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fourier transform 2cos(2t)+2sin(4t)

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fourier transform 2cos(2t)+2sin(4t)

Solution

2π(δ(ω−2)+δ(ω+2))−2iπ(δ(ω−4)−δ(ω+4))

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F{2cos(2t)+2sin(4t)}

Use the linearity property of Fourier Transform:
For functions f(t), g(t) and constants a, b: F{a·f(t)+b·g(t)}=a·F{f(t)}+b·F{g(t)}

=2F{cos(2t)}+2F{sin(4t)}

F{cos(2t)}: π(δ(ω−2)+δ(ω+2))

F{sin(4t)}: −iπ(δ(ω−4)−δ(ω+4))

=2π(δ(ω−2)+δ(ω+2))+2(−iπ(δ(ω−4)−δ(ω+4)))

=2π(δ(ω−2)+δ(ω+2))−2iπ(δ(ω−4)−δ(ω+4))

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fourier transform 2cos(2t)+2sin(4t)

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