1. Convolution of Discrete Time Signals Analytically determine the convolutions: (a) Find yn]-nun], where un] is...
Consider a discrete-time LTI system with impulse response hn on-un-1), where jal < 1. Find the output y[n] of the system to the input x[n] = un +1].
solve with steps and please write as clear as possible. Determine, analytically, the convolution y(t)-r(t) * h(t), where a(t)0, otherwise, and h(t) 1, 1<t < 3 o, otherwise.
1. Discrete Fourier Analysis. Given the following periodic function: 50. 0<t<2s a) Find discrete time rot and amplitude y(rSi) values for y(t). Find time values t1, t2, ..tN with ot-0.2 s over the interval -2.0 to 1.8 s, amplitudes yl, y2, y3,.. .,yN. and N.
QUESTION THREE With the aid of a diagram define impulse response fully using correct 141 a) Notation 141 Find the impulse response of a discrete time accumulator b) 15) c) Derive the convolution sum esent the operations in cji) with a diagram and explain the importance of an impulse response to a discrete time L.TI system 16) in) Consider a causal L.TI discrete-time system with an impulse response h1n1-r 비nl where pct Determine the output sequence yln] 161 for a...
Consider the discrete-time signal given below. Ş ()", n20 X = 0 n < 0 where a=8. Find the average power Poo
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is...
2. Determine whether the following discrete-time signals are periodic or not? For the periodic ones, find their fundamental period. (5 points each) n12 c. z[n] sin (3rn7)2sin(n/10)
Part 1 (Calculation): The Z-transform (ZT) converts a discrete time-domain signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation. It is the equivalent of the Laplace transform for discrete systems. The one-sided ZT, used for causal signals and systems, is defined as follows: Consider the digital system (filter) described by the input/output difference equation and z-domain transfer function Hz: yn-0.88 yn-1=0.52 xn-0.4 xn-1 Hzz=Y(z)X(z)=0.52-0.4 z-11-0.88 z-1=0.52 z-0.4z-0.88 Assuming a unit step function input, i.e.,...
x[n] = { Consider the discrete sequence S (0.5)" 0<n<N-1 otherwise a) Determine the z-transform X(2)! b) Determine and plot the poles and zeros of X(2) when N = 8!
elsewhere elsewhere 6. Convolution between two discrete time signals, #1 [n] and 12[n] is given by: y[m] = $R=0[n] ru[m sin (Pan) ,n=0,1,2,3 cos (27) ,n=0,1,2,3 n, m 7. Let 21 [n] 10. with N = 4 find y(0) and y[1]. (10 points) 7. The taylor series expansion of c" = = 1+++++ and sin(x) = 1 - 3 +420 ko 15x24. Using this, can you write the taylor series expansion of esin(x”)? (just write the first two lower order...