B.TECH - Semester 6 signals and systems Question Paper 2013 (apr)
Practice authentic previous year university questions for better exam preparation.
Sample Questions
- Check whether the system represented by the equation $y(n)=n^{2} x(n)$ is linear or not.
- Define aliasing. Explain with relevant sketches.
- Narrate the relation between Fourier Transform and Laplace Transform.
- List the properties of ROC of z-Transform.
- Compare the cascade and parallel structures of IIR filter. ( $5 \times 4=20$ Marks) PART - B Answer any one full questions from each module. Each question carries 20 marks
- (a) For a signal $x(t)$ shown in figure sketch the signals
- (i) $x(t+2)$ (ii) $x\left(\frac{5}{3} t\right)$ and (iii) $x(2 t+2)$
- (b) Differentiate between the following category of signals citing examples for each
- (i) Even and odd signals (ii) Causal and non causal signals OR
- (a) Determine whether the signal $x(t)=A \sin \left(\omega_{0} t+\theta\right)$ is an energy signal or power signal.
- (b) A system is represented by the impulse response $h(n)=3^{n} u(-n)$. Is it a causal system or non-causal system?
- (c) Write note on transient and steady state response of a system.
- (a) Discuss the significance of impulse response and step response of an LTI system.
- (b) What is autocorrelation function? Find the autocorrelation function of the sequence $x(n)=\{1,2,3,4\}$.
- (c) For a system with transfer function $H(S)=\frac{s+2}{s^{2}+4 s+3}$ find the zero state response if the input $x(t)$ is $e^{-t} u(t)$. OR
- (a) Find the convolution of the signals $x_{1}(t)=e^{-3 t} u(t)$ and $x_{2}(t)=u(t+3)$.
- (b) State and prove time scaling property and differentiation in s-domain property of Laplace Transforms.
- (c) Find the Laplace Transform of the signal $x(t)=e^{2 t} u(t)+e^{-2 t} u(-t)$.
- (a) Describe the relation between Laplace Transform and $z$-Transform. 5
- (b) Find the Fourier Transform of the signal $x(t)=\left\{\begin{array}{cc}e^{-|t|} & \text { for }-2 \leq t \leq 2 \\ 0 & \text { else }\end{array}\right.$
- (c) Determine the z -Transform of
- (i) $y(n)=x(n+1) u(n)$ (ii) $\quad x(n)=2^{n} u(n-2)$
- (a) State and prove any two properties of Fourier series.
- (b) Determine the transfer function of LTI system described by the difference equation $y(n)=x(n)+0.81 x(n-1)-0.81 x(n-2)-0.45 y(n-2)$. Sketch the poles and zeros on the z-plane and assess the stability of the system.
- (a) Compare DTFT and DFT
- (b) Realize the direct form I and II structures of IIR system represented by the transfer function $H(z)=\frac{3\left(2 z^{2}+5 z+4\right)}{(2 z+1)(z+2)}$.
- (a) Obtain the lattice structure for the FIR filter $H(z)=1+2 z^{-1}+\frac{1}{3} z^{-2}$.
- (b) Computes point DFT of a sequence $x(n)=\{0,1,2,3\}$ by
- (i) DIT radix-2 FFT and (ii) DIF radix-2 FFT