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Questions from the topic - 1. Discrete time signals and systems [8 hours] - Digital Signal Analysis and Processing
1. Find the even and odd part of signal x[n], $$x[n] = \begin{cases}1 & for \space -4\leq n \leq 0\\2 & for \space 1\leq n\le4\end{cases}$$. - 2070 Ashad
2. Illustrate the significance of convolution summation in digital signal analysis. Compute the convolution of the following signals: h(n) = {1, 0, 1} and x(n) = {1, -2, -2, 3, 4}. - 2070 Ashad
3. Define Energy and Power type signal with suitable example. Check the signal $x[n] = \cos(2n\pi /5) + \sin(\pi n/3)$ is periodic or not. - 2069 Chaitra
4. Define LTI system. Find the output of LTI system having impulse response h[n] = 2u[n] - 2u[n-4] and input signal x[n] = $(1/3)^{n}u[n]$. - 2069 Chaitra
5. Compute and plot even and odd component of the sequence x(n) = 2u[n] - 2u[n - 4] where u[n] is unit step sequence. - 2067 Mangsir
6. Write whether or not the following sequences are periodic and write the period.
a) $x[n] = \cos\left(\frac{5\pi}{3}n\right)$
b) $x[n] = \sin\left(\frac{\pi n}{\sqrt{2}} + \frac{\pi}{8}\right)$ - 2067 Mangsir
7. Find the discrete Fourier coefficients of the periodic sequence with period N=11 defined over a period as $x[n] = \begin{cases}1, & |n|\leq{2}\\0, & 2\lt{|n|}\leq{5}\end{cases}$ - 2067 Mangsir
8. Show whether or not the system y(n) = nx[2(n - 2)], n > 0 is (a) linear, (b) time invariant, (c)memoryless. - 2067 Mangsir
9. Find the energy and power of the signal x[n] = u[n]. - 2068 Bhadra
10. Find the period of the signal $x[n] = \sum_{m=-\infty}^{\infty}\delta [n-2-3m].$ Find the Fourier series coefficients of the signal x[n]. - 2068 Bhadra
11. State whether or not the system $y[n] = e^{x[2n]}$ is (a) linear (b) time invariant (c) memoryless (d) causal. Where x[n] is input to the system and y[n] is output of system. - 2068 Bhadra
12. Convolve the sequence $x[n] = 3^{n}u[-n-5]$ and y[n] = u[n-5]. - 2068 Bhadra
13. How the spectrum of continuous time signal is related to spectrum of corresponding discrete time signal obtained by sampling the continuous time signal? Explain. Discuss what is aliasing and how it occurs. - 2068 Bhadra
14. Define energy and power type signals with suitable equations. Calculate and plot Fourier coefficients for $x[n] = \sin(3\pi/5)n.$ - 2065 Baisakh
15. What is a stability? Explain it with suitable derivations and examples. - 2065 Baisakh
16. If input sequences are x[-4] = 2, x[-2] = -1, x[0] = -2 and x[1] = 3, impulse responses to the system are h[-2] = 1, h[-1] = 0.75, h[0] = 0.5 and h[1] = 0.25, calculate output sequences and plot input, impulse response and output. - 2065 Baisakh
17. Define a difference equation. Draw the block diagram for y[n] - 2y[n - 2] + 3y[n - 3] - 4[y - 4] = 3x[n] + x[n - 1]. - 2065 Baisakh
18. What is convolution summation? Explain it with derivations and examples. - 2065 Baisakh-Old
19. Explain the properties of LTI systems with suitable examples. - 2065 Baisakh-Old
20. If input sequences are x[-4] = 2, x[-2] = -1, x[0] = -2 and x[1] = 3, impulse responses to the system are h[-2] = 1, h[-1] = 0.75, h[0] = 0.5 and h[1] = 0.25, calculate output sequences and plot input, impulse response and output. - 2065 Baisakh-Old