Adiscrete-time signal x(n) is defined as n 1+ −3 ≤ n ≤ 13 x(n) = { 1 0 ≤ n ≤ 0 elsewℎere
[3 marks]Determine its value and Sketch the signal.
[ marks]Sketch the signal if I. First fold x(n)and then delay the resulting signal by four samples II. First delay x(n) by four samples and then fold the resulting signal
[ marks]Compare above results. Is folding and Delay Operation is commutative operation?
[ marks]Can you express the signal x(n) in terms of 𝛿(n) and u(n) ?
[ marks]For each of following system determine whether system is stable, causal, Linear, Time invariant or not. 1. y(n)= ∑n+1 x(k) k=−∞ 2. y(n)= x(n2) 3. y(n)= logx(n)
[7 marks]Prove that convergence of absolute sum of the impulse response is a sufficient condition for BIBO (bounded input bounded output) stability of LTI system.
[7 marks]Obtain a linear convolution of following two discrete-time signals:2 x(n)= ∑𝛿(n−k) k=0 ℎ(n)= 2n[u(n)−u(n−3)]
[7 marks]Enlist Properties of linear convolution. Obtain linear Convolution for x(n)= {1,1,0,1,1} and ℎ(n)= {1,−2,−3,4}
[7 marks]What is ROC? Explain the properties of ROC in Z-Transform.
[7 marks]Find magnitude Response and Phase Response of system described by differential equation11 y(n)− y(n−1)= x(n)− x(n−1)24 OR1
[7 marks]What is canonic and non-canonic structure? Obtain Direct form-Iand Direct form II realization of the following transfer function. 3+3.6z−1+0.6z−2 H(z) = 1+0.1z−1−0.2z−2
[7 marks]Prove differentiation property of Z-transform and obtain the Z-transform of nu(n) using the same.
[7 marks]The system function of the analog filter is given as s+0.1 H = a (s+0.1)2+9 Obtain the system function of the IIR digital filter by using impulse invariance method.
[7 marks]State and Prove following Properties in terms of DFT. 1. Time Reversal 2. Periodicity
[7 marks]Compare FIR and IIR filters.
[7 marks]Determine the response of FIR filter using DFT if x(n)= {1,2} and ℎ(n)= {2,2}
[7 marks]Explain Decimation in Time FFT algorithm.
[7 marks]Derive the DFT of the sample data sequence x(n)= {1,1,2,2,3,3} determine the corresponding amplitude and phase spectrum.
[7 marks]Explain multiplier-Accumulator (MAC) hardware in DSP processors.
[7 marks]Discuss the applications of digital signal processing with suitable examples.
[7 marks]