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c) Find the Fourier transform of the function et. Using this find the Fourier transform of re-.
Find Laplace transform of ?(?) = 2 + 5? Find Laplace transform of ?(?) = 2?-t + 3??-4t Find time function corresponding to this Laplace transform: ?(?) = (2s2+s+1)/(s3-1) Solve this ODE using Laplace transform : ?̈(?)+2?̇(?)+4?(?)=0; ?(0)=1, ?̇(0)=2 Solve this ODE using the Laplace transform : ?̈(?)−2?̇(?)+3?(?)=0; ?(0)=2, ?̇(0)=1
e +e- 4. a. Find the inverse Laplace transform of b. Find the inverse Laplace transform f(t) of: then sketch the graph of f(t).
Please solve the following differential equation problem.
find the inverse transform
11 Find the inverse transform: b) {265+15)
Using the z-Transform Tables, find the inverse
z-Transform of the following function, this is, find
y[n]
find the inverse z-Transform of the following function, this is, find y[n] z Y(z) = 2 + 1.5z + + 0.25 z z+1 (2-1)2 (2+0.5)
2. (a) Find Laplace transform of tecosht s2 - 65+7 (b) Find inverse Laplace transform of (52 – 4s +5)
A function is sampled and the resultant sequence has the
z-transform as
Find the z-transform of
Find the z-transform of
Use tables of Fourier transform pairs and properties to find the
Fourier transform of each of the signals
a) f(t)=(1-eb )u(t) b) f(t)= Acos(@t+) c) f(t)=e"u(-t), a>0 d) f(t)=C/(t+t)
[3] [6 POINTS] Using the definition of the Laplace transform, find the Laplace transform of the function below. (The graph consists of two linear functions.) 4+ -3 2- 1 1 2 3 4 5
Problem 5: Use the duality property of the Fourier transform to find the Fourier transform of x(t) = sinc(Wt).