Starting with the Fourier transform pair
x ( t ) = u ( t + 1 ) - u ( t
- 1 ) ⇔ X ( Ω ) = 2
sin ( Ω ) / Ω
and using no integration indicate the properties of the Fourier
transform that will allow you to compute the Fourier transform of
the following signals
x 1 ( t ) = - u ( t + 2 ) + 2
u ( t ) - u ( t - 2...
1) Find the Laplace transform of
f(t)=−(2u(t−3)+4u(t−5)+u(t−8))
F(s)=
2) Find the Laplace transform of f(t)=−3+u(t−2)⋅(t+6)
F(s)=
3) Find the Laplace transform of f(t)=u(t−6)⋅t^2
F(s)=
1. Find the Laplace transform of each of the following
functions: (a). f(t) = t , (b). f(t) = t2 ,
(c) f(t) = tn where n is a positive
integer
Laplace transform of the given function
2. . f(t) = sin bt
3. f(t) = eat sin bt
E ::= E + T | T
T ::= T * F | F
F ::= num | (E) Num ::= 0 | 1 | 2 | 3 | 4 | 5 | . . . . . .
.
Question: 1
a. Show the Left-most derivation for the expression: 5 * 7 + 6 * (1
+ 2).
b. Show the Right-most derivation for the expression: 5 * 7 + 6
* (1 + 2).
Use the Fourier transform to find the solution of the following
initial boundaryvalue Laplace equations
uxx + uyy = 0, −∞ < x < ∞ 0 < y < a,
u(x, 0) = f(x), u(x, a) = 0, −∞ < x < ∞
u(x, y) → 0 uniformlyiny as|x| → ∞.
Using Matlab Simulink, find Fourier transform of the following
signal;
?(?) = 2 + ∑
1 ?
sin (20???)
4
?=1
.
Set simulation stop time = 20 seconds, sample time = (1/1024)
seconds, buffer size =1024, and frequency range in Hz for the
vector scope is −100 ≤ ? ≤ 100