The questions are given, High school final essays of Sociology

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2022/2023

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UNIT-I
SAQ’S
1. Define Energy signal.
2. Estimate when the set of vectors are orthogonal over an interval (t1,t2).
3. Write a short note on unit impulse function
4. Define Causality and stability of a signal.
5. Explain the analogy between vectors and signals
6. List conditions defined for a signal to be energy or power
7. Define Orthogonality in complex functions.
8. Discuss about unit step, ramp, and parabolic functions and Outline the relation among
the functions.
LAQ’S
1. Apply basic operations on signals. Illustrate with relevant examples
2. Illustrate the Orthogonality in Complex functions
3. Illustrate the concept of impulse function. Explain how signum function is expressed
in terms of unit step function.
4. Solve the system
d3y(t)
dt3+2d2y(t)
dt2+4dy (t)
dt +3y2(t)=x(t+1)
is
i) Static or Dynamic ii)Linear or Non-Linear
iii)Causal or Non-causal iv)Time-invariant or time variant
5. Develop the expression for mean square error when a function is approximated in set
of mutually orthogonal functions.
6. Discuss in detail about the classification of signals
7. Solve the following system y(t)=t2x(t)+x(t-4) is
a)static or dynamic b) linear or non-linear
c) causal or non-causal d) time variant or invariant
8. Relate the properties of unit impulse function.
9. Analyze the following signals sinnω0t and cosmω0t are orthogonal or not over the
interval (t0 ,t0 + 2π/ω0).
10. Define Linear and Non-Linear systems. Apply the conditions and check whether the
following systems are linear or not.
i) y(t)=ex(t) ii) y(n)=nx(n)
11. Define various elementary continuous time signals. Illustrate them graphically
UNIT-II
SAQ’S
1. Define the trigonometric Fourier series.
2. Write the conditions for the existence of Fourier transform.
3. List the Dirichlet’s conditions for existence of Fourier Series.
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UNIT-I

SAQ’S

  1. Define Energy signal.
  2. Estimate when the set of vectors are orthogonal over an interval (t1,t2).
  3. Write a short note on unit impulse function
  4. Define Causality and stability of a signal.
  5. Explain the analogy between vectors and signals
  6. List conditions defined for a signal to be energy or power
  7. Define Orthogonality in complex functions.
  8. Discuss about unit step, ramp, and parabolic functions and Outline the relation among the functions. LAQ’S
  9. Apply basic operations on signals. Illustrate with relevant examples
  10. Illustrate the Orthogonality in Complex functions
  11. Illustrate the concept of impulse function. Explain how signum function is expressed in terms of unit step function.
  12. Solve the system d 3 y ( t ) dt

3 +^2

d 2 y ( t ) dt

2 +^4

dy ( t ) dt

  • 3 y^2 ( t )= x ( t + 1 ) is i) Static or Dynamic ii)Linear or Non-Linear iii)Causal or Non-causal iv)Time-invariant or time variant
  1. Develop the expression for mean square error when a function is approximated in set of mutually orthogonal functions.
  2. Discuss in detail about the classification of signals
  3. Solve the following system y(t)=t^2 x(t)+x(t-4) is a)static or dynamic b) linear or non-linear c) causal or non-causal d) time variant or invariant
  4. Relate the properties of unit impulse function.
  5. Analyze the following signals sinnω 0 t and cosmω 0 t are orthogonal or not over the interval (t 0 ,t 0 + 2π/ ω 0 ).
  6. Define Linear and Non-Linear systems. Apply the conditions and check whether the following systems are linear or not. i) y(t)=ex(t)^ ii) y(n)=nx(n)
  7. Define various elementary continuous time signals. Illustrate them graphically UNIT-II SAQ’S
  8. Define the trigonometric Fourier series.
  9. Write the conditions for the existence of Fourier transform.
  10. List the Dirichlet’s conditions for existence of Fourier Series.
  1. Explain what is frequency spectrum?
  2. Identify periodic signal to a non periodic signal with an example.
  3. Discuss the effect of wave symmetry?
  4. Differentiate among Trigonometric and Exponential Fourier Series
  5. Define Fourier transform of a signal. LAQ’S
  6. Analyze Fourier series under even symmetry & determine its Fourier series coefficients.
  7. Apply the Fourier Transform of following signal.
  8. Compose the Trigonometric Fourier series of the half wave rectified sine wave as shown below.
  9. Analyze the Fourier Transform of the following signals & plot frequency response. a) δ(t) b)Rectangular pulse c) u(t)
  10. Analyze the wave symmetry of Fourier Series in detail.
  11. Compose the Fourier Transform of the signals a) signum function b) e- a│t│
  12. a) What do you infer from the below signal. [ b) Transform the given signal shown below into its equivalent frequency domain.
  13. Use fourier transform to find X(ω) for the given signals. i) x(t)= e-at^ u(t) ii) x(t) = δ(t+2)+δ(t+1)+δ(t-1)+δ(t-2)
  14. Analyze Time Scaling property of Fourier Transform
  1. Define Power Spectral Density.
  2. Define Energy Spectral Density
  3. Distinguish between correlation and autocorrelation LAQ’S
  4. Solve the convolution for the signals x 1 (t) = cost u(t) ; x 2 (t)=u(t).
  5. Illustrate time convolution theorem
  6. Distinguish the ESD and PSD
  7. Contrast the relation between convolution & correlation.
  8. Analyze time convolution theorem with Fourier transforms.
  9. What is Correlation. Classify the types of correlation and explain.
  10. Demonstrate the properties of Auto-correlation of energy signals.
  11. Apply and prove Frequency convolution theorem associated with Fourier transform.
  12. Relate signal comparison: Correlation of functions
  13. Calculate convolution between the signals x 1 (t) =e-2tu(t) ; x 2 (t)=e-4t^ u(t)
  14. List and build the graphical procedure to perform convolution.
  15. Report properties of cross correlation function for energy or power signals UNIT-V SAQ’S
  16. Define LTI system.
  17. Predict the need of state space analysis.
  18. Associate the relationship between impulse response and transfer function
  19. Discuss about the term Physical realizability
  20. Define Impulse response of a system
  21. State the conditions required for as system to be LTI System? LAQ’S
  22. Solve the impulse response of the system, if LTI system is described by d 2 y ( t ) dt (^2) +

dy ( t )

dt + 6 y^ (^ t^ )^ =x(t)

  1. Illustrate on state space analysis and state model.
  2. Relate between rise time and bandwidth.
  3. Illustrate on state space analysis and state model.
  4. Contrast among Ideal filter characteristics
  5. Illustrate the conditions for distortion less transmission through a system.
  6. Apply the knowledge of frequency response and Illustrate characteristics of filters with respect to ideal versions.
  7. A system produces an output of y(t)=e-tu(t) for an input of x(t)= e-2tu(t). Solve to find the impulse response.