Signals & Systems (EC-402) - Important Questions

Explain and distinguish the classification of signals: continuous-time vs discrete-time, unit step vs unit ramp, periodic vs aperiodic, deterministic vs random, energy vs power, and even vs odd, with suitable examples.

Determine whether the given signals are energy, power, or neither signals, for a single-tone periodic signal x(t)=cos t or e^{j(2t+pi/4)} and a decaying exponential x(n)=(1/3)^n u(n).

Determine/check whether given systems described by input-output equations are linear, time-invariant, causal, static/memoryless, dynamic, and stable with justification.

Define a system and define/describe system properties: linearity (additivity and homogeneity), time-invariance, causality and realizability, stability, and static vs dynamic systems.

Explain the impulse response of a discrete-time LTI system, its properties, and derive the convolution sum.

Explain Direct Form-I, Direct Form-II, Cascade Form and Parallel Form realization structures with block diagrams.

Find the continuous-time convolution / LTI output y(t) = x(t)*h(t) for given x(t) and h(t) using the convolution integral, e.g., x(t)=u(t-1)-u(t+1) and h(t)=e^{-at}u(t), a>0.

State and prove/explain the properties of Z-transform including time shifting, convolution, initial value theorem, differentiation and integration.

Define the Region of Convergence (ROC) of the z-transform and explain its properties.

Using Z-transform properties, find the Z-transform and ROC of a given signal, e.g., 1/(1-z^{-1})^2.

Find the inverse Z-transform for an exterior ROC |z| > r (causal sequence), e.g., via partial fraction expansion.

Explain the properties and applications of the Discrete-Time Fourier Series (DTFS) / Fourier series.

What is the (continuous-time) Fourier transform? Explain its properties.

Explain state-space analysis and state-variable / matrix representation of dynamic systems.

Define the state transition matrix and explain its role / importance in dynamic system analysis.

State and prove the sampling theorem for band-limited signals, including effect of under-sampling and reconstruction from samples.