**Important RGPV Question**

Table of Contents

Toggle** EX-302 (Signals And Systems)**

**III Sem, EX**

**UNIT-1 : ****Classifications of signals and systems**

**Q.1) **What are the basic operations on signals? Explain.

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**Q.2) **The output of the system is given as y (1) = x (1) +x(1+2) + x (t- 3), then check the given system is time variant or not.

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**Q.3) **Define basic properties of systems.

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**Q.4) **Define basic standard signals with suitable diagrams.

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**Q.5) **Describe Briefly:

i) Find whether the following signals are energy or power signal or neither:

ii) Check whether the following systems are time invariant or not:

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**Q.6) ** Write the classification of systems based on certain properties.

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**Q.7) **Explain the various operations on signals with examples.

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** ****Q.8)** What are the types of representation of discrete time signals? Illustrate with an example.

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**Q.9) **How are signals classified ? Differentiate between them.

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**Q.10) **Discuss random signals and its statistical properties.

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**Q.11) **Derive the relation between complex exponential and sinusoidal signals.

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**Q.12) **How are systems classified ? Define each one of them.

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**Q.13)** Classify signals. Why the unit step signal u(t) is not even and not odd? Separate even and odd parts of u (t).

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**UNIT-2 : ****Analysis of continuous time signals**

**Q.1)** Find the Fourier Transform of x (1) =coswt.

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**Q.2) **List out the properties of Laplace transform.

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**Q.3)** Write down the properties of Fourier transform and Laplace transform.

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**Q.4)** Write short note on Dirichlets conditions for Fourier series. Find the Fourier series for

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**Q.5)** Find the impulse response of the system.

**Q.6)** What do you understand by Region of Convergence (RoC). Give an example.

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**Q.7)** What is the difference between Fourier transform and Laplace transform? Define wavelet transform also.

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**Q.8)** State the properties of Fourier Series.

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**Q.9) **Write a short note on complex Fourier spectrum.

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**Q.10)** Make comparison between Fourier transform and Laplace. transform.

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**Q.11)** Discuss different advantages of wavelet transform on other transforms. Also discuss few properties that a function need to satisfy.

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**Q.12)** Define and discuss the conditions for orthogonality of

functions.

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**Q.13)** Derive the expressions for the trigonometric Fourier series coefficients.

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**Q.14)** State and prove the time shifting and frequency shifting properties of Fourier Transform.

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**Q.15)** Derive the Fourier transform from exponential Fourier series.

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**UNIT-3 : ****Linear time invariant continuous time signals**

**Q.1)** Find the transfer function of the system governed by the following impulse response.

h(t)=u(t)+3e-4tu(t).

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**Q.2) **Obtain the conditions for distortion less transmission through a system. Explain ideal filters.

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**UNIT-4 : ****Analysis of discrete time signals**

**Q.1)** Find the inverse z-transform of the function

X(z)=z/(z+1)(z+2).

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**Q.2) **Define sampling and how to avoid aliasing effect in sampling.

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**Q.3) **Write a short note on properties of convolution.

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**Q.4) **Determine the Z-transform of the signal:

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**Q.5) **State sampling Theorem for band-limited signals. What is Aliasing effect? How it can be reduced?

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**Q.6) **State and prove the time convolution theorem associated with Fourier transform.

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**Q.7)** Explain the sampling of Continuous Transform signals and Aliasing.

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**Q.8) **Convolute graphically the following sequences and verify the results.

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**Q.9) **State and prove the time convolution theorem associated with Fourier transform.

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**Q.10) **Explain the sampling of Continuous Transform signals and Aliasing.

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**Q.11) **State and explain the sampling theorem for band pass signal.

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**Q.12) **Explain the signal recovery (reconstruction) from its sampled signals.

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**UNIT-5 : ****Linear time invariant discrete time systems**

**Q.1) **Discuss difference equations of Linear Time Invariant Discrete Time Systems.

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**Q.2) **Describe analysis of DT LTI systems using DTFT.

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**Q.3) **Explain with suitable example what is state variable representation of an LTI CT system.

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**Q.4) **Discuss state variable representation and matrix representation of systems.

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**Q.5)** The input and output of a causal LTI system are related by the differential equation:

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**Q.6) **A LTI system is characterized by the transfer function

Determine the h(n) for the following conditions:

i) The system is stable.

ii) The system is causal.

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**Q.7) **Briefly describe:

i) Block diagram representation of LTI continuous time systems.

ii) ROC

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**Q.8) **Differentiate between analog and digital filters.

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**Q.9) **Discuss different advantages of LTI system on linear time variant system. Also discuss two properties of LTI and prove it.

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**Q.10) **A LTI system is described by following differential equation. Find out its impulse response assuming all conditions to be zero.

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**Q.11)** The input x(t) and output y(t) for a system satisfy the differential equation.

i) Compute the transfer function and impulse response.

ii)Draw the block diagram representation and other representations.

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**Q.12) **For a given LTI system determine formula for convolution integral.

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