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c) ωτ Assume the Fourier transform of a function u(t) is U(w) = 3τsinc. Deduce the Fourier transforms H₁(w) and H₂(w) of the following two waveforms constructed from u(t). h₁(t) = u(t+3) h₂(t) = u(t − 3) + 2u(t − 3) + 3u(t − 3) d) Assume the Fourier transform of a function v(t) is V (w). The expression of v(t) in the time domain is τ 3 t: v(t): = τ 0 t<- and t> 2 Deduce the waveform v'(t) if its Fourier transform is V(w - 3).

c) ωτ Assume the Fourier transform of a function u(t) is U(w) = 3τsinc. Deduce the Fourier transforms H₁(w) and H₂(w) of the following two waveforms constructed from u(t). h₁(t) = u(t+3) h₂(t) = u(t − 3) + 2u(t − 3) + 3u(t − 3) d) Assume the Fourier transform of a function v(t) is V (w). The expression of v(t) in the time domain is τ 3 t: v(t): = τ 0 t<- and t> 2 Deduce the waveform v'(t) if its Fourier transform is V(w - 3).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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c) ωτ Assume the Fourier transform of a function u(t) is U(w) = 3τsinc. Deduce the Fourier transforms H₁(w) and H₂(w) of the following two waveforms constructed from u(t). h₁(t) = u(t+3) h₂(t) = u(t − 3) + 2u(t − 3) + 3u(t − 3) d) Assume the Fourier transform of a function v(t) is V (w). The expression of v(t) in the time domain is τ 3 t: v(t): = τ 0 t<- and t> 2 Deduce the waveform v'(t) if its Fourier transform is V(w - 3).
Transcribed Image Text:c) ωτ Assume the Fourier transform of a function u(t) is U(w) = 3τsinc. Deduce the Fourier transforms H₁(w) and H₂(w) of the following two waveforms constructed from u(t). h₁(t) = u(t+3) h₂(t) = u(t − 3) + 2u(t − 3) + 3u(t − 3) d) Assume the Fourier transform of a function v(t) is V (w). The expression of v(t) in the time domain is τ 3 t: v(t): = τ 0 t<- and t> 2 Deduce the waveform v'(t) if its Fourier transform is V(w - 3).
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