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
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]
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]
Consider the linear time invariant system described by the
transfer function G(s) given below. Find the steady-state response
of this system for two cases: G(s) = X(s)/F(s) =
(s+2)/(3(s^2)+6s+24) when the input is f(t) = 5sin(2t) and f(t) =
5sin(2t) + 3sin(2sqrt(3)t)
A discrete system is described by the difference equation y(n)=
2.5y(n-1)-y(n-2)+3x(n)+3x(n-2)
a. Using Z-transform, Determine all
possible impulse responses h(n) and indicate the casuality and
stability
properties.
b.For the casual filter, determine the output y(n) if the input
is x(n)=g(n)-2g(n-1) where g(n)=cos (pin/s)u(n).
Consider the following discrete-time system: y[n] = 100 x[n]
cos(0.45πn + 0.5π)
(a) Determine if the system is linear, time-invariant, causal
and stable. Justify your answers.
(b) Find the impulse response h[n] for the system and sketch the
waveform.
(c) Draw the system block diagram using adder, multiplier and
delay elements.