PART – A
What is signal and Signal processing?
List the advantages of Digital Signal processing.
Mention few applications of Digital Signal processing.
Classify discrete time signals.
What are Energy and Power signals?
What do you mean by periodic and Aperiodic signals?
When a signal is said to be symmetric and Anti symmetric?
What are deterministic and random signals?
What are the elementary signals?
What are the different types of representation of discrete time signals?
Draw the basic block diagram of digital signal processing of analog signals.
What are the basic time domain operations of discrete time signal?
What is the significance of unit sample response of a system?
Classify discrete time systems.
Whether the system defined by the impulse response h(n) = 2n u(-n) + 2-n u(n) is causal ? Justify your answer.
Compute the energy of the signal x(n) = 2-n u(n)
Compute the energy of the signal x(n) = (0.5)n u(n)
Define convolution.
List out the properties of convolution.
What do you mean by BIBO stable?
What is linear time invariant system?
Compute the convolution of x(n) = {1,2,1,-1} and h(n) = {1,2,1,-1} using
↑ ↑
tabulation method.
Check whether the system defined by h (n) = [5 (1/2)n + 4 (1/3)n ] u(n) is stable.
Differentiate between analog, discrete, quantized and digital signals.
Differentiate between analog
and digital signals.
Differentiate between one dimensional and two dimensional signal with an example for each.
Name any four elementary time domain operations for discrete time signals.
For the signal f (t) = 5 cos (5000πt) + sin2 (3000πt), determine the minimum sampling rate for recovery without aliasing.
Ω1 = 5000π = 2πF1 Ω2 = 3000π = 2πF2
F1 = 2.5 kHz F2=1.5 kHz
Fmax = 2.5 kHz
According to sampling theorem Fs ≥ 2 Fmax
So, Fs = 5 kHz
For the signal f (t) = cos2 (4000πt) + 2 sin (6000πt), determine the minimum sampling rate for recovery without aliasing.
Ω1 = 4000π = 2πF1 Ω2 = 6000π = 2πF2
F1 = 2 kHz F2 =3 kHz
Fmax = 3 kHz
According to sampling theorem Fs ≥ 2 Fmax
So, Fs = 6 kHz
What is sampling?
State sampling theorem and what is Nyquist frequency?
Sampling theorem - Fs ≥ 2 Fmax
Nyquist frequency or Nyquist rate FN = 2 Fmax
What is known as aliasing?
Define the criteria to perform sampling process without aliasing.
Differentiate between anti aliasing and anti imaging filters.
What are the effects of aliasing?
What is anti aliasing filter? What is the need for it?
Draw the basic block diagram of a digital processing of an analog signal.
Draw the basic structure of linear constant difference equation.
What is sample and Hold circuit?
If a minimum signal to noise ratio (SQR) of 33 dB is desired, how many bits per code word are required in a linearly quantized system?
SQR =1.76 +6.02b
SQR given is 33 dB
1.76+6.02b = 33 dB
6.02 b = 31.24
b = 5.18 = 6 bits
Determine the number of bits required in computing the DFT of a 1024 – point sequence with an SQR of 30 dB
The size of the sequence is N = 1024 = 210
SQR is σX2 / σq2 = 22b / N2
10 log [σX2 / σq2] = 10 log [22b / N2]
N2 = 220
10 log [σX2 / σq2] = 10 log [22b / 220]
SNR = 10 log [22b - 20] = 30 dB
3(2b-20) =30
b=15 bits is the precision for both multiplication and addition
Determine the system described by the equation y (n) = n x (n) is linear or not.
What is the total energy of the discrete time signal x(n) which takes the value of unity at n =-1,0,1?
Draw the signal x(n) = u(n) – u(n-3)
PART - B
For each of the following systems, determine whether the system is static stable, causal, linear and time invariant
y(n) = e x(n)
y(n) = ax(n) +b
y(n) = Σnk=n0 x(k)
y(n) = Σn+1k= -∞ x(k
y(n) = n x2(n)
y(n) = x(-n+2)
y(n) = nx(n)
y(n) = x(n) +C
y(n) = x(n) – x(n-1)
y(n) = x(-n)
y(n) = Δ x(n) where Δ x(n) = [x(n+1) – x(n)]
y(n) = g(n) x(n)
y(n) = x(n2)
y(n) = x2(n)
y(n) = cos x(n)
y(n) = x(n) cos ω0n
Compute the linear convolution of h(n) = {1,2,1} and x(n) ={1,-3,0,2,2}
Aim for high dot blog spot dot com
Explain the concept of Energy and Power signals and determine whether the following are energy or power signals
x(n) = (1/3)n u(n)
x(n) = sin (π / 4)n
The unit sample response h(n) of a system is represented by
h (n) = n2u(n+1) – 3 u(n) +2n u(n-1) for -5≤ n ≤5. Plot the unit sample response.
State and prove sampling theorem. How do you recover continuous signals from
its samples? Discuss the various parameters involved in sampling and
reconstruction.
What is the input x(n) that will generate an output sequence
y(n) = {1,5,10,11,8,4,1} for a system with impulse response h(n) = {1,2,1}
Check whether the system defined by h(n) = [5 (1/2)n +4(1/3)n] u(n) is stable?
Explain the analog to digital conversion process and reconstruction of analog signal from digital signal.
What are the advantages and disadvantages of digital signal processing compared with analog signal processing?
Classify and explain different types of signals.
Explain the various elementary discrete time signals.
Explain the different types of mathematical operations that can be performed on a discrete time signal.
Explain the different types of representation of discrete time signals.
Determine whether the systems having the following impulse responses are causal and stable
h(n) = 2n u(-n)
h(n) = sin nπ / 2
h(n) = sin nπ + δ (n)
h(n) = e2n u(n-1)
For the given discrete time signal
x (n) = { -0.5,0.5, for n = -2, -1
1, n = 0
3, 2, 0.4 n > 0}
Sketch the following a) x (n-3), b) x (3-n) c) x (2n) d) x (n/2) e) [x (n) + x (-n)] / 2
Find the convolution of x (n) = an u (n), a < 1 with h(n) = 1for 0 ≤ n ≤ N-1 Draw the analog, discrete, quantized and digital signal with an example. Explain the properties of linearity and stability of discrete time systems with examples. The impulse response of a linear time invariant system is h (n) = {1, 2, 1,-1}. ↑ Determine the response of the system to the input signal x (n) = {1, 2, 3, 1}. ↑ Determine whether or not each of the following signals are periodic. If a signal is Periodic specify its fundamental time period. i. x(t) = 2 cos 3 πt ii. x(t) = sin 15 πt + sin 20 πt iii. x(n) = 5 sin 2n iv. x(n) = cos (n/8) cos (πn / 8) UNIT –II PART - A Define Z-transform Define ROC in Z-transform Determine Z-transform of the sequence x(n)= {2,1,-1,0, 3} ↑ Determine Z-transform of x(n) = - 0.5 u (-n-1) Find Z- transform of x(n) = - bn u(-n-1) and its ROC Find Z- transform of x(n) = an u(n) and its ROC What are the properties of ROC in Z- transform? State the initial value theorem of Z- transforms. State the final value theorem of Z- transforms. Obtain the inverse Z – transform of X(Z) = log ( 1 + Z-1) for │Z │ < 1 Obtain the inverse Z – transform of X(Z) = log ( 1-2z) for │Z │ < 1/2 What is the condition for stability in Z-domain? Mention the basic factors that affect thr ROC of z- transform. Find the z- transform of a digita limpulse signal and digital step signal PART - B 1. Determine the Z-transform and ROC of a. x(n) = rn cos ωn u(n) b. x(n) = n2an u(n) c. x(n) = -1/3 (-1/4)n u(n) – 4/3 (2)n u(-n-1) d. x(n) = an u(n) + bn u(n) + cn u(-n-1) , |a | < | b| < |c| e. x(n) = cos ωn u(n) f. x(n) = sin ω0n . u(n) g. x(n) = an u(n) h. x(n) = [ 3 (2n) – 4 (3n)] u(n) 2. Find the inverse Z-transform of a. X(z) = z (z+1) / (z-0.5)3 b. X(z) = 1+3z-1 / 1 + 3z-1 + 2z-2 c. H(z) = 1 / [1 - 3z-1 + 0.5z-2] |z | > 1
d. X(z) = [z (z2- 4z +5)] / [(z-3) (z-2) ( z-1)] for ROC |2 | < | z| < |3|, |z| > 3, |z|< 1
3. Determine the system function and pole zero pattern for the system described by
difference equation y (n) -0.6 y (n-1) +0.5 y (n-2) = x (n) – 0.7 x (n-2)
4. Determine the pole –zero plot for the system described by the difference
equation y (n) – 3/4 y (n-1) +1/8 y (n-2) = x(n) – x(n-1)
5. Explain the properties of Z-transform.
6. Perform the convolution of the following two sequences using Z-transforms.
x(n) = 0.2n u(n) and h(n) = (0.3)n u(n)
7. A causal LTI system has an impulse response h(n) for which the Z-transform is
given by H(z) = (1+z-1) / [(1 + 1/2z-1) (1 + 1/4z-1). What is the ROC of H (z)? Is
the system stable? 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).Find the impulse response
h (n) of the system.
8. Solve the difference equation y(n) -3y(n-1) – 4y(n-2) = 0, n ≥ 0 ,y(-1) = 5
9. Compute the response of the system y(n) = 0.7 y(n-1)-0.12y(n-2) +x(n-1)+
x (n-2)to the input x(n) = n u(n)
10. What is ROC? Explain with an example.
11. A causal LTI IIR digital filter is characterized by a constant co-efficient difference equation given by y(n) = x(n-1)-1.2x(n-2)+x(n-3)+1.3 y(n-1) – 1.04 y(n-2)+0.222y(n-3),obtain its transfer function.
12. Determine the system function and impulse response of the system described by the difference equation y(n) = x(n) +2x(n-1)- 4x(n-2) + x(n-3)
13. Solve the difference equation y(n) - 4y(n-1) - +4 y(n-2) = x(n) – x(n-1) with the initial condition y(-1) = y(-2) = 1
14. Find the impulse response of the system described by the difference equation y(n) = 0.7 y(n-1) -0.1 y(n-2) +2 x(n) – x(n-2)
15. Determine the z- transform and ROC of the signal x (n) = [3 (2n) – 4 (3n)] u(n).
16. State and prove convolution theorem in z-transform.
17. Given x(n) = δ(n) + 2 δ(n-1) and y(n) = 3 δ(n+1) + δ(n)- δ(n-1). Find x(n) * y(n) and X(z).Y(z).
UNIT - III
PART – A
Compute the DFT of x(n) = δ(n – no)
State and prove the Parseval’s relation of DFT.
What do you mean by the term bit reversal as applied to DFT?
Define discrete Fourier series.
Draw the basic butterfly diagram of DIF –FFT algorithm.
Compute the DFT of x(n) = an
State the time shifting and frequency shifting properties of DFT.
What is twiddle factor? What are its properties?
Draw the basic butterfly diagram of DIT –FFT algorithm.
Determine the 3 point circular convolution of x(n) = {1,2,3} and h(n) = {0.5,0,1}
If an N-point sequence x(n) has N-point DFT of X(K) then what is the DFT of the following i) x*(n) ii) x*(N-n) iii) x((n-l))N iv) x(n) ej2πln/N
What is FFT and what are its advantages?
Distinguish between DFT and DTFT (Fourier transform)
What is the basic operation of DIT –FFT algorithm?
What is zero padding? What are its uses?
State and prove Parseval’s relation for DFT.
Draw the flow graph of radix – 2 DIF - FFT algorithm for N= 4
What do you mean by bit reversal in DFT?
20. Write the periodicity and symmetry property of twiddle factor.
21. Give the relationship between z-domain and frequency domain.
22. Distinguish between discrete Fourier series and discrete Fourier transform.
23. What is the relationship between Fourier series co-efficient of a periodic
sequence and DFT?
24. What is the circular frequency shifting property of DFT?
25. Establish the relation between DFT and z-transform.
26. Define DFT pair.
27. Define overshoot.
28. Define Gibbs phenomenon.
29. How many multiplications and additions are required to compute N-point DFT
using radix – 2 FFT?
PART – B
Perform circular convolution of the sequence using DFT and IDFT technique
x1(n) = {2, 1,2,1} x2 (n) = {0,1,2,3} (8)
2. Compute the DFT of the sequence x(n) = {1,1,1,1,1,1,0,0} (8)
From the first principles obtain the signal flow graph for computing 8 – point DFT using radix-2 DIT FFT algorithm. Using the above compute the DFT of sequence x(n) = {0.5,0.5,0.5,0.5,0,0,0,0} (16)
State and prove the circular convolution property of DFT.Compute the circular
convolution of x(n) = {0,1,2,3,4} and h(n) = {0,1,0,0,0} (8)
Perform circular convolution of the sequence using DFT and IDFT technique
x1(n) = {1,1,2,1} x2 (n) = {1,2,3,4} (8)
Compute the DFT of the sequence x(n) = {1,1,1,1,1,1,0,0} (8)
From the first principles obtain the signal flow graph for computing 8 – point DFT using radix-2 DIF-FFT algorithm. An 8 point sequence is given by x(n)={2,2,2,2,1,1,1,1} compute its 8 point DFT of x(n) by radix-2 DIF-FFT (16)
Compute 5 point circular convolution of x1(n) = δ (n) +δ (n-1)-δ (n-2) - δ (n-3) and x2(n) = δ (n) – δ (n-2)+ δ (n-4) (8)
Explain any five properties of DFT. (10)
Derive DIF – FFT algorithm. Draw its basic butterfly structure and compute the DFT x(n) = (-1)n using radix 2 DIF – FFT algorithm. (16)
Perform circular convolution of the sequence using DFT and IDFT technique
x1(n) = {0,1,2,3} x2 (n) = {1,0,0,1} ( 8 )
Compute the DFT of the sequence x (n) = 1/3 δ (n) – 1/3 δ (n-1) +1/3 δ (n -2) (6)
From the first principles obtain the signal flow graph for computing 8 – point DFT using radix-2 DIT - FFT algorithm. Using the above compute the DFT of sequence x(n) = 2 sin nπ / 4 for 0 ≤ n ≤ 7 (16)
What is circular convolution? Explain the circular convolution property of DFT and compute the circular convolution of the sequence x(n)=(2,1,0,1,0) with
itself (8)
Perform circular convolution of the sequence using DFT and IDFT technique
x1(n) = {0,1,2,3} x2 (n) = {1,0,0,1} ( 8 )
i) Compute the DFT of the sequence x (n) = (-1)n (4)
ii) What are the differences and similarities between DIT – FFT and DIF – FFT
algorithms? (4)
From the first principles obtain the signal flow graph for computing 8 – point DFT using radix-2 DIT - FFT algorithm. Using the above compute the DFT of sequence x(n) = cos nπ / 4 for 0 ≤ n ≤ 7 (16)
18. Compute 4-point DFT of the sequence x (n) = (0, 1, 2, 3) (6)
19. Compute 4-point DFT of the sequence x (n) = (1, 0, 0, 1) (6)
20. Explain the procedure for finding IDFT using FFT algorithm (6)
21. Compute the output using 8 point DIT – FFT algorithm for the sequence
x(n) = {1,2,3,4,5,6,7,8} (16)
22.Determine the 8-point DFT of the sequence x(n) = {0,0,1,1,1,0,0,0}
23. Find the circular convolution of x(n) = 1,2,3,4} and h(n) = {4,3,2,1}
24. Determine the 8 point DFT of the signal x(n) = {1,1,1,1,1,1,0,0}. Sketch its
magnitude and phase.
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