B.TECH - Semester 6 signals and systems Question Paper 2020 (jan)
Practice authentic previous year university questions for better exam preparation.
Sample Questions
- Determine whether or not each of the following signals are periodic. If periodic, specify its fundamental period (a) $\quad x[n]=e^{j 6 \pi n}$
- Determine whether or not each of the following signals are periodic. If periodic, specify its fundamental period (b) $x[n]=e^{j \frac{3}{5}(n+0.5)}$
- Represent the sequence $x[n]=\{4,2,-1,0,3,6,1,0,1,2\}$ as a sum of shifted impulses.
- Test the stability of the system whose impulse response is $h[n]=\left(\frac{1}{2}\right)^{n} u[n]$.
- List any five properties of Region of Convergence of $Z$ - transform.
- (b) (i) Show that with $x[n]$ as an N -point sequence and $X[k]$ as its N -point DFT $$ \sum_{n=0}^{N-1}|x[n]|^{2}=\frac{1}{N} \sum_{k=0}^{N-1}|X[k]|^{2} $$ (ii) Find the DFT of the sequence $x[n]=\{1,1,0,0\}$.
- Given the sequences $x_{1}[n]=\{1,2,3,1\} ; \quad x_{2}[n]=\{4,3,2,2\}$, find the sequence $x_{3}[n]$ such that $X_{3}[k]=X_{1}[k] X_{2}[k]$ where $X_{1}[k], X_{2}[k], X_{3}[k]$ are the discrete fourier transforms of $X_{1}[n], X_{2}[n], X_{3}[n]$ re...
- A continuous time signal $x(t)$ is shown in Figure. Sketch and label carefully each of the following signals. (a) $\quad x(t-1)$
- A continuous time signal $x(t)$ is shown in Figure. Sketch and label carefully each of the following signals. (b) $x(2 t+1)$
- A continuous time signal $x(t)$ is shown in Figure. Sketch and label carefully each of the following signals. (c) $x\left(4-\frac{1}{2}\right)$
- A continuous time signal $x(t)$ is shown in Figure. Sketch and label carefully each of the following signals. (d) $[x(t)+x(-t)] u(t)$
- A continuous time signal $x(t)$ is shown in Figure. Sketch and label carefully each of the following signals. (e) $\quad x(t)\left[\delta\left(t+\frac{3}{2}\right)-\delta\left(t-\frac{3}{2}\right)\right]$ OR
- Determine which of the properties listed below (a) Memoryless
- Determine which of the properties listed below (b) Time invariant
- Determine which of the properties listed below (c) Linear
- Determine which of the properties listed below (d) Casual
- Determine which of the properties listed below (e) Stable hold and which do not hold for each of the following discrete - time systems. Justify your answer. In each example, $y[n]$ denotes the system output and $x[n]$ is the system input.
- Determine which of the properties listed below (f) $y[n]=x[-n]$
- Determine which of the properties listed below (g) $y[n]=n x[n]$
- Impulse response of a LTI system is given by $$ h[n]=\left\{\begin{array}{cc} \alpha^{n}, & 0 \leq n \leq 6 \\ 0, & \text { otherwise } \end{array}\right. $$ Find the response $y(t)$ of the system when the input is $$ x[n]=\left\{\begin{array}{cc}...
- State and prove the following properties of Laplace transform (a) Linearity property
- State and prove the following properties of Laplace transform (b) Time shifting property
- State and prove the following properties of Laplace transform (c) Time Scaling property
- State and prove the following properties of Laplace transform (d) Convolution property
- State and prove the following properties of Laplace transform (e) Initial and final value theorems
- (a) Find the $Z$ - transform of the following signals
- (i) $\quad x[n]=a^{n} u[n]$ (ii) $\quad x[n]=-a^{n} u[-n-1]$
- (b) Find the inverse $Z$ - transform of the following $Z$ - transforms
- (i) $\quad X(z)=\frac{3-\frac{5}{6} z^{-1}}{\left(1-\frac{1}{4} z^{-1}\right)\left(1-\frac{1}{3}\right) z^{-1}} \operatorname{ROC}|z|>\frac{1}{3}$ (ii) $X(z)=\log \left(1+a z^{-1}\right), \operatorname{ROC}|z|>|a|$
- (a) Determine the fourier series representation for the following signal:
- (b) Give the correlation between
- (i) CTFT and DTFT (ii) Laplace transform and Z-transform
- (a) Determine the 8 - point DFT of a sequence $x[n]=\{1,2,3,4,4,3,2,1\}$ using DIF algorithm.
- (b) Obtain the direct from II and parallel form relization for the system $y[n]=-0.1 y[n-1]+0.2 y[n-2]+3 x[n]+3.6 x[n-1]+0.6 x[n-2]$.
- (a) Find the output $y[n]$ of a filter whose impulse response is $h[n]=\{1,1,1\}$ and input signal $x[n]=\{3,-1,0,1,3,2,0,1,2,1\}$ using
- (i) Overlap - save method (ii) Overlap - add method