Table of Contents

Toggle**Important RGPV Question**

**EC-402 (Signal & System)**

**IV Sem, EC**

**UNIT-1 Introduction of Signals, Systems & their Classification**

**Q.1**Β Define signal. Classify the different types of signal in detail using time domain technique.

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**Q.2Β I**dentify the following signals are energy signal or power signal or neither-

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**Q.3**Β Define system. Explain the different types of system with examples.

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**Q.4**Β Determine whether the following systems-

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**Q.5**Β Define signal and classify different types of signals with proper representation.

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**Q.6**Β Differentiate following

i) Periodic and aperiodic signals

ii) Random and deterministic signals

iii) Even and odd signals

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**Q.7**Β Describe following in brief

i) Causal and noncausal system

ii) Additivity and homogeneity

iii) Causality and realizability

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**Q.8Β **Explain the following signals with examples.

i) Continuous Time and discrete time

ii) Periodic and Aperiodic

iii) Energy and Power

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**Q.9**Β Check whether the following are stable, causal and memory less

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**Q.10**Β Find out whether the following signals are periodic or not. If periodic find the period

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**Q.11**Β Obtain the parallel realization of the system given by

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**Q.12**Β With the help of examples, explain the following properties of signals.

i) Time shifting

ii) Time scaling

iii) Time reversal

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**Q.13** Which of the following systems are BIBO stable?

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**Q.14Β **Which of the following systems are non linear?

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**Q.15**Β Write short notes on Classification of signals

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**UNIT β 2 Linear Time-Invariant Systems**

**Q.1**Β What is Convolution? Find the Convolution integral of the signals *x(t) = e-2tΒ u(t)*Β and *h(t) = e-4tΒ u(t).*Β

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**Q.2**Β Comment on the causality and stability of the given system

*h(t)= (2+ e-3t) u(t)*Β

Also find the step response of the system.

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**Q.3**Β Write properties of the impulse response representation for LTI systems.

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**Q.4**Β Discuss impulse response representation for LTI system and describe LTI system by difference equations.

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**Q.5**Β Explain block diagram representations for following:

i) Direct form – I and Direct form – II

ii) Cascade and parallel form

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**Q.6Β **Given the impulse response of a discrete time LTI system

i) Find the system function H(z) of the system.

ii) Find the difference equation representation of the system.

iii) Find the step response of the system.

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**Q.7**Β Write short note on Convolution.

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**Q.8**Β What is convolution integral? State the distributive, commutative and associative property of convolution.

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**Q.9**Β The unit impulse response of a linear time invariant system is the unit step function u(t). For t >0, find the response of the system to an excitation e-atΒ u(t) for a>0.

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**Q.10**Β What is the necessary and sufficient condition on the impulse response for

i) Causality

ii) Stability

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**Q.11**Β The impulse response h(n) of a linear time invariant system is given *by h(n) = u(n+3)+u(n-2)-2u(n-7)*Β Is the system stable? Is the system causal?

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**Q.12Β **Find the convolution of

X1(n)={1,-2,3,1}

X2(n)={2,-3,2}

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**UNIT β 3 z-TransformΒ **

**Q.1**Β Show a direct form-I realization of the transfer function-

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**Q.2** State and prove initial value theorem of z transform. Also find the initial value and final value of the given signal.

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**Q.3** Find z-transform of the given signal-

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Β **Q.4** State and prove any four z-transform properties.

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**Q.5** Using partial fraction expansion find the inverse z-transform of

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**Β Q.6** Consider the signalΒ Β

Β Evaluate the z-transform of this signal and specify the corresponding region of convergence.

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**Q.7** Describe following in brief

i) ROC of finite and infinite duration sequence

ii) Properties of the ROC and Z-transform

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**Q.8** Discuss properties and application of discrete time Fourier series.

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**Q.9** Derive the following properties of Z Transform

i) Time Shifting

ii) Initial Value Theorem

iii) Convolution

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Β **Q.10** Define the ROC and its Properties.

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Β **Q.11**Β

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**Q.12**Β Write short notes on Unilateral Z transforms.

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**Q.13** Find the z-transform and ROC of the following sequences

i) *x(n)=u(n)-u (n-3)*

ii) *x(n)= (1, 2, 3, 2)*

iii) *x(n)={1,2,-1, 2, 3}*

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**Q.14** State and prove the scaling and time shifting properties of z transform.

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**Q.15** Write short notes on ROC of finite duration sequence

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**UNIT β 4 Fourier Analysis of Discrete Time Signals**Β

**Q.1 **Find the exponential Fourier series and plot the magnitude and phase spectra of the following triangular wave form.

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**Q.2** Find the Fourier Transform of Rectangular pulse. Sketch the signal and Fourier transform.

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**Q.3** Demonstrate time shifting property and time-scaling property of Fourier transform.

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Β **Q.4** Obtain DTFT of following signals-

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**Q.5** Use the Fourier series analysis to calculate the coefficients a for the continuous time periodic signal.

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**Q.6** Compute the Fourier transform of the following signals.

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**Q.7** Discuss convergence of discrete time Fourier transform and write applications of DTFT.

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**Q.8** State and prove any three properties of Fourier Transform

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**Q.9** Using the properties of Fourier Transform find the X(jΟ) and G(jΟ)

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**Q.10** Write short note on Applications of DTFT.

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**Q.11** Write any two properties of Discrete Time Fourier Transform (DTFT) and prove them.

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**Q.12** Find the Fourier series of the following discrete-time signal.

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**Q.13** Obtain the direct form-I realization for the system described by the difference equation

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**Q.14 **Obtain parallel form realization of the discrete time system described by the difference equation

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**UNIT β 5 State-space Analysis & Multi-input**Β

**Q.1** State and prove sampling theorem and discuss the effect of under sampling.

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**Q.2** Write short notes on –

i) State space analysis

ii) State transition matrix

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**Q.3** How multi-input, multi-output systems are represented in state space? Take 3 input 2 output system and represent it in state space form.

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**Q.4** Write properties and role of state transition matrix. Also describe any two methods to determine state transition matrix.

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**Q.5** Discuss following in detail:

i) Sampling theorem and its implications

ii) Reconstruction of a signal from its samples

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**Q.6** State and explain sampling theorem with necessary equation and illustration.

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**Q.7 **Explain various methods of evaluation of state transition matrix with suitable example.

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**Q.8** Write short note on State space analysis.

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**— Best of Luck for Exam —**