ANNA UNIVERSITY
GE2021 ENVIRONMENTAL SCIENCE IMPORTANT QUESTIONS
GE2021 ENVIRONMENTAL SCIENCE IMPORTANT QUESTIONS
Anna University Important Questions
CS2405 important questions from all 5 units - common for
CSE 7th semester & IT 5th Semester
UNIT 1
1. Determine the energy of the discrete time sequence (2)
x(n) = (½)n, n≥0
=3 n, n<0
2. Define multi channel and multi dimensional signals (2)
3. Define symmetric and anti symmetric signals. (2)
4. Differentiate recursive and non recursive difference equations. (2)
5. What is meant by impulse response? (2)
6. What is meant by LTI system? (2)
7. What are the basic steps involved in convolution? (2)
8. Define the Auto correlation and Cross correlation? (2)
9. What is the causality condition for an LTI system? (2)
10. What is zero padding? What are it uses? (2)
11. State the Sampling Theorem. (2)
12 What is an anti imaging and anti aliasing filter? (2)
13. Determine the signals are periodic and find the fundamental period (2)
in√ 2 πt
i) sin 20πt+ sin5πt
14. Give the mathematical and graphical representations of a unit sample, unit step
sequence. (2)
15. Sketch the discrete time signal x(n) =4 δ (n+4) + δ(n)+ 2 δ (n-1) + δ (n-2) -5 δ (n-3) (2)
16. Find the periodicity of x(n) =cost(2πn / 7) (2)
17. What is inverse system? (2)
18. Write the relationship between system function and the frequency response. (2)
19. Define commutative and associative law of convolutions. (2)
20. What is meant by Nyquist rate and Nyquist interval? (2)
21. What is an aliasing? How to overcome this effect? (2)
22. What are the disadvantages of DSP? (2)
23. State initial value theorem of Z transform. (2)
24 What are the different methods of evaluating inverse z transform? (2)
25 What is meant by ROC? (2)
26 What are the properties of ROC?(2)
27 What is zero padding? What are it uses?(2)
28 State convolution property of Z transform. (2)
29 State Cauchy residue theorem. (2)
30 Define fourier transform. (2)
31 Define discrete fourier series. (2)
32 Compare linear and circular convolution. (2)
33 Distinguish between Fourier series and Fourier transform. (2)
34 What is the relation between fourier transform and z transform. (2)
35 What is the use of Fourier transform? (2)
36. Define system function. (2)
37. State Parseval relation in z transform (2)
CLASSIFICATION OF SYSTEMS:
1. Determine whether the following system are linear, time-invariant (16)
i)y(n) = Ax(n) +B
ii)y(n) =x(2n)
iii)y(n) =n x2 (n)
iv)y(n) = a x(n)
2. Check for following systems are linear, causal, time in variant, stable, static (16)
i) y(n) =x(2n)
ii) y(n) = cos (x(n))
iii) y(n) = x(n) cos (x(n)
iv) y(n) =x(-n+2)
v) y(n) =x(n) +n x (n+1)
3.a) For each impulse response determine the system is i) stable ii) causal (8)
i) h(n)= sin (π n / 2)
ii) h(n) = δ(n) + sin π n
iii) h(n) = 2 n u(-n)
. b)Find the periodicity of the signal x(n) =sin (2πn / 3)+ cos (π n / 2) (8)
4. Explain in detail about A to D conversion with suitable block diagram and to
reconstruct the signal. (16)
5 a) State and proof of sampling theorem. (8)
b)What are the advantages of DSP over analog signal processing? (8)
6 a)Explain successive approximation technique. (8)
b)Explain the sample and hold circuit. (8)
Z TRANSFORM:
1. a)State and proof the properties of Z transform. (8)
b)Find the Z transform of (8)
i) x(n) =[ (1/2)n – (1/4)n ] u(n)
ii) x(n) = n(-1)n u(n)
iii) x(n) (-1)n cos (πn/3) u(n)
iv) x(n) = (½) n-5 u(n-2) +8(n-5)
2 a) Find the Z transform of the following sequence and ROC and sketch the pole zero
diagram (8)
i) x(n) = an u(n) +b n u(n) + c n u(-n-1) , |a| <|b| <| c|
ii) x(n) =n2 an u(n)
b)Find the convolution of using z transform (8)
x1(n) ={ (1/3) n, n>=0
(1/2) - n n<0 }
x2(n) = (1/2) n
INVERSE Z TRANSFORM:
5. Find the inverse z transform (16)
X(z) = log (1-2z) z < |1/2 |
X(z) = log (1+az-1) |z| > |a|
X(z) =1/1+az-1 where a is a constant
X(z)=z2/(z-1)(z-2)
X(z) =1/ (1-z-1) (1-z-1)2
X(z)= Z+0.2/(Z+0.5)(Z-1) Z>1 using long division method.
X(z) =1- 11/4 z-1 / 1-1/9 z-2 using residue method.
X(z) =1- 11/4 z-1 / 1-1/9 z-2 using convolution method.
6.. A causal LTI system has impulse response h(n) for which Z transform is given by H(z)
1+ z -1 / (1-1/2 z -1 ) (1+1/4 z -1 ) (16)
i) What is the ROC of H (z)? Is the system stable?
ii) Find THE Z transform X(z) of an input x(n) that will produce the output y(n) = - 1/3
(-1/4)n u(n)- 4/3 (2) n u(-n-1)
iii) Find the impulse response h(n) of the system.
ANALYSIS OF LTI SYSTEM:
7. a)The impulse response of LTI system is h(n)=(1,2,1,-1).Find the response of the system to
the input x(n)=(2,1,0,2) (8)
b). Determine the response of the causal system y(n) – y(n-1) =x(n) + x(n-1) to inputs
x(n)=u(n) and x(n) =2 –n u(n).Test its stability (8)
8. Determine the magnitude and phase response of the given equation
y(n) =x(n)+x(n-2) (16)
9. a)Determine the frequency response for the system given by
y(n)-y3/4y(n-1)+1/8 y(n-2) = x(n)- x(n-1) (8)
b). Determine the pole and zero plot for the system described difference equations
y(n)=x(n)+2x(n-1)-4x(n-2)+x(n-3) (8)
10. Find the output of the system whose input- output is related by the difference equation
y(n) -5/6 y(n-1) +1/6 y(n-2) = x(n) -1/2 x(n-1) for the step input. (16)
11. Find the output of the system whose input- output is related by the difference equation
y(n) -5/6 y(n-1) +1/6 y(n-2) = x(n) -1/2 x(n-1) for the x(n) =4 n u(n). (16)
CONVOLUTION:
12. Find the output of an LTI system if the input is x(n) =(n+2) for 0≤ n≤ 3
and h(n) =an u(n) for all n (16)
13. Find the convolution sum of x(n) =1 n = -2,0,1
= 2 n= -1
= 0 elsewhere
and h(n) = δ (n) – δ (n-1) + δ( n-2) - δ (n-3) (16).
14. Find the convolution of the following sequence x(n) =(1,2,-1,1) , h(n) =(1, 0 ,1,1) (16)
15.Find the output sequence y(n) if h(n) =(1,1,1) and x(n) =(1,2,3,1) using a circular
Convolution. (16)
16. Find the convolution y(n) of the signals (16)
x(n) ={ α n, -3 ≤ n ≤ 5 and h(n) ={ 1, 0 ≤ n ≤ 4
0, elsewhere } 0, elsewhere }
UNIT 2
1. How many multiplication and additions are required to compute N point DFT using
radix 2 FFT? (2)
2. Define DTFT pair. (2)
3. What are Twiddle factors of the DFT? (2)
4. State Periodicity Property of DFT. (2)
5. What is the difference between DFT and DTFT? (2)
6. Why need of FFT? (2)
7. Find the IDFT of Y (k) = (1, 0, 1, 0) (2)
8. Compute the Fourier transform of the signal x(n) = u(n) – u(n-1). (2)
9. Compare DIT and DIF? (2)
10. What is meant by in place in DIT and DIF algorithm? (2)
11. Is the DFT of a finite length sequence is periodic? If so, state the reason. (2)
12. Draw the butterfly operation in DIT and DIF algorithm? (2)
13. What is meant by radix 2 FFT? (2)
14. State the properties of W N
k ? (2)
15. What is bit reversal in FFT? (2)
16. Determine the no of bits required in computing the DFT of a 1024 point sequence
with SNR of 30dB. (2)
17. What is the use of Fourier transform? (2)
18. What are the advantages FFT over DFT?
FOURIER TRANSFORM:
1. a) Determine the Fourier transform of x (n) =a |n|; -1<a<1
(8)
b) Determine the Inverse Fourier transform H (w) = (1-ae-jw) -1 (8)
2. State and proof the properties of Fourier transform (16)
FFT:
3. Determine the Discrete Fourier transform x (n) = (1, 1, 1, 1) and
Proof x(n)*h(n) =X(z) H(z (16)
4. Derive and draw the 8 point FFT-DIT butterfly structure. (16)
5. Derive and draw the 8 point FFT-DIF butterfly structure. (16)
6.Compute the DFT for the sequence.(0.5,0.5,0.5,0.5,0,0,0,0) (16)
7.Compute the DFT for the sequence.(1,1,1,1,1,1,0,0) (16)
8.Find the DFT of a sequence x(n)=(1,1,0,0) and find IDFT of Y(k) =(1,0,1,0) (16)
9. If x (n) = sin (nΠ/2), n=0, 1, 2, 3 (16)
10. h (n) = 2 n , n=0,1,2,3.Find IDFT and sketch it. (16)
11.Find 4 point DFT using DIF of x(n) =(0,1,2,3) (16)
12.a)Discuss the properties of DFT. (10)
b).Discuss the use of FFT algorithm in linear filtering. (6)
UNIT 3
1. Obtain the cascade and parallel form realizations for the following systems (16)
Y (n) = -0.1(n-1) + 0.2 y (n-2) + 3x (n) +3.6 x (n-1) +0.6 x (n-2)
2.a) Obtain the Direct form II
y (n) = -0.1(n-1) + 0.72 y(n-2) + 0.7x(n) -0.252 x(n-2) (8)
b) .Find the direct form II
H (z) =8z-2+5z-1+1 / 7z-3+8z-2+1 (8)
3. Obtain the i) Direct forms ii) cascade iii) parallel form realizations for the following systems
y (n) = 3/4(n-1) – 1/8 y(n-2) + x(n) +1/3 x(n-1) (16)
4.Find the direct form –I, cascade and parallel form for (16)
H(Z) = z -1 -1 / 1 – 0.5 z-1+0.06 z-2
IIR FILTER DESIGN:
6. Explain the method of design of IIR filters using bilinear transform method. (16)
7. a)Derive bilinear transformation for an analog filter with system function H(s) = b/ s + a (8)
b) For the analog transfer function H(s) = 2 / (s+1) (s+3) .
Determine H (z) using bilinear transformation. With T=0.1 sec (8)
8. a)Convert the analog filter H(s) = 0.5 (s+4) / (s+1)(s+2) using impulse invariant transformation
T=0.31416s (8)
b)The normalized transfer function of an analog filter is given by H a (sn) = 1/ sn
2 +1.414 s n +1.
Convert analog filter to digital filter with cut off frequency of 0.4 π using bilinear transformation.
(8)
9. Design a single pole low pass digital IIR filter with -3db bandwidth of 0.2Π by using bilinear
transformation. (16)
10. For the constraints
0.8 ≤ |H (e jw)| ≤1, 0 ≤ ω ≤ 0.2π
|H (e jw)| ≤0.2, 0.6π ≤ ω ≤π with T= 1 sec .Determine system function H(z) for a Butterworth
filter using Bilinear transformation. (16)
11.Design a digital Butterworth filter satisfying the following specifications
0.7 ≤ |H (e jw)| ≤1, 0 ≤ ω ≤ 0.2π
|H (e jw)| ≤0.2, 0.6π ≤ ω ≤π with T= 1 sec .Determine system function H(z) for a Butterworth
filter using impulse invariant transformation. (16)
12. Design a digital Chebyshev low pass filter satisfying the following specifications 0.707 ≤ |H (e
jw)| ≤1, 0 ≤ ω ≤ 0.2π
|H (e jw)| ≤0.1 0.5 ≤ ω ≤π with T= 1 sec using for bilinear transformation. (16)
13.Design a digital Butterworth High pass filter satisfying the following specifications
0.9 ≤ |H (e jw)| ≤1, 0 ≤ ω ≤ π/2
|H (e jw)| ≤0.2, 3π/4 ≤ ω ≤π with T= 1 sec. using impulse invariant transformation (16)
14. Design a realize a digital filter using bilinear transformation for the following specifications
i) Monotonic pass band and stop band
ii) -3.01 db cut off at 0.5 π rad
iii) Magnitude down at least 15 db at ω = 0.75 π rad. (16)
FIR FILTER
15.a) Prove that an FIR filter has linear phase if the unit sample response satisfies the condition h(n)
= ± h(M-1-n), n =0,1,….. M-1.Also discuss symmetric and anti symmetric cases of FIR filter.
(8)
b) Explain the need for the use of window sequence in the design of FIR filter. Describe the
window sequence generally used and compare the properties. (8)
16. Design a HPF of length 7 with cut off frequency of 2 rad/sec using Hamming window. Plot the
magnitude and phase response. (16)
17. Explain the principle and procedure for designing FIR filter using rectangular window (16)
18. Design a filter with
H d (e
jώ) = e - 3 jώ , π/4 ≤ ω ≤ π/4
0. π/4 ≤ ω ≤ π using a Hamming window with N=7. (16)
19. H (w) =1 for | ω | ≤ π/3 and | ω | ≥2 π/3
0 otherwise for N=11. and find the response. (16)
20.Design a FIR filter whose frequency response (16)
H (e jώ) = 1 π/4 ≤ ω ≤ 3π/4
0. | ω | ≤3 π/4.
Calculate the value of h(n) for N=11 and hence find H(z).
21.Design an ideal differentiator with frequency response H (e jώ) = jw -π ≤ ω ≤ π
using hamming window for N=8 and find the frequency response. (16)
22.Design an ideal Hilbert transformer having frequency response
H (e jώ) = j -π ≤ ω ≤ 0
-j 0 ≤ ω ≤ π for N=11 using rectangular window. (16)
FIR structures:
23.a) Determine the direct form of following system (8)
H (z) =1+2z-1 - 3z-2 + 4z-3 - 5z-4
b). Obtain the cascade form realizations of FIR systems (8)
H (z) = 1+5/2 z-1+ 2z-2 +2 z-3
UNIT 5
1) Give some example of DSP
2) Explain Interpolation
3) Explain decimation
4) What is know to be subband coding
5) Define sampling rate conversion
6) How the image enchancement is achieved using DSP
7) Define compression
8) What are various compression technique
9) Explain subband coding
10) Define vocoders
11) Explain adaptive filtering
1) Explain the concept of deciation by a factor D and interpolation by factor I
2) With help of equation explain sampling rate conversion by a rational factor I/D
3) Explain the following application
i) speech compression
ii) sound processing
4) With help diagram explain adaptive filtering process
5) Explain speech vocoders and subband coding6) Explain how image enchancement was achieved
CSE 7th semester & IT 5th Semester
2 marks and 16 marks
1. Determine the energy of the discrete time sequence (2)
x(n) = (½)n, n≥0
=3 n, n<0
2. Define multi channel and multi dimensional signals (2)
3. Define symmetric and anti symmetric signals. (2)
4. Differentiate recursive and non recursive difference equations. (2)
5. What is meant by impulse response? (2)
6. What is meant by LTI system? (2)
7. What are the basic steps involved in convolution? (2)
8. Define the Auto correlation and Cross correlation? (2)
9. What is the causality condition for an LTI system? (2)
10. What is zero padding? What are it uses? (2)
11. State the Sampling Theorem. (2)
12 What is an anti imaging and anti aliasing filter? (2)
13. Determine the signals are periodic and find the fundamental period (2)
in√ 2 πt
i) sin 20πt+ sin5πt
14. Give the mathematical and graphical representations of a unit sample, unit step
sequence. (2)
15. Sketch the discrete time signal x(n) =4 δ (n+4) + δ(n)+ 2 δ (n-1) + δ (n-2) -5 δ (n-3) (2)
16. Find the periodicity of x(n) =cost(2πn / 7) (2)
17. What is inverse system? (2)
18. Write the relationship between system function and the frequency response. (2)
19. Define commutative and associative law of convolutions. (2)
20. What is meant by Nyquist rate and Nyquist interval? (2)
21. What is an aliasing? How to overcome this effect? (2)
22. What are the disadvantages of DSP? (2)
23. State initial value theorem of Z transform. (2)
24 What are the different methods of evaluating inverse z transform? (2)
25 What is meant by ROC? (2)
26 What are the properties of ROC?(2)
27 What is zero padding? What are it uses?(2)
28 State convolution property of Z transform. (2)
29 State Cauchy residue theorem. (2)
30 Define fourier transform. (2)
31 Define discrete fourier series. (2)
32 Compare linear and circular convolution. (2)
33 Distinguish between Fourier series and Fourier transform. (2)
34 What is the relation between fourier transform and z transform. (2)
35 What is the use of Fourier transform? (2)
36. Define system function. (2)
37. State Parseval relation in z transform (2)
CLASSIFICATION OF SYSTEMS:
1. Determine whether the following system are linear, time-invariant (16)
i)y(n) = Ax(n) +B
ii)y(n) =x(2n)
iii)y(n) =n x2 (n)
iv)y(n) = a x(n)
2. Check for following systems are linear, causal, time in variant, stable, static (16)
i) y(n) =x(2n)
ii) y(n) = cos (x(n))
iii) y(n) = x(n) cos (x(n)
iv) y(n) =x(-n+2)
v) y(n) =x(n) +n x (n+1)
3.a) For each impulse response determine the system is i) stable ii) causal (8)
i) h(n)= sin (π n / 2)
ii) h(n) = δ(n) + sin π n
iii) h(n) = 2 n u(-n)
. b)Find the periodicity of the signal x(n) =sin (2πn / 3)+ cos (π n / 2) (8)
4. Explain in detail about A to D conversion with suitable block diagram and to
reconstruct the signal. (16)
5 a) State and proof of sampling theorem. (8)
b)What are the advantages of DSP over analog signal processing? (8)
6 a)Explain successive approximation technique. (8)
b)Explain the sample and hold circuit. (8)
Z TRANSFORM:
1. a)State and proof the properties of Z transform. (8)
b)Find the Z transform of (8)
i) x(n) =[ (1/2)n – (1/4)n ] u(n)
ii) x(n) = n(-1)n u(n)
iii) x(n) (-1)n cos (πn/3) u(n)
iv) x(n) = (½) n-5 u(n-2) +8(n-5)
2 a) Find the Z transform of the following sequence and ROC and sketch the pole zero
diagram (8)
i) x(n) = an u(n) +b n u(n) + c n u(-n-1) , |a| <|b| <| c|
ii) x(n) =n2 an u(n)
b)Find the convolution of using z transform (8)
x1(n) ={ (1/3) n, n>=0
(1/2) - n n<0 }
x2(n) = (1/2) n
INVERSE Z TRANSFORM:
5. Find the inverse z transform (16)
X(z) = log (1-2z) z < |1/2 |
X(z) = log (1+az-1) |z| > |a|
X(z) =1/1+az-1 where a is a constant
X(z)=z2/(z-1)(z-2)
X(z) =1/ (1-z-1) (1-z-1)2
X(z)= Z+0.2/(Z+0.5)(Z-1) Z>1 using long division method.
X(z) =1- 11/4 z-1 / 1-1/9 z-2 using residue method.
X(z) =1- 11/4 z-1 / 1-1/9 z-2 using convolution method.
6.. A causal LTI system has impulse response h(n) for which Z transform is given by H(z)
1+ z -1 / (1-1/2 z -1 ) (1+1/4 z -1 ) (16)
i) What is the ROC of H (z)? Is the system stable?
ii) Find THE Z transform X(z) of an input x(n) that will produce the output y(n) = - 1/3
(-1/4)n u(n)- 4/3 (2) n u(-n-1)
iii) Find the impulse response h(n) of the system.
ANALYSIS OF LTI SYSTEM:
7. a)The impulse response of LTI system is h(n)=(1,2,1,-1).Find the response of the system to
the input x(n)=(2,1,0,2) (8)
b). Determine the response of the causal system y(n) – y(n-1) =x(n) + x(n-1) to inputs
x(n)=u(n) and x(n) =2 –n u(n).Test its stability (8)
8. Determine the magnitude and phase response of the given equation
y(n) =x(n)+x(n-2) (16)
9. a)Determine the frequency response for the system given by
y(n)-y3/4y(n-1)+1/8 y(n-2) = x(n)- x(n-1) (8)
b). Determine the pole and zero plot for the system described difference equations
y(n)=x(n)+2x(n-1)-4x(n-2)+x(n-3) (8)
10. Find the output of the system whose input- output is related by the difference equation
y(n) -5/6 y(n-1) +1/6 y(n-2) = x(n) -1/2 x(n-1) for the step input. (16)
11. Find the output of the system whose input- output is related by the difference equation
y(n) -5/6 y(n-1) +1/6 y(n-2) = x(n) -1/2 x(n-1) for the x(n) =4 n u(n). (16)
CONVOLUTION:
12. Find the output of an LTI system if the input is x(n) =(n+2) for 0≤ n≤ 3
and h(n) =an u(n) for all n (16)
13. Find the convolution sum of x(n) =1 n = -2,0,1
= 2 n= -1
= 0 elsewhere
and h(n) = δ (n) – δ (n-1) + δ( n-2) - δ (n-3) (16).
14. Find the convolution of the following sequence x(n) =(1,2,-1,1) , h(n) =(1, 0 ,1,1) (16)
15.Find the output sequence y(n) if h(n) =(1,1,1) and x(n) =(1,2,3,1) using a circular
Convolution. (16)
16. Find the convolution y(n) of the signals (16)
x(n) ={ α n, -3 ≤ n ≤ 5 and h(n) ={ 1, 0 ≤ n ≤ 4
0, elsewhere } 0, elsewhere }
UNIT 2
1. How many multiplication and additions are required to compute N point DFT using
radix 2 FFT? (2)
2. Define DTFT pair. (2)
3. What are Twiddle factors of the DFT? (2)
4. State Periodicity Property of DFT. (2)
5. What is the difference between DFT and DTFT? (2)
6. Why need of FFT? (2)
7. Find the IDFT of Y (k) = (1, 0, 1, 0) (2)
8. Compute the Fourier transform of the signal x(n) = u(n) – u(n-1). (2)
9. Compare DIT and DIF? (2)
10. What is meant by in place in DIT and DIF algorithm? (2)
11. Is the DFT of a finite length sequence is periodic? If so, state the reason. (2)
12. Draw the butterfly operation in DIT and DIF algorithm? (2)
13. What is meant by radix 2 FFT? (2)
14. State the properties of W N
k ? (2)
15. What is bit reversal in FFT? (2)
16. Determine the no of bits required in computing the DFT of a 1024 point sequence
with SNR of 30dB. (2)
17. What is the use of Fourier transform? (2)
18. What are the advantages FFT over DFT?
FOURIER TRANSFORM:
1. a) Determine the Fourier transform of x (n) =a |n|; -1<a<1
(8)
b) Determine the Inverse Fourier transform H (w) = (1-ae-jw) -1 (8)
2. State and proof the properties of Fourier transform (16)
FFT:
3. Determine the Discrete Fourier transform x (n) = (1, 1, 1, 1) and
Proof x(n)*h(n) =X(z) H(z (16)
4. Derive and draw the 8 point FFT-DIT butterfly structure. (16)
5. Derive and draw the 8 point FFT-DIF butterfly structure. (16)
6.Compute the DFT for the sequence.(0.5,0.5,0.5,0.5,0,0,0,0) (16)
7.Compute the DFT for the sequence.(1,1,1,1,1,1,0,0) (16)
8.Find the DFT of a sequence x(n)=(1,1,0,0) and find IDFT of Y(k) =(1,0,1,0) (16)
9. If x (n) = sin (nΠ/2), n=0, 1, 2, 3 (16)
10. h (n) = 2 n , n=0,1,2,3.Find IDFT and sketch it. (16)
11.Find 4 point DFT using DIF of x(n) =(0,1,2,3) (16)
12.a)Discuss the properties of DFT. (10)
b).Discuss the use of FFT algorithm in linear filtering. (6)
UNIT 3
1. Define canonic and non canonic form realizations. (2)
2. Draw the direct form realizations of FIR systems? (2)
3. Mention advantages of direct form II and cascade structure? (2)
4. Define Bilinear Transformation. (2)
5. What is prewar ping? Why is it needed? (2)
6. Write the expression for location of poles of normalized Butterworth filter. (2)
7. Distinguish between FIR and IIR Filters. (2)
8. What is linear phase filter? (2)
9. What are the design techniques available for IIR filter? (2)
10. What is the main drawback of impulse invariant mapping? (2)
11. Compare impulse invariant and bilinear transformation. (2)
12. Why IIR filters do not have linear phase? (2)
13. Mention the properties of Butterworth filter? (2)
14. Mention the properties of Chebyshev filter? (2)
15. Why impulse invariant method is not preferred in the design of high pass IIR filter? (2)
16. Give the transform relation for converting LPF to BPF in digital domain. (2)
17. What are Gibbs oscillations? (2)
18. Explain briefly Hamming window (2).
19. If the impulse response of the symmetric linear phase FIR filter of length 5 is h(n) =
{2, 3, 0, x, y), then find the values of x and y. (2)
20. What are the desirable properties of windowing technique? (2)
21. Write the equation of Bartlett window. (2)
22.Why IIR filters do not have linear phase? (2)
23.Why FIR filters are always stable? (2)
24.Why rectangular window are not used in FIR filter design using window method? (2)
25.What are the advantages of FIR filter? (2)
26.What are the advantages and disadvantages of window? (2)
27.What is the necessary condition and sufficient condition for the linear phase characteristic of a
FIR filter? (2)
28.Compare Hamming and Hanning window? (2)
29.Why triangular window is not a good choice for designing FIR Filter? (2)
30.Why Kaiser window is most used for designing FIR Filter? (2)
31.What is the advantages in linear phase realization of FIR systems? (2)
Structures of IIR systems:
2. Draw the direct form realizations of FIR systems? (2)
3. Mention advantages of direct form II and cascade structure? (2)
4. Define Bilinear Transformation. (2)
5. What is prewar ping? Why is it needed? (2)
6. Write the expression for location of poles of normalized Butterworth filter. (2)
7. Distinguish between FIR and IIR Filters. (2)
8. What is linear phase filter? (2)
9. What are the design techniques available for IIR filter? (2)
10. What is the main drawback of impulse invariant mapping? (2)
11. Compare impulse invariant and bilinear transformation. (2)
12. Why IIR filters do not have linear phase? (2)
13. Mention the properties of Butterworth filter? (2)
14. Mention the properties of Chebyshev filter? (2)
15. Why impulse invariant method is not preferred in the design of high pass IIR filter? (2)
16. Give the transform relation for converting LPF to BPF in digital domain. (2)
17. What are Gibbs oscillations? (2)
18. Explain briefly Hamming window (2).
19. If the impulse response of the symmetric linear phase FIR filter of length 5 is h(n) =
{2, 3, 0, x, y), then find the values of x and y. (2)
20. What are the desirable properties of windowing technique? (2)
21. Write the equation of Bartlett window. (2)
22.Why IIR filters do not have linear phase? (2)
23.Why FIR filters are always stable? (2)
24.Why rectangular window are not used in FIR filter design using window method? (2)
25.What are the advantages of FIR filter? (2)
26.What are the advantages and disadvantages of window? (2)
27.What is the necessary condition and sufficient condition for the linear phase characteristic of a
FIR filter? (2)
28.Compare Hamming and Hanning window? (2)
29.Why triangular window is not a good choice for designing FIR Filter? (2)
30.Why Kaiser window is most used for designing FIR Filter? (2)
31.What is the advantages in linear phase realization of FIR systems? (2)
Structures of IIR systems:
1. Obtain the cascade and parallel form realizations for the following systems (16)
Y (n) = -0.1(n-1) + 0.2 y (n-2) + 3x (n) +3.6 x (n-1) +0.6 x (n-2)
2.a) Obtain the Direct form II
y (n) = -0.1(n-1) + 0.72 y(n-2) + 0.7x(n) -0.252 x(n-2) (8)
b) .Find the direct form II
H (z) =8z-2+5z-1+1 / 7z-3+8z-2+1 (8)
3. Obtain the i) Direct forms ii) cascade iii) parallel form realizations for the following systems
y (n) = 3/4(n-1) – 1/8 y(n-2) + x(n) +1/3 x(n-1) (16)
4.Find the direct form –I, cascade and parallel form for (16)
H(Z) = z -1 -1 / 1 – 0.5 z-1+0.06 z-2
IIR FILTER DESIGN:
6. Explain the method of design of IIR filters using bilinear transform method. (16)
7. a)Derive bilinear transformation for an analog filter with system function H(s) = b/ s + a (8)
b) For the analog transfer function H(s) = 2 / (s+1) (s+3) .
Determine H (z) using bilinear transformation. With T=0.1 sec (8)
8. a)Convert the analog filter H(s) = 0.5 (s+4) / (s+1)(s+2) using impulse invariant transformation
T=0.31416s (8)
b)The normalized transfer function of an analog filter is given by H a (sn) = 1/ sn
2 +1.414 s n +1.
Convert analog filter to digital filter with cut off frequency of 0.4 π using bilinear transformation.
(8)
9. Design a single pole low pass digital IIR filter with -3db bandwidth of 0.2Π by using bilinear
transformation. (16)
10. For the constraints
0.8 ≤ |H (e jw)| ≤1, 0 ≤ ω ≤ 0.2π
|H (e jw)| ≤0.2, 0.6π ≤ ω ≤π with T= 1 sec .Determine system function H(z) for a Butterworth
filter using Bilinear transformation. (16)
11.Design a digital Butterworth filter satisfying the following specifications
0.7 ≤ |H (e jw)| ≤1, 0 ≤ ω ≤ 0.2π
|H (e jw)| ≤0.2, 0.6π ≤ ω ≤π with T= 1 sec .Determine system function H(z) for a Butterworth
filter using impulse invariant transformation. (16)
12. Design a digital Chebyshev low pass filter satisfying the following specifications 0.707 ≤ |H (e
jw)| ≤1, 0 ≤ ω ≤ 0.2π
|H (e jw)| ≤0.1 0.5 ≤ ω ≤π with T= 1 sec using for bilinear transformation. (16)
13.Design a digital Butterworth High pass filter satisfying the following specifications
0.9 ≤ |H (e jw)| ≤1, 0 ≤ ω ≤ π/2
|H (e jw)| ≤0.2, 3π/4 ≤ ω ≤π with T= 1 sec. using impulse invariant transformation (16)
14. Design a realize a digital filter using bilinear transformation for the following specifications
i) Monotonic pass band and stop band
ii) -3.01 db cut off at 0.5 π rad
iii) Magnitude down at least 15 db at ω = 0.75 π rad. (16)
FIR FILTER
15.a) Prove that an FIR filter has linear phase if the unit sample response satisfies the condition h(n)
= ± h(M-1-n), n =0,1,….. M-1.Also discuss symmetric and anti symmetric cases of FIR filter.
(8)
b) Explain the need for the use of window sequence in the design of FIR filter. Describe the
window sequence generally used and compare the properties. (8)
16. Design a HPF of length 7 with cut off frequency of 2 rad/sec using Hamming window. Plot the
magnitude and phase response. (16)
17. Explain the principle and procedure for designing FIR filter using rectangular window (16)
18. Design a filter with
H d (e
jώ) = e - 3 jώ , π/4 ≤ ω ≤ π/4
0. π/4 ≤ ω ≤ π using a Hamming window with N=7. (16)
19. H (w) =1 for | ω | ≤ π/3 and | ω | ≥2 π/3
0 otherwise for N=11. and find the response. (16)
20.Design a FIR filter whose frequency response (16)
H (e jώ) = 1 π/4 ≤ ω ≤ 3π/4
0. | ω | ≤3 π/4.
Calculate the value of h(n) for N=11 and hence find H(z).
21.Design an ideal differentiator with frequency response H (e jώ) = jw -π ≤ ω ≤ π
using hamming window for N=8 and find the frequency response. (16)
22.Design an ideal Hilbert transformer having frequency response
H (e jώ) = j -π ≤ ω ≤ 0
-j 0 ≤ ω ≤ π for N=11 using rectangular window. (16)
FIR structures:
23.a) Determine the direct form of following system (8)
H (z) =1+2z-1 - 3z-2 + 4z-3 - 5z-4
b). Obtain the cascade form realizations of FIR systems (8)
H (z) = 1+5/2 z-1+ 2z-2 +2 z-3
UNIT 5
1) Give some example of DSP
2) Explain Interpolation
3) Explain decimation
4) What is know to be subband coding
5) Define sampling rate conversion
6) How the image enchancement is achieved using DSP
7) Define compression
8) What are various compression technique
9) Explain subband coding
10) Define vocoders
11) Explain adaptive filtering
1) Explain the concept of deciation by a factor D and interpolation by factor I
2) With help of equation explain sampling rate conversion by a rational factor I/D
3) Explain the following application
i) speech compression
ii) sound processing
4) With help diagram explain adaptive filtering process
5) Explain speech vocoders and subband coding6) Explain how image enchancement was achieved
SSC Question Paper
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jee main 2012
JOINT ENTRANCE EXAMINATION MAIN ENTRANCE SCHEDULE 2013 :
LAST DATE 26 DECEMBER 2012
The Paper-1 (described below) of JEE (Main) will be conducted in two separate modes i.e. Offline (Pen and Paper Based Examination) mode and Online (Computer Based Examination) mode. The Paper-2 of JEE (Main) will be conducted only in Pen and Paper based examination mode. A candidate will opt for either Pen and Paper Based or Computer Based examination modes for Paper-1 only.
TIME SCHEDULE FOR
JEE (Main) – 2013 :
(A)TIME SCHEDULE FOR
Pen and Paper based examination
Paper-1
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Paper-2
|
|
DATES OF EXAMINATION
|
07.04.2013
|
07.04.2013
|
a) Entry in the
Examination Hall
|
0900 HRS.
|
1330 HRS.
|
b) Distribution of Test
Booklet
|
0920 HRS
|
1350 HRS
|
c) Seal of the Test
Booklet to be broken/opened to take out the Answer Sheet
|
0925 HRS
|
1355 HRS
|
d) Last entry in the
Examination Hall
|
0930 HRS
|
1400 HRS
|
e) Test commences
|
0930 HRS
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1400 HRS
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f) Test concludes
|
1230 HRS
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1700 HRS
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(B) TIME SCHEDULE FOR
COMPUTER BASED EXAMINATION
DATES OF EXAMINATION FOR
PAPER-1: 08.04.2013 to 25.04.2013
Morning Session
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Afternoon Session
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a) Entry in the
Examination Hall
|
7.30 am
|
12.30 pm
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b) Last entry in the
Examination Hall
|
8.30 am
|
1.30 pm
|
c) Test commences
|
9.00 am
|
2.00 pm
|
d) Test concludes
|
12.00 noon
|
5.00 pm
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Where and How to Send the Confirmation Page
The Confirmation Page is to be printed on A-4 size paper and kept in an A-4 size envelope/proper size envelope.The completed Confirmation Page must be sent only by registered/speed post to the Executive Director JEE (Main) - 2013 at the address given below.
Executive Director
JEE (Main) Secretariat
Central Board of Secondary Education,
PS-1-2, Institutional Area,
I.P.Extn. Patparganj,
Delhi-110 092.
The candidates are advised to download their admit cards from JEE (Main) website only. The Candidates are also advised to regularly see JEE (Main) website for updates. A call center will also be functional on all working days from 1st February 2013 onwards for general facilitation.
Materials to be brought on the day of examination Admit Card and Ball Point Pen of good quality. For Paper-2 of JEE (Main), the candidates are advised to bring their own clip board, geometry box set,
pencils, erasers and colour pencils or crayons.
Rough Work (Pen and Paper Based Examination) Rough Work (Computer Based Examination). All rough work is to be done in the Test Booklet only. The candidate should NOT do any rough work or put stray mark on the Answer Sheet. Paper for Rough work will be provided at the examination centre.
Candidates are allowed to submit only one application form. Multiple applications of a candidate are liable to be rejected. The name in the application form must be the same as in class Xth pass certificate.
The fee may be submitted either by credit/debit card or through Demand Draft. In case of Demand Draft, the same may be made in favour of Secretary, CBSE, payable at Delhi. In case the payment is made through Demand Draft, please mention your computer generated application no. and name on the reverse side of Demand Draft.
The computer generated Confirmation Page with photograph pasted, address written and signed by the candidate and his/her parent must reach the JEE (Main) office on or before 26th December 2012. The completed Confirmation Page must be sent only by registered/speed post to the Executive Director, JEE (Main) - 2013 at the given below address:
Executive Director
JEE (Main) Secretariat
Central Board of Secondary Education,
PS-1-2, Institutional Area, I.P.Extn.
Patparganj,
Delhi-110 092.
After submission of an application no options can be changed at a later stage.
All correspondence related to JEE (Main) – 2013 should be addressedto the Executive Director, JEE (Main).
The application no. printed on the computer generated Confirmation Page must be mentioned in all such correspondences. It is therefore essential to note down the application number printed on the Confirmation Page.
Candidates may check the status of their application on JEE (Main) - 2013 website by giving the application number and date of birth.
Application fee once paid is non-refundable.
The Honb’le High Court of Delhi at New Delhi alone will have the jurisdiction to settle and decide all matters and disputes related to JEE (Main) - 2013 as Joint Apex Board located at CBSE Delhi is organising
the JEE (Main) - 2013 examination.
The offer of admission is subject to verification of original certificates/ documents at the time of admission. If any candidate is found ineligible
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