B.TECH - Semester 4 signals and systems Question Paper 2021 (dec)
Practice authentic previous year university questions for better exam preparation.
Sample Questions
- Graphically represent $x[3 n-2]$ and $x[-n+3]$ for the given sequence | $n$ | 0 | 1 | 2 | $\frac{3}{3}$ | 4 | 5 | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | $x[a]$ | 0 | 1 | 2 | 3 | 4 | 4 |
- Examine whether lhe signal $x(t)=\cos 2 t+\sin \sqrt{3} t$ is periodic or nol.
- Differenliate between causal and non-causal syslems wilh examples.
- Find the odd part of the signal $x(t)=t^{2} \div 5 t+10$.
- State and prove the lime shilling property of Fourier Series for a signal $x(9)$.
- Using the properties of Founier Iranslorm find FT of $e^{j 4!}$.
- With regard to Fourier series representation juslify ihat odd functions have only sine lerms.
- Datermine $f(t)$ if $F(s)=\frac{s+3}{s(s+1)(s+2)}$. What is the value at $t=0$ and $t=\infty$.
- Find the $z$ Iransform of the signal $x(n)=n a^{\prime \prime} v(n)$.
- Explain random process. ( $10 \times 4=40$ Marks) Arswer any two full questions from each Mocule. Each queslion caries 10 marks,
- (a) What is BIBO stability?
- (b) Check whether the system $y(t)=5 e^{-2 t} u(t)$ is slable or not.
- For the discrele time LTI system with impulse response $h(n)=\{1,3,2,-1,1\}$. Determine the outpul sequence if the inpul $x(n)=2 \delta(n)-\delta(n-1)$.
- (a) Check whether $x(t)=e^{-3 t} u(t)$ is an energy signal or power signal
- (b) For a RC highpass circuil find the outpul for the input $x(t)=5[t(t)-u(t-T)]$
- Explain time shïling property and Parsevals theorem for conlinuous lime Fourier Sories.
- Delermine the Fourier Iransform of square wave shown in fig.
- Stale and prove sampling theorem. Derive the expression for the reconstrucled signal if the samples are passed through an ideal reconslruction bandpass filier.
- (a) Derive a relation between Fourier and Laplace transform.
- (b) Using Laplace transform solve the following differential equation $\left(\frac{d^{2} y(t)}{d t^{2}}+3 \frac{d y}{d t}+2 y(t)=\frac{d x(t)}{d t}\right) \nabla y\left(0^{-}\right)=2, \frac{d y 0^{-}}{d t}=1$ and $x(t)=e^{-t} \mathrm{u}(t)-6$
- Delemine the inverse $z$ |ransform of $X(z)=\frac{2 z^{-1}}{1-\frac{1}{4} z^{-1}}, \operatorname{ROC}|z|>\frac{1}{4}$,
- Explain Ergodicity and Power Spectral Density w.r.I random process. ( $6 \times 10=60$ Marks)