Question

QUESTION 1

(a) Explain the significant of causal system compare to non-causal
system.

(b) Consider a system ?(?)=4??(?)+4?(?−1). Determine the system
properties in term of:

(i) Linear.

(ii) Time-Invariant.

Answer #1

subject-DSP
1)y(n)=2x^2(n-1)
determine the system is(and justify your decision)
a)linear
b)time invariant
c)stable
d)causal

Demonstrate step by step if the following system
is:
1. Static or dynamic.
2. Linear or non-linear.
3. Invariant or variant in time.
4. Causal or not causal.
5. Stable or unstable.
y(n)=x(n)+nx(n-2)

A discrete time system can be
i. Linear or non-linear
ii. Time invariant or Time Variant
iii. Causal or noncausal
iv. Stable or unstable
v. Static Vs Dynamic
Examine the following systems with respect to every property
mentioned above and give a brief
explanation.
a. y[n] = x[n]δ[n − 1]
b. y[n] = x[n] + nu[n + 1]
c. y(n) = x(2. n)
d. y(n) = 3. x(n)

1. Give three linear systems and three non-linear system, and
specify whether one is time variant or time invariant.

4) a) Describe what is meant when one says that a system is
linear. Use mathematical expressions to describe.
b) Describe what is meant when one says that a system is time
invariant. Use mathematical expressions to describe.
c) Show that the following systems are non-linear:
i) y(t) = x(t) + 2
ii) y(t) = (x(t))^2

1.28 Dectermine which of the properties listed in 1.27 hold and
which do not hold for each of the following discrite-time systems.
Justify your answers. In each example, y[n] denotes the system
output and x[n] is the system input.
b) y[n] = x[n-2]-2x[n-8]
c) y[n]=nx[n]
system may or may not be:
1) Memoryless
2) Time invariant
3) Linear
4) causal

Determine if the system ?[?]=sin(0.2?∙?[?])is (1) linear, (2)
time-invariant.

Consider a causal LTI system described by the difference
equation:
y[n] = 0.5 y[n-1] + x[n] – x[n-1]
(a) Determine the system function H(z) and plot a pole-zero pattern
in the complex z-plane.
(b) Find the system response using partial fraction expansion when
the input is x[n] = 2u[n]. Plot the result.

4. [10] Consider the system of linear equations
x + y + z = 4
x + y + 2z = 6
x + y + (b2 − 3)z = b + 2
where b is an unspecified real number. Determine, with
justification, the values of b (if any) for which the system
has
(i) no solutions;
(ii) a unique solution;
(ii) infinitely many solutions.

Which of the following systems are dynamical? Stable? Causal?
Time-invariant? Linear?
1. y(t) = 5x(t)
2. y(t) = x(t)^4
3. y(t) = x(t−1)^2
4. dy/dt = x(t)
5. dy/dt = y(t) + x(t)
6. dy/dt = −y(t) + x(t)^2
7. dy/dt = −y(t) + x(t + 4)
8. dy/dt = tx(t)

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