Question
Download Solution PDFThe Fourier Transform of an real and even function results in:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept: Fourier Transform Symmetry Property
If a time-domain function is:
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Real: It has no imaginary part
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Even:
Then it's Fourier Transform will be:
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Purely real
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Even: F(ω)=F(−ω)
🔍 Example: Cosine Wave
Let’s take: f(t) = cos(ω0t)
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It is real.
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It is even, because
Fourier Transform of is: F(ω)=π [δ(ω−ω0)+δ(ω+ω0)]
This result is:
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Purely real (involves delta functions, no imaginary component)
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Even since it's symmetric around
Last updated on Jun 7, 2025
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