AMIETE – ET/CS (NEW SCHEME)   -    Code: AE77/AC77

 

Subject: DIGITAL SIGNAL PROCESSING

Flowchart: Alternate Process: JUNE 2010
 


Time: 3 Hours                                                                                                     Max. Marks: 100

 

NOTE: There are 9 Questions in all.

·      Question 1 is compulsory and carries 20 marks. Answer to Q.1 must be written in the space provided for it in the answer book supplied and nowhere else.

·      Out of the remaining EIGHT Questions, answer any FIVE Questions. Each question carries 16 marks.

·      Any required data not explicitly given, may be suitably assumed and stated.

 

 

Q.1       Choose the correct or the best alternative in the following:                                  (210)

       

a.  If the continuous signal xc(t) = cos(16000pt) is sampled with a sampling period of    T = 1/6000, then

.   

                  (A) Aliasing is not present                     (B) Ideal sampling

                  (C) Aliasing is present                           (D) Ideal reconstruction is possible                       

 

             b. In two’s complement representation, with B = 2, 0.75 is represented as   

 

                  (A) 0.10                                               (B) 1.10

                  (C) 0.11                                               (D) 1.01

 

             c.  For a stop band attenuation of 40dB in a linear phase FIR filter _________window is used.

 

                  (A) Rectangular                                    (B) Blackman

                  (C) Hanning                                          (D) Hamming

 

             d.  If the ROC of a system function is outside the outermost pole and includes the unit circle, then the system is

 

                  (A) Causal and unstable                        (B) Non-causal and unstable

                  (C) Non-causal and stable                    (D) Causal and stable

 

             e.  Linear phase systems have a constant _________

                                           

                  (A) Phase                                             (B) Magnitude

                  (C) Group Delay                                  (D) Angle

 

             f.   A digital filter is said to be an IIR if

 

                  (A) All poles outside the unit circle       

                  (B) It oscillates

                  (C) One of the denominator coefficients is nonzero

                  (D) Current output depends on previous output

 

              g. A discrete-time filter transfer function is given by     What is the amplitude response      at dc?  

 

                  (A) 1                                                    (B) 1.33

                  (C) 0                                                    (D) 1.6

            

             h.  A data sequence consisting of 32 samples is stored in memory in natural order. If the data sequence is subsequently scrambled using a bit reversal algorithm, what will be the bit reversed indices for the data samples x(7) and x(13)? Assume a 32-point FFT processor is to be used.

  

(A)   x(11) and x(14)                            (B)  x(14) and x(11)

                  (C)  x(22) and x(28)                            (D)  x(28) and x(22)

 

             i.   A rational system function with all its poles and zeros inside the unit circle is said to have

                 

                  (A) Linear phase                                   (B) Rational phase

                  (C) Minimum Phase                              (D) Maximum Phase

 

             j.   The algorithm used to compute any set of equally spaced samples of Fourier Transform on the unit circle is

                      

                  (A) DFT Algorithm                               (B) FFT Algorithm                                                            

                  (C) Goertzel Algorithm                         (D) Chirp Transform Algorithm

                 

 

Answer any FIVE Questions out of EIGHT Questions.

Each question carries 16 marks.

 

 

  Q.2     a.   Explain analog to digital conversion. Describe the resulting quantization errors.                    (10)

                                                                             

             b.   Determine the minimum sampling frequency for each of the following bandpass signals. (i) x(t) is real with X(f) nonzero only for 9 kHz < |f| < 12 kHz (ii) x(t) is real with X(f) nonzero only for 18 kHz < |f| < 22 kHz (iii) x(t) is complex with X(f) nonzero only for 30 kHz < f < 35 kHz.                   (6)

                                                                             

  Q.3     a.   Describe all-pass systems with necessary equations and pole-zero plot.               (6)

                                                                             

             b.   When the input to a linear time-invariant system is the output is      (i) Find the system function H(z) of the system. Plot the poles and zeros of H(z) and indicate the ROC and check for stability & causality of the system (ii) Write the difference equation that characterizes the system. (iii) Find the impulse response h[n]                          (10)

                                                                                                           

Q.4       a.   Draw the Direct Form I and Direct Form II implementation of the LTI system with system function  Compare the two implementations, in term of number of delay operation.                                                           (8)

       

             b.   For draw the direct form and Linear-Phase FIR implementation. Compare the implementations.                                            (8)

            

  Q.5     a.   Explain bilinear transformation and discuss frequency warping.                           (6)

                  

             b.   Design a low pass discrete-time filter with the following specifications:  

                   Use Kaiser window for the design.                                                                   (10)

            

  Q.6     a.   Given two four-point sequences and , (i) Calculate the four-point DFT X[k] (ii) Calculate the four-point DFT H[k] (iii) Calculate the four-point circular convolution of x[n] with h[n] directly. (iv) Calculate the four-point circular convolution of x[n] with h[n] by multiplying X[k] and H[k] and performing an inverse DFT.                                                                              (12)

 

             b.   Explain the overlap-add or overlap-save methods to perform linear convolution.                 (4)

       

  Q.7     a.   Derive the DIT-FFT algorithm using signal flow graphs for N = 8. Derive its computational complexity and compare with DFT.                             (8)      

             b.   Find the DFT of the sequence [4, 3, 2, 1] using DIF-FFT algorithm.                   (8)

            

  Q.8     a.    Write short notes on (i) Spectrogram (ii) Periodogram                                        (8)

 

             b.   Describe how correlation and power spectrum can be estimated using the DFT.                 (8)

                  

  Q.9     a.   What is Hilbert Transform? Explain how band pass signals are represented using Hilbert transform.                                                            (8)

 

             b.   Consider a real, causal sequence x[n] for which the real part of the DTFT is Determine the original sequence x[n], its Fourier transform and the imaginary part of the Fourier transform.                                                              (8)