Signals and Systems (EX-302) - Important Questions

Explain even and odd signals with examples, including decomposition of the unit step signal and relation between impulse and unit step functions.

Determine whether given continuous-time signals are periodic and find the fundamental period if periodic.

Describe periodic vs aperiodic signals and energy vs power signals with neat sketches.

Determine whether given signals (a growing $t^2$-type signal and a finite-duration step-difference pulse) are energy signals, power signals, or neither.

Explain the classification of signals in detail and differentiate between the types.

Define Signal. Compare continuous time and discrete time signal.

Define the basic properties of signals.

Compare even vs odd signals and energy vs power signals with examples.

Classify given signals as energy/power/neither and check given systems for time-invariance.

Derive the relation between complex exponential and sinusoidal signals.

Write short notes on digital filters, analog filters, and linear time-invariant systems and their properties.

Explain energy and power signals and determine whether given signals are energy or power signals.

State and prove the convolution property of Laplace transform.

Write down the properties of Fourier transform and Laplace transform.

Discuss the advantages of the wavelet transform over other transforms and the properties a function must satisfy to be a wavelet.

Write short notes on wavelet transform, DTFT and its properties, digital filters, and inverse z-transform.

Write down the properties of Fourier transform including duality.

Define Laplace transform and derive the relationship between Laplace and Fourier transform.

Explain limitations of Fourier series and Dirichlet's conditions.

Determine Fourier series expansion for the given waveform.

Explain the Laplace transform and region of convergence in detail.

Derive the Laplace and Fourier transform of $e^{-at}u(t)$ and $t \cdot u(t)$.

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

Explain the Region of Convergence (RoC) with a suitable 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.

Explain the block diagram representation of LTI continuous-time systems, its advantages, and the concept of ROC.

Write short notes on LTI systems and analog filters.

Explain analog filters in brief and describe the properties of LTI systems.

Find the impulse response of an LTI system given its input-output convolution integral relation.

Find the impulse response of a causal LTI system described by a linear constant-coefficient differential equation assuming zero initial conditions.

Describe the differential equation representation of LTI continuous-time systems.

Explain the impulse response and step response of an LTI system.

Write short note on analog filters and ROC (Region of Convergence).

Discuss analog filters with their types, diagrams and applications.

Given the second-order differential equation of a causal stable continuous-time LTI system, determine whether the system is overdamped, underdamped or critically damped.

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

Explain ROC of Z-transform and describe the properties of Z-transform with example.

Determine Z-transform with ROC of $x(n)=(n+1)u(n)$ and $x(n)=3(4^n+3^n)u(n)$.

Find the linear convolution sum of the given sequences $x(n)$ and $h(n)$, e.g. by graphical/tabular method, and verify the result.

Using properties of Z-transform, find Z-transform and ROC of $\frac{1}{(1-z^{-1})^2}$.

Compute the DTFT $X(e^{j\omega})$ of the given finite sequence $x(n)$

Determine the Z-transform of $x(n) = (-1)^n \cos\left(\frac{\pi}{3}n\right) u(n)$.

Find $h(n)$ from $H(z)=\frac{3-4z^{-1}}{1-3.5z^{-1}+1.5z^{-2}}$ for (i) stable system and (ii) causal system.

Explain signal reconstruction / recovery from its sampled signal

Write short notes on digital filters, DTFT and its properties, even and odd signals, and aliasing

Explain linear convolution of a sequence with an example.

Find the inverse z-transform of $X(z)=z/(z+1)(z+2)$.

Determine the response/output of the given DT LTI difference equation system to the given impulse-based input.

Define first-order discrete-time LTI system and give its step response and impulse response.

Explain the block diagram representation of LTI discrete-time systems.

Write short notes on two: digital filters, non-ideal frequency selective filter, invertible and inverse system.

Draw the direct form, cascade form and parallel form block diagram realizations for the discrete-time LTI system with $H(z) = \frac{1}{(1+z^{-1}/3)(1-z^{-1}/6)}$.

Discuss difference equations of linear time-invariant discrete-time systems.

Describe/explain the analysis of DT LTI systems using the DTFT.