . ii) All Questions carry equal marks. iii) Suitable assumptions may be made wherever required,. Maximum marks: 100 SECTION I Q1 a) Find the Z-transform of the following and give their ROC i) x(n) = -αn U(-n-1) ii) x(n) = cos (n π/2)U(n) b) Obtain the parallel structure for the following system 1(2 − z −1 )(1+ 2z −1 + z −2 ) H ()z = 1( + 5.0 z −1 )(1− 9.0 z −1 + 0.81z −2 ) OR Q1 a) Determine the causal signal x(n) having the Z-Transform 1 i) X ()z = 1( − 2z −1 )(1− z −1) 2 1− 1 z −1 ii) X ()z = 2 1− z −1 + z −2 b) Obtain the cascade structure for the system 1+ 1 z −1 H ()z = 2 ()− −1 + 1 −2 ()− −1 + 1 −2 1 z 4 z 1 z 2 z Q2 a) Define (i) FIR, (ii) IIR and (iii) LTI Systems. The LTI system described by 1 y() n = y( n − )2 + x() n 4 is initially at rest. Determine its impulse response and sketch roughly its magnitude response. b) The sequence x(nT) is derived from a continuous time waveform x(t). Find the relationship between the frequency response of the discrete sequence to the Fourier transform of the continuous time waveform and explain. Q3 a) Using the DFT, IDFT find the convolution of the following two sequences x1(n) = (2,1,2,1) x2(n) = (1,2,3,4) b) Write notes on the following (i) Periodogram (ii) Use of DFT in Power Spectral Estimation 2 OR Q3 a) Describe fully the overlap add method. b) Discuss Decimation in Frequency algorithm to find DFT and draw the signal flow graph for N = 4 c) Write a note on Chirp-Z transform and its applications SECTION II jw Q4 a) If y[n] = a 1x[n+k] +a 2x[n+k −1]+ a 3x[n+k −2]+ a 2x[n+k −3]+ a 1x[n+k −4], find H(e ). For what k will the frequency response be a real function of w? b) Explain the terms Linearity, Time invariance, Causality and Stability with respect to discrete time systems. Give an example of each with your explanation. OR Q4 a) Discuss the properties of the discrete time sinusoid and compare them with those of the continuous time sinusoidal function. b) A system is defined by the transfer function given below −1 2 H(z) = b 0/(1 −pz ) Is it an IIR or FIR filter? Is it High-Pass, Band-Pass, or Low-Pass? What is the condition for its stability? Assuming that it is stable, Determine b 0 and p such that H(0) = 1 and the 3-dB cut-off is at w c = π/4. Q5 a) Discuss the Notch filter, give the pole-zero diagram and explain how the notch bandwidth may be reduced. How can you convert a notch filter into a comb filter with 4 notches? b) Discuss qualitatively the differences between the Rectangular and the Kaiser windows. (Equations are not required). c) What is the alteration theorem? How is it helpful in computer-aided FIR filter design? OR Q5 a) Write a note on linear phase filters having symmetric impulse response with even length. State if the following can or cannot have a symmetric impulse response with even length: 1) a Band-pass filter and 2) High-pass filter – explain why in each case. b) Explain how you will design a band-stop IIR digital filter using a standard normalised analogue low-pass filter transfer function. Q6 Write short notes on any three a) Compare and contrast IIR and FIR filters, and give the advantages of each. b) Graphical method of evaluating the magnitude frequency response from the pole-zero plot in z-plane. c) Harvard architecture and pipelining. d) Pre-warping of the critical frequencies in some IIR design methods. --END-- THE MAHARAJA SAYAJIRAO UNIVERSITY OF BARODA First Semester of BE IV (Electronics) examination 2001 th Thursday, 19 April 3 PM to 6 PM Digital Signal Processing N.B.: i) Answer the two sections in separate answer-books . ii) All Questions carry equal marks. iii) Suitable assumptions may be made wherever required,. Maximum marks: 100 SECTION I Q1 a) Define Z-transform. Find Z transform of the following : (i) 2n δ(n-3) (ii) an cos n θ U(n) b) Using the first order sections obtain the cascade realization for the following system 1 − 1 − 1( + z 1 1)( + z 1 ) 2 4 H z)( = 1 − 1 − 1 − 1( − z 1 1)( − z 1 1)( − z 1 ) 2 4 8 OR Q1 a) (i) Explain the term “LTI System” and “Causal System”.
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