Question
In: Electrical Engineering
The impulse response of a discrete-time LTI system is given as ℎ[?] = ?[? + 1]...
The impulse response of a discrete-time LTI system is given as ℎ[?] = ?[? + 1] − ?[? − 1] a) State whether or not the system is (i) memoryless, (ii) causal, (iii) stable. Justify your answers mathematically. b) Find the output ?[?] of the system for input ?[?] = (0.5) ??[?].
Solutions
where y(n)=output.
Manojponduru answered 1 year agoRelated Solutions
the following are impulse responses/outputs of discrete -time LTI systems. Determine whether each system is causal...
the following are impulse responses/outputs of
discrete -time LTI systems. Determine whether each system is causal
and/or stable. justify your answers
1. h [n] = 1/5^n u [n]
2. h [n] = 5^n u [3-n]
3. y [n] = 3x [n] - 0.15y [n-1]
4. y [n] = 2e^-x [n]
5. y [n] = n^2 4x [n]
B. Show if the systems defined in 1 to 5 above have
bounded input and output (BIBO) from the summation of their impulse...
x[n] is the input of an LTI system with the impulse response of h[n]. x[n] =...
x[n] is the input of an LTI system with the impulse response of
h[n]. x[n] = [1, 2, 3] and h[n] = [4, 6]. Use 4-point DFT and IDFT
and zero padding of x[n] and h[n] to find the output y[n].
CHAPTER 13: DISCRETE-TIME SIGNAL (TEXTBOOK SIGNALS AND SYSTEM BY MAHMOOD NAHVI) 12. In an LTI system,...
CHAPTER 13: DISCRETE-TIME SIGNAL (TEXTBOOK SIGNALS AND SYSTEM BY
MAHMOOD NAHVI)
12. In an LTI system, x(n) is the input and h(n) is the
unit-sample response. Find and sketch the
output y(n) for the following cases:
i) x(n) = 2[u(n) - u(n - 11)] and h(n) = 0.5nu(n)
ii) x(n) = 2[u(n) - u(n - 11)] and h(n) = (-0.5)nu(n)
iii) x(n) = u(n) - u(n - 5) and h(n) = 0.5|n|u(n)
iv) x(n) = u(n) - u(n - 5)...
Consider the discrete-time LTI system characterized by the following difference equation with input and initial conditions specified
Consider the discrete-time LTI system characterized by the following difference equation with input and initial conditions specified: y[n] - 2 y[n-1] – 3 y[n-2] = x[n] , with y[0] = -1 and y[1] = 0, x[n] = (-1/2)n u[n-2]. ? Write a MATLAB program to simulate this difference equation. You may try the commands ‘filter’ or ‘filtic’ or create a loop to compute the values recursively. ? Printout and plot the values of the input signal, x[n] and the...
Consider the first order linear time-invariant (LTI) system given by, ??(?) ?? + 4?(?) = ?(?)...
Consider the first order linear time-invariant (LTI) system
given by,
??(?) ?? + 4?(?) = ?(?)
Where the system is initially at rest.
Part a: Determine the Frequency Response H(jω) and impulse
response h(t).
Part b: When the input ?(?) = ?23?(?), determine the output of
the system ?(?).
Part c: Is the system; memoryless? causal? Stable? please
justify your answer
1. a) Compute the impulse response of the following filters. If the impulse response is infinite,...
1. a) Compute the impulse response of the following filters. If
the impulse response is infinite, feel free to stop once a pattern
becomes apparent.
i. y[n] = 2/3 · x[n − 1] − 1/3 x[n − 2]
ii. y[n] = x[n − 1] − x[n − 2] − 1/3 y[n − 2]
b) What are the feed-back (b[k]) and feed-forward (a[k])
coefficients of the following filters? You may assume that a starts
at delay of k = 1 (i.e.,...
????????? ?ℎ? ??? ?? ?ℎ? ?????? ?? ?ℎ??ℎ ???ℎ ????? ???????? ?? ??????????: 1) ?(?, ?)...
????????? ?ℎ? ??? ?? ?ℎ? ?????? ?? ?ℎ??ℎ ???ℎ ????? ???????? ??
??????????:
1) ?(?, ?) = ?−? 4−? 2− ?2
2) ?(?, ?, ?) = ln |? 2 + ? 2 − 6| ???? (? 2 − ? 2 + ? 2)
3) ℎ(?, ?, ?) = √? + 2? − ? ? 2 + ? 2
Compute the unit-pulse response h[n] for the discrete-time system y[n + 2] - 2y[n + 1]...
Compute the unit-pulse response h[n] for the discrete-time
system y[n + 2] - 2y[n + 1] + y[n] = x[n] (for n = 0, 1, 2, 3)
Write a function softMax_M(Q) to return a 2darray of softmax function values ??ℎ=???ℎ−?∑??=1???ℎ−? for ?=0,1,⋯,?−1,ℎ=0,1,⋯,?−1 ,...
Write a function softMax_M(Q) to return a 2darray of softmax
function values ??ℎ=???ℎ−?∑??=1???ℎ−? for ?=0,1,⋯,?−1,ℎ=0,1,⋯,?−1 ,
where ? is a 2darray of floats with shape ( ? , ? ), ??ℎ is the
element at the (?+1) -th row and the (ℎ+1) -th column of array ? ,
and ? is the largest element in array ? . (Hint: operations should
be performed down the rows; a returned 2darray and ? are of the
same shape.) Sample: if D =...
Write a function softMax_M(Q) to return a 2darray of softmax function values ??ℎ=???ℎ−?∑??=1???ℎ−? for ?=0,1,⋯,?−1,ℎ=0,1,⋯,?−1 ,...
Write a function softMax_M(Q) to return a 2darray of softmax
function values ??ℎ=???ℎ−?∑??=1???ℎ−? for ?=0,1,⋯,?−1,ℎ=0,1,⋯,?−1 ,
where ? is a 2darray of floats with shape ( ? , ? ), ??ℎ is the
element at the (?+1) -th row and the (ℎ+1) -th column of array ? ,
and ? is the largest element in array ? . (Hint: operations should
be performed down the rows; a returned 2darray and ? are of the
same shape.) Sample: if D =...
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