Sketch the Fourier transforms of the following functions assuming |omega_1|>|omega_2| a) f(t)=[cos(omega_1 t)+i sin(omega_1 t)]-[cos(omega_2 t)+i sin(omega_2 t)] b) f(t)=[cos(omega_0 t)]e^{-frac{t}{T_2}}

Ayaana Buck 2021-01-10 Answered
Sketch the Fourier transforms of the following functions assuming |ω1|>|omega2|
a)f(t)=[cos(ω1t)+isin(ω1t)][cos(ω2t)+isin(ω2t)]
b)f(t)=[cos(ω0t)]etT2
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Expert Answer

Szeteib
Answered 2021-01-11 Author has 102 answers

Step 1
Consider the equation
Step 2
(a)f(t)=[cos(ω1t)+isin(ω1t)][cos(ω2t)+isin(ω2t)] F is a function of a real variable omega ,the function value F(ω) is a complex number.
|F(t)| is called amplitude specturm of f
F=f(T) means F is the Fourier transform of f as for Laplace transform Laplace transform of f
f(t)=[cos(ω1t)+isin(ω1t)][cos(ω2t)+isin(ω2t)]
=cos(ω1t)+isin(ω1t)cos(ω2t)+isin(ω2t)
(b) f(t)=[cos(ω0t)]etT2
F is a function of real variable t the function value F(t) is a complex number, F=f(t) means F is the Fourier transform of f as for Laplace transform
f(t)=[cos(ω0t)]etT2

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