Signals and Systems

Differentiate between Even and odd signals.

Define the unit impulse sequence.

What do you mean by the Causal and Non-causal systems.

Write the condition for stability of system.

Differentiate continuous - time and discrete - time systems.

What are linear constant - coefficient differential equations.

Define Region of convergence (ROC) for Laplace transform.

Find the Laplace transform of unit impulse function.

Define interpolation.

State the formula for Fourier transform.

State and explain the Parseval's theorem.

Find the orthogonality of the signals $\sin (\omega t)$ and $\sin (2\omega t)$ over the time interval $(0,T)$.

Compute the output y(t) for a continuous - time LTI system whose impulse response h(t) and the input x(t) are given by $h(t)=e^{-at}u(t)$ and $x(t)=e^{at}u(-t)$.

Find the minimum sampling frequency for non - zero frequency spectra $X(j\omega )$ defined between $10\text{kHz}<|\omega |<20\text{kHz}$.

What are energy and power signals?

Explain the properties of Laplace transform.

What is zero - order hold, derive the expression for transfer function of zero - order hold?

The discrete - time system shown in Fig. 1 is known as unit delay element. Determine whether system is (a) memoryless (b) causal (c) linear (d) time - invariant (e) stable. $$\text{x[n]}⟶\boxed{\text{Unit Delay}}⟶\text{y[n] = x[n-1]}$$ $$\text{Fig. 1 Unit Delay Element}$$

Find the Z-transform X(z) and sketch the pole zero plot with the ROC for $x[n]={\left(\frac{1}{3}\right)}^{n}u[n]+{\left(\frac{1}{2}\right)}^{n}u[-n-1]$.

Consider a continuous - time LTI system described by $$\frac{dy(t)}{dt}+2y(t)=x(t)$$ using fourier transform, find the output y(t) to the input $x(t)=u(t)$.

Describe the various methods of reconstruction of signals from its samples.

Compute $y[n]=x[n]\ast h[n]$, where $x[n]=a^{n}u[n]$, $h[n]=a^{-n}u[-n]$, $0<a<1$.