## Anna University Important Questions

Download Anna University 3rd Semester Important Questions for ECE EC2204 Signals and Systems , Unit Wise ( All 5 Units ) .

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## EC 2204 Signals and Systems Important Questions

** UNIT I**

**REPRESENTATION OF SIGNALS**

**PART-A (2 Marks)**

**1. Define Signal.**

**2. Define system.**

**3. What are the major classifications of the signal?**

**4. Define discrete time signals and classify them.**

**5. Define continuous time signals and classify them.**

**6. Define discrete time unit step &unit impulse.**

**7. Define continuous time unit step and unit impulse.**

**8. Define unit ramp signal.**

**9. Define periodic signal and non-periodic signal.**

**10. Define even and odd signal ?**

**11. Define Energy and power signal.**

**12. Define unit pulse function.**

**13. Define continuous time complex exponential signal.**

**14. What is continuous time real exponential signal.**

**15. What is continuous time growing exponential signal?**

**16. State the BIBO criterion for stability.**

**17. Find whether the signal given by x (n) = 5cos (6 _n) is periodic**

**18. Write down the exponential form of the Fourier series representation of a**

**Periodic signal?**

**19. Write down the trigonometric form of the fourier series representation of a**

**periodic signal?**

**20. Write short notes on dirichlets conditions for fourier series.**

**21. State Time Shifting property in relation to fourier series.**

**22. State parseval’s theorem for continuous time periodic signals.**

**PART – B**

**1. (a) For the systems represented by the following functions. Determine whether**

**every system is (1) stable (2) Causal (3) linear (4) Shift invariant (4)**

**(i) T[x(n)]= ex(n)**

**(ii) T[x(n)]=ax(n)+6**

**2. Determine whether the following systems are static or Dynamic, Linear or Nonlinear,Shift variant or Invarient, Causal or Non-causal, Stable or unstable. (4)**

**(i) y(t) = x(t+10) + x2(t)**

**(ii) dy(t)/dt + 10 y(t) = x(t)**

**3. Explain about the properties of continuous time fourier series. (8)**

**4. Find the fourier coefficients of the given signal. (4)**

**x(t) = 1+ sin 2_ot + 2 cos 2_ot + cos (3_ot + _/3)**

**5. Determine the Fourier series coefficient of exponential representation of x(t)**

**x(t) = 1, ItI (8)**

**0, T1< ItI < T/ 2 **

**6. Find the exponential series of the following signal. (8) **

**7. Find which of the following signal are energy or power signals. (8)**

** a) x(t)=e-3t u(t) b) x(t) = ej(2t+_/4) c) x(n)= cos(_/4n) **

**8. Explain the properties of Discrete time fourier serier (8) **

**9. Find the cosine fourier series of an half wave rectified sine function. (8)**

**10. Explain the classification of signals with examples. (8) **

** **

**UNIT II ANALYSIS OF CONTINUOUS TIME SIGNALS AND SYSTEMS **

** **

**PART-A (2 Marks)**

**1. Define continuous time system. **

**2. Define Fourier transform pair. **

**3. Write short notes on dirichlets conditions for fourier transform. **

**4. Explain how aperiodic signals can be represented by fourier transform.**

**5. State convolution property in relation to fourier transform. **

**6. State parseval’s relation for continuous time fourier transform. **

**7. What is the use of Laplace transform? **

**8. What are the types of laplace transform? **

**9. Define Bilateral and unilateral laplace transform. **

**10. Define inverse laplace transform. **

**11. State the linearity property for laplace transform. **

**12. State the time shifting property for laplace transform. **

**13. Region of convergence of the laplace transform. **

**14. What is pole zero plot. **

**15. State initial value theorem and final value theorem for laplace transform. **

**16. State Convolution property. **

**17. Define a causal system. **

**18. What is meant by linear system? **

**19. Define time invariant system. **

**20. Define stable system? **

**21. Define memory and memoryless system. **

**22. Define invertible system. **

**23. What is superposition property? **

**24. Find the fourier transform of x(t)=cos(_0t) **

** **

**PART – B **

**1. Determine the inverse laplace of the following functions. (6) **

**1) 1/s(s+1) 2) 3s2 +8s+6 (s+2)(s2+2s+1) **

**2. Explain about the classifications of continuous time system. (8) **

**3. A system is described by the differential equation. (10) d2y(t)/dt2+3dy(t)/dt+2y(t)=dx(t)/dt if y(0) =2;dy(0)/dt = 1 and x(t)=e-t u(t) Use laplace transform to determine the response of the system to a unit step input applied at t=0. **

**4. Obtain the transfer function of the system when y(t) = e-t-2 e-2t+ e-3t and x(t)= e-0.5t (8) 5. a) Discuss the condition on stability of an LTI system based on Laplace domain representation. (3)**

** b) Bring the equivalence between Laplace transform and Fourier transform.(5) **

**6. Explain the properties of laplace transform (8) **

**7. Find the impulse and step response of the following systems H(s) = 10/s2+6s+10 (6) **

**8.For the transfer function H(s) = s+10/ s2+3s+2 find the response due to input x(t) = sin2(t) u(t) (6) **

**9. Find the fourier transform of triangular pulse (10) x(t) = _(t/m) ={1-2|t|/m |t| 0 otherwise **

**10. The input and output of a causal LTI system are related by the differential equation. (10)**

** d2y(t)/dt2+6dy(t)/dt+8y(t)=2x(t) i) Find the impulse response of the system. ii) What is the **

** response of this system if x(t) = t e-2t u(t) 11. Consider a causal LTI system with frequency **

** response. (10) H(j_) = 1/ j_ +2 For a particular input x(t) this system is y(t)= e-2t u(t) – e-3t u(t) **

** **

** **

**UNIT III SAMPLING THEOREM AND Z – TRANSFORMS **

** **

**PART-A (2 Marks)**

**1. Why CT**** signals are represented by samples. **

**2. What is meant by sampling. **

**3. State Sampling theorem. **

**4. What is meant by aliasing. **

**5. What are the effects aliasing. **

**6. How the aliasing process is eliminated. **

**7. Define Nyquist rate.and Nyquist interval. **

**8. Define sampling of band pass signals. **

**9. Define Z transform. **

**10. What are the two types of Z transform? **

**11. Define unilateral Z transform. **

**13. What is region of Convergence. **

**14. What are the Properties of ROC. **

**15. What is the time shifting property of Z transform. **

**16. What is the differentiation property in Z domain. **

**17. State convolution property of Z transform. **

**18.**** State**** the methods to find inverse Z transform. **

**19. State multiplication property in relation to Z transform. **

**20. State parseval’s relation for Z transform.**

** 21. What is the relationship between Z transform and fourier transform. **

**22. What is meant by step response of the DT system.**

** **

** PART – B **

**1.State and prove the sampling theorem. Also explain how reconstruction of original signal is done from sampled signal (16) **

**2. Find the Z – transform of the signal (8) (i)x(n)= nan u(n) (ii)x(n)= an cos(_0) u(n) **

**3. Determine the inverse z transform of the following function x(z)=1/(1+z-1) (1-z-1 )2 ROC : |Z>1|**

**4. Explain the properties of z-transform (8)**

**5. Find the z-transform of x(z)= 1+2z-1 / 1- 2z-1 + z-2 if x(n) is anticausal using long**

**division method. (8)**

**6. find the inverse z-transform of x(z)= 1+3z-1 / 1+ 3z-1 + 2z-2 using residue method(8)**

**7. Give the relationship between z-transform and fourier transform. (8)**

** UNIT IV** **DISCRETE TIME SYSTEMS**

**PART-A (2 Marks)**

**1. Define Transfer function of the DT system.**

**2. Define impulse response of a DT system.**

**3. State the significance of difference equations.**

**4. Write the differece equation for Discrete time system.**

**5. Define frequency response of the DT system.**

**6. What is the condition for stable system.**

**7. What are the blocks used for block diagram representation.**

**8. State the significance of block diagram representation.**

**9. What are the properties of convolution?**

**10. State theCommutative properties of convolution?**

**11. State the Associative properties of convolution**

**12. State Distributive properties of convolution**

**13. Define causal system.**

**14. What is the impulse response of the system y(t)=x(t-t0).**

**15. What is the condition for causality if H(z) is given.**

**16. What is the condition for stability if H(z) is given.**

**17. Check whether the system is causal or not ,the H(z) is given by (z3 + z)/(z+1).**

**18. Check whether the system is stable or not ,the H(z) is given by (z/z-a).,|a|<1.**

**19. Determine the transfer function for the sys tem described by the difference**

**equation y(n)- y(n-1) = x(n)- x(n-2).**

**20. How the discrete time system is represented.**

**PART – B**

**1. Give the properties of convolution (6)**

**2. Determine the step response of the difference equation, y(n)-(1/9)y(n-2)=x(n-1)**

**with y(-1)=1 and y(-2)=0 (8)**

**3. Find the impulse response and step response.**

**Y(n)-3/4y(n-1) +1/8 y(n-2) = x(n) (8)**

**4. Find the output y(n) of a linear time invariant discrete time system specified by the**

**equation. (16)**

**Y(n)-3/2y(n-1) +1/2 y(n-2) = 2x(n) +3/2 x(n-1) when initial conditions are y(-1)**

**=0,y(-2) = 1 and input x(n)=(1/4)n u(n)**

**5. Determine the Nyquist sampling rate and Nyquist sampling intervals for**

**sinc(200_t) + 3sinc2(120_t) (6)**

**6. Find the frequency response of the following causal system.**

**Y(n)=1/2x(n)+x(n-1)+1/2 x(n-2) (4)**

**7. Determine inverse Discrete Time Fourier Transform of**

**X(k)={1,0,1,0} (8)**

**8. Give the summary of elementary blocks used to represent discrete (4)**

**time systems.**

**UNIT V** **SYSTEM WITH FINITE AND INFINITE DURATION IMPULSE RESPONSE**

**PART-A (2 Marks)**

**1. What is meant by FIR system.**

**2. What is meant by IIR system.**

**3. What is recursive system?**

**4. What is Non recursive system?**

**5. What is the difference between recursive and non recursive system**

**6. Define realization structure.**

**7. What are the different types of structure realization.**

**8. What is natural response?**

**9. What is zero input Response?**

**10. What is forced response?**

**11. What is complete response?**

**12. Give the direct form I structure.**

**13. Give the direct form II structure..**

**14. How the Cascade realization structure obtained.**

**15. Give the parallel for Realization structure.**

**16. What is transformed structure representation?**

**PART – B**

**1..a) Determine the transposed structure for the system given by difference equation**

**y(n)=(1/2)y(n-1)-(1/4)y(n-2)+x(n)+x(n-1) (16)**

**b) Realize H(s)=s(s+2)/(s+1)(s+3)(s+4) in cascade form**

**2. A difference equation of a discrete time system is given below:**

**y(n)-3/4 y(n-1) +1/8 y(n-1) = x(n) +1/2 x(n-1)**

**draw direct form I and direct form II. (6)**

**3. Realize the following structure in direct form II and direct form I**

**H(s) = s+1/s2 + 3s+5 (10)**

**4. Determine the recursive and nonrecursive system (16)**

**5. Determine the parallel form realization of the discrete time system is**

**y(n) -1/4y(n-1) -1/8 y(n-2) = x(n) +3x(n-1)+2x(n-2) (10)**

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