3RD Bio Medical & ECE SEMESTER 1 JNTU B.TECH ENGINEERING QUESTION PAPER - DIGITAL SIGNAL PROCESSING

Code No:  R05311101                    R05          Set No.   2

 

 

III  B.Tech I Semester Supplementary Examinations,June 2010

DIGITAL SIGNAL PROCESSING

Common to Bio-Medical Engineering, Electronics And Computer

Engineering

Time: 3 hours                                                                                  Max Marks:  80

Answer any FIVE Questions

All  Questions carry equal marks

? ? ? ? ?

 

 

1. Design one stage and two stage interpolators to meet following specifications.

 

 

I = 20

 

(a)  Pass band                                     : 0 ≤ F ≤ 90 (b)  Transition band                         : 90 ≤ F ≤ 100 (c)  Input  sampling rate                    :    10,000HZ

(d)  Ripple : δ1 = 10−2 ,  δ2 = 10−3 .                                                                           [16]

 

2.   (a)  Implement the Decimation in frequency FFT algorithm of N-point DFT where

N=8.  Also explain the steps involved in this algorithm.

(b)  Compute  the FFT  for the sequence x(n) = { 1, 1, 1, 1, 1, 1, 1, 1 }         [8+8]

 

3.   (a)  Explain  how the  analysis  of discrete  time  invariant  system  can be obtained

using convolution properties  of Z transform.

(b)  Determine  the  impulse  response  of the  system  described  by  the  difference equation  y(n)-3y(n-1)-4y(n-2)=x(n)+2x(n-1) using Z transform.              [8+8]

 

4.   (a)  Discuss the need for frequency transformations.

(b)  Show that  the bilinear transformation maps the jΩ axis in the s - plane onto the unit circle, |Z| =1  and maps left half of s -plane , Re(s)<0 into inside the unit  circle |Z| <1 and right half of s -plane , Re(s)> 0 into outside  the  unit circle|Z| >1.                                                                                            [6+10]

 

5.   (a)  The  DTFT  of x (n)  =   1  n  u(n+2) is X (ejw ), find the  sequence that  has a

DTFT  given by Y (ejw ) = X (ej2w )

(b)  A causal LTI system is defined by the difference equation 2y(n)-y(n-2)=

            x(n-1)+3x(n-2)+2x(n-3). Find the frequency response H(e jw ),  magnitude  re- sponse and phase response.                                                                            [8+8]

 

6. Consider the  sequence x(n)=4δ(n)+3δ(n-1)+2δ(n-2)+δ(n-3).  Let X(K)  be the  6-

point DFT  of x(n)

 

(a)  Find the finite length sequence y1(n) that  has a 6-point DFT Y1 (K ) = w 4k X (K )

(b)  Find the finite length sequence y2(n) that  has a 6-point DFT  that  is equal to

the real part  of X(K) written  as

            Y2 (k) = Re [X (K )]

 

 

1

Code No:  R05311101                    R05          Set No.   2

 

 

(c)  Find  the  finite length  sequence y3 (n)that has a 3-Point DFT.  Y3(K)=X(2k), k=0,  1, 2.                                                                                                    [6+5+5]

 

7.   (a)  Describe programmable  Digital signal processor with RISC and CISC.

 

(b)  Mention  some applications  of on chip timer  in programmable  Digital  signal processor.                                                                                                          [8+8]

 

8.   (a)  Describe the FIR filter characteristics in Z - domain

 

(b)  The length  of an FIR  filter is '13'. If the  filter has linear phase , show that following equation  is satisfied.

(M−1)/2

P

 

n=0

h(n)Sin(ωτ −ωn) = 0.                                                                      [6+10]

 

 

 

? ? ? ? ?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

Code No:  R05311101                    R05          Set No.   4

 

 

III  B.Tech I Semester Supplementary Examinations,June 2010

DIGITAL SIGNAL PROCESSING

Common to Bio-Medical Engineering, Electronics And Computer

Engineering

Time: 3 hours                                                                                  Max Marks:  80

Answer any FIVE Questions

All  Questions carry equal marks

? ? ? ? ?

 

 

1.   (a)  Explain  how the  analysis  of discrete  time  invariant  system  can be obtained

using convolution properties  of Z transform.

 

(b)  Determine  the  impulse  response  of the  system  described  by  the  difference

equation  y(n)-3y(n-1)-4y(n-2)=x(n)+2x(n-1) using Z transform.              [8+8]

 

2.   (a)  Describe programmable  Digital signal processor with RISC and CISC.

 

(b)  Mention  some applications  of on chip timer  in programmable  Digital  signal processor.                                                                                                          [8+8]

 

3. Consider  the  sequence x(n)=4δ(n)+3δ(n-1)+2δ(n-2)+δ(n-3).  Let X(K)  be the  6- point DFT  of x(n)

 

(a)  Find the finite length sequence y1(n) that  has a 6-point DFT Y1 (K ) = w 4k X (K ) (b)  Find the finite length sequence y2(n) that  has a 6-point DFT  that  is equal to

the real part  of X(K) written  as

            Y2 (k) = Re [X (K )]

(c)  Find  the  finite length  sequence y3 (n)that has a 3-Point DFT.  Y3(K)=X(2k),

k=0,  1, 2.                                                                                                    [6+5+5]

 

4.   (a)  Discuss the need for frequency transformations.

 

(b)  Show that  the bilinear transformation maps the jΩ axis in the s - plane onto the unit circle, |Z| =1  and maps left half of s -plane , Re(s)<0 into inside the unit  circle |Z| <1 and right half of s -plane , Re(s)> 0 into outside  the  unit circle|Z| >1.                                                                                            [6+10]

 

5. Design one stage and two stage interpolators to meet following specifications.

 

 

I = 20

 

(a)  Pass band                                     : 0 ≤ F ≤ 90 (b)  Transition band                         : 90 ≤ F ≤ 100 (c)  Input  sampling rate                    :    10,000HZ

(d)  Ripple : δ1 = 10−2 ,  δ2 = 10−3 .                                                                           [16]

 

6.   (a)  The  DTFT  of x (n)  =   1  n  u(n+2) is X (ejw ), find the  sequence that  has a

DTFT  given by Y (ejw ) = X (ej2w )

 

 

3

Code No:  R05311101                    R05          Set No.   4

 

 

(b)  A causal LTI system is defined by the difference equation 2y(n)-y(n-2) =

              x(n-1) + 3x(n-2)+2x(n-3).

Find  the  frequency  response  H (ejw ),  magnitude  response and phase

response.                                                                            [8+8]

 

7.   (a)  Describe the FIR filter characteristics in Z - domain

 

(b)  The length  of an FIR  filter is '13'. If the  filter has linear phase , show that

following equation  is satisfied.

(M−1)/2

P

 

n=0

h(n)Sin(ωτ −ωn) = 0.                                                                      [6+10]

 

8.   (a)  Implement the Decimation in frequency FFT algorithm of N-point DFT where

N-8. Also explain the steps involved in this algorithm.

 

(b)  Compute  the FFT  for the sequence x(n) = { 1, 1, 1, 1, 1, 1, 1, 1 }         [8+8]

 

 

? ? ? ? ?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4

Code No:  R05311101                    R05          Set No.   1

 

 

III  B.Tech I Semester Supplementary Examinations,June 2010

DIGITAL SIGNAL PROCESSING

Common to Bio-Medical Engineering, Electronics And Computer

Engineering

Time: 3 hours                                                                                  Max Marks:  80

Answer any FIVE Questions

All  Questions carry equal marks

? ? ? ? ?

 

 

1.   (a)  Implement the Decimation in frequency FFT algorithm of N-point DFT where

N-8. Also explain the steps involved in this algorithm.

 

(b)  Compute  the FFT  for the sequence x(n) = { 1, 1, 1, 1, 1, 1, 1, 1 }         [8+8]

 

2.   (a)  The  DTFT  of x (n)  =   1  n  u(n+2) is X (ejw ), find the  sequence that  has a

DTFT  given by Y (ejw ) = X (ej2w )

 

(b)  A causal LTI system is defined by the difference equation 2y(n)-y(n-2) =

            x(n-1)+3x(n-2)+2x(n-3). Find the frequency response H(e jw ),  magnitude  re-

sponse and phase response.                                                                            [8+8]

 

3.   (a)  Discuss the need for frequency transformations.

 

(b)  Show that  the bilinear transformation maps the jΩ axis in the s - plane onto the unit circle, |Z| =1  and maps left half of s -plane , Re(s)<0 into inside the unit  circle |Z| <1 and right half of s -plane , Re(s)> 0 into outside  the  unit circle|Z| >1.                                                                                            [6+10]

 

4.   (a)  Describe programmable  Digital signal processor with RISC and CISC.

 

(b)  Mention  some applications  of on chip timer  in programmable  Digital  signal

processor.                                                                                                          [8+8]

 

5. Design one stage and two stage interpolators to meet following specifications.

 

 

I = 20

 

(a)  Pass band                                     : 0 ≤ F ≤ 90 (b)  Transition band                         : 90 ≤ F ≤ 100 (c)  Input  sampling rate                    :    10,000HZ

(d)  Ripple : δ1 = 10−2 ,  δ2 = 10−3 .                                                                           [16]

 

6.   (a)  Describe the FIR filter characteristics in Z - domain

 

(b)  The length  of an FIR  filter is '13'. If the  filter has linear phase , show that following equation  is satisfied.

(M−1)/2

P

 

n=0

h(n)Sin(ωτ −ωn) = 0.                                                                      [6+10]

 

 

 

 

5

Code No:  R05311101                    R05          Set No.   1

 

 

7.   (a)  Explain  how the  analysis  of discrete  time  invariant  system  can be obtained using convolution properties  of Z transform.

 

(b)  Determine  the  impulse  response  of the  system  described  by  the  difference equation  y(n)-3y(n-1)-4y(n-2)=x(n)+2x(n-1) using Z transform.              [8+8]

 

8. Consider the  sequence x(n)=4δ(n)+3δ(n-1)+2δ(n-2)+δ(n-3).  Let X(K)  be the  6- point DFT  of x(n)

 

(a)  Find the finite length sequence y1(n) that  has a 6-point DFT Y1 (K ) = w 4k X (K ) (b)  Find the finite length sequence y2(n) that  has a 6-point DFT  that  is equal to

the real part  of X(K) written  as

            Y2 (k) = Re [X (K )]

(c)  Find  the  finite length  sequence y3 (n)that has a 3-Point DFT.  Y3(K)=X(2k),

k=0,  1, 2.                                                                                                    [6+5+5]

 

 

? ? ? ? ?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6

Code No:  R05311101                    R05          Set No.   3

 

 

III  B.Tech I Semester Supplementary Examinations,June 2010

DIGITAL SIGNAL PROCESSING

Common to Bio-Medical Engineering, Electronics And Computer

Engineering

Time: 3 hours                                                                                  Max Marks:  80

Answer any FIVE Questions

All  Questions carry equal marks

? ? ? ? ?

 

 

1. Design one stage and two stage interpolators to meet following specifications.

 

 

I = 20

 

(a)  Pass band                                     : 0 ≤ F ≤ 90 (b)  Transition band                         : 90 ≤ F ≤ 100 (c)  Input  sampling rate                    :    10,000HZ

(d)  Ripple : δ1 = 10−2 ,  δ2 = 10−3 .                                                                           [16]

 

2.   (a)  The  DTFT  of x (n)  =   1  n  u(n+2) is X (ejw ), find the  sequence that  has a

DTFT  given by Y (ejw ) = X (ej2w )

 

(b)  A causal LTI system is defined by the difference equation 2y(n)-y(n-2) =

          x(n-1)+3x(n-2)+2x(n-3). Find the frequency response   H(e jw ),  magnitude  re-

sponse and phase response.                                                                            [8+8]

 

3.   (a)  Describe the FIR filter characteristics in Z - domain

 

(b)  The length  of an FIR  filter is '13'. If the  filter has linear phase , show that

following equation  is satisfied.

(M−1)/2

P

 

n=0

h(n)Sin(ωτ −ωn) = 0.                                                                      [6+10]

 

4.   (a)  Describe programmable  Digital signal processor with RISC and CISC.

 

(b)  Mention  some applications  of on chip timer  in programmable  Digital  signal processor.                                                                                                          [8+8]

 

5.   (a)  Explain  how the  analysis  of discrete  time  invariant  system  can be obtained

using convolution properties  of Z transform.

 

(b)  Determine  the  impulse  response  of the  system  described  by  the  difference equation  y(n)-3y(n-1)-4y(n-2)=x(n)+2x(n-1) using Z transform.              [8+8]

 

6.   (a)  Implement the Decimation in frequency FFT algorithm of N-point DFT where

N-8. Also explain the steps involved in this algorithm.

 

(b)  Compute  the FFT  for the sequence x(n) = { 1, 1, 1, 1, 1, 1, 1, 1 }         [8+8]

 

7.   (a)  Discuss the need for frequency transformations.

 

 

 

7

Code No:  R05311101                    R05          Set No.   3

 

 

(b)  Show that  the bilinear transformation maps the jΩ axis in the s - plane onto the unit circle, |Z| =1  and maps left half of s -plane , Re(s)<0 into inside the unit  circle |Z| <1 and right half of s -plane , Re(s)> 0 into outside  the  unit circle|Z| >1.                                                                                            [6+10]

 

8. Consider the  sequence x(n)=4δ(n)+3δ(n-1)+2δ(n-2)+δ(n-3).  Let X(K)  be the  6- point DFT  of x(n)

 

(a)  Find the finite length sequence y1(n) that  has a 6-point DFT Y1 (K ) = w 4k X (K ) (b)  Find the finite length sequence y2(n) that  has a 6-point DFT  that  is equal to

the real part  of X(K) written  as

            Y2 (k) = Re [X (K )]

(c)  Find  the  finite length  sequence y3 (n)that has a 3-Point DFT.  Y3(K)=X(2k), k=0,  1, 2.                                                                                                    [6+5+5]