Signals and Systems (EX-302) - Important Questions

Determine whether the following continuous-time signals are periodic or non-periodic, and if periodic find the fundamental period: (i) x(t) = cos(4c0t) + sin(6c0t) (ii) x(t) = e^{j3t} + e^{j5t}.

Determine whether the following signals are energy signals, power signals or neither: (i) x(t) = t^2 u(t-1) (ii) x(t) = 2u(t) - u(t-3). Justify with calculation of energy and power.

Explain even and odd signals with suitable examples. Show how any signal can be decomposed into even and odd parts and derive the relationship between unit impulse and unit step functions.

Define a system. Explain/classify the basic properties of systems - linearity, time-invariance, causality, stability and memory with examples.

State and prove the convolution property of Laplace transform. Illustrate with a suitable example.

Determine the trigonometric Fourier series expansion for the given periodic rectangular/square waveform and discuss Dirichlet's conditions for its existence.

State and prove the time convolution theorem associated with Fourier transform.

Discuss the advantages of wavelet transform over Fourier and Laplace transforms. Explain the properties a function must satisfy to be a wavelet with example.

Explain the state variable representation and matrix representation of an LTI continuous-time system with a suitable example.

Define impulse response, step response and frequency response of an LTI continuous-time system and explain their interrelation.

Find the impulse response of a causal LTI system described by a linear constant-coefficient differential equation, e.g. d^2y/dt^2 + 5dy/dt + 6y = dx/dt + x, assuming zero initial conditions.

Explain the basic operations on signals - time shifting, time scaling, time reversal, addition and multiplication - with suitable examples and sketches.

State and explain the sampling theorem for band-limited continuous-time signals. Explain aliasing effect, its causes and how to avoid/reduce it.

Explain the Region of Convergence (ROC) of Z-transform and describe the properties of Z-transform with suitable example.

Find the DTFT X(e^{jc9}) of the finite-duration sequence x(n) = {1,5,-2,1,3,4,2,0,5} and state the properties of DTFT used.

Determine the response of the DT LTI system described by y(n) = (5/6)y(n-1) - (1/6)y(n-2) + x(n) to the input x(n) = b4(n) - (1/3)b4(n-1) using DTFT / Z-transform.