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) ??[?].
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.
using matlab, compute and plot y [n] = x [n]* h [n],
where
a. x [n] = h [n] = a^n (0 <=n <=40) & a = 0.5
b. x [n] = cos [n]; h [n] = u [n]; n = 0:4:360
c. x [n] = sin [n] ; h [n] = a^n; n:4:360; a = 0.9
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].
Explain why a discrete time system is stable if its eigenvalues
are all in the unit circle.
Explain why a symmetric matrix will always have real
eigenvalues.
Explain why a continuous time system is stable if the real part
of its eigenvalues are negative.