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
Consider each of the following systems for long times, at which
their behacioor is time invariant. Identify each system as
equilibrium or steady state.
1) A hose supplies water at a constant rate to a bucket with a
hole in it. A constant water level is maintained
2)A mixture of reacting gas
molecules is constrained to a fixed temperature, e.g., H2, O2 and
H2O at 600 K.
3) Ice floats in water, thermally
insulated from its surroundings.
4) Molten steel...
Consider each of the following systems for long times, at which
their behacioor is time invariant. Identify each system as
equilibrium or steady state.
1) A hose supplies water at a constant rate to a bucket with a
hole in it. A constant water level is maintained
2)A mixture of reacting gas molecules is constrained to a fixed
temperature, e.g., H2, O2 and H2O at 600 K.
3) Ice floats in water, thermally insulated from its
surroundings.
4) Molten steel...
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)
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...
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.
prove the following statement: If the augmented matrices of two
linear systems are row equivalent, then those systems are
equivalent.
(To do this, start with a solution to one of the systems and
show that it is still a solution of the other system under each of
the three elementary row operations.)
Write down your answers to the following question and
upload a scanned copy of your answer on blackboard (e.g. using the
Adobe Scan App on your phone). Only PDF documents will be
accepted.
Suppose the long-run production function of Curry’s brewing
company is given by: Q = 3K0.25L0.75.
K is the total operating hours of all brewing machines and L is
the total working hours of all workers.
Q is the number of beers produced per day.
The current rental...
Let a and b be rational numbers. As always, prove your answers.
(a) For which choices of a, b is there a rational number x such
that ax = b? (b) For which choices of a, b is there exactly one
rational number x such that ax = b?