1. is sin(pi/4) causal?
2. is sin(pi/4) stable?
3. is delta(n+1) causal?
4. = ?
5. If function w [ n ] is convolved with , what will the result
be?
6. if a system with signal length 4 is convolved with its own
system response, what will the length of that signal be?
7. In an LTI system, x[n] * h[n]= y[n]. What is x[n-3] * h[n-2]
=?
Using MATLAB, determine whether the system below are a)
linear/non-linear b) time-invariant/timevariant, c)
causal/noncausal, d) has memory/memoryless:
y(t) = x(t) + x(t -1)
Provide MATLAB code and graphs to show your work for the
linearity and time-invariance testing.
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
For the following causal difference equation,
given that y[-1] = 2, y[-2] = 3, and x[n] = 3nu[n],
solve using z-Transforms.
(Hint: convert to delay operator form, find the z-Transform, use
PFE to find the inverse z-Transform)
y[n + 2] – 3y[n + 1] + 2y[n] = x[n + 1]
Determine whether each system is LTI, causal and/or stable and
with or without memory. Justify answers.
a) y[n + 1] + 4y[n] = 3x[n + 1] - x[n]
b) y[n] = nx[2n]
For the following causal difference equation,
given that y[-1] = 0, y[-2] = 1, and x[n] = u[n], solve using
z-Transforms.
(Hint: convert to delay operator form, find the z-Transform, use
PFE to find the inverse z-Transform)
4y[n + 2] + 4y[n + 1] + 2y[n] = x[n + 1]
1. Determine forced and natural response for the following
equation, where y[-1] =1, y[-2]=1 and x[n] = delta[n].
y[n]+1/2 y[n-1] -1/4 y[n-2] = x[n]
2. find the impulse response of the system described below
y[n]=1/2 y[n-1] + 2x[n]