c) Assume the Fourier transform of a function u(t) is U(@) = 6tsinc Deduce the Fourier transforms H, (@) and H, (w) of the following two waveforms constructed from u(t). h,(t) = u(t + 6) h2 (t) = u(t - 6) + 2u(t – 6) + 3u(t-6) %3D

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Part c only
(iii)
Comparing the amplitude spectra of f(t) [in Q4-a)] and g(t), explain
the relationship between Fourier series and Fourier transform.
Assume the Fourier transform of a function u(t) is U(w) = 6tsinc. Deduce
the Fourier transforms H, (ao) and H, (w) of the following two waveforms
constructed from u(t).
c)
%3D
h,(t) = u(t + 6)
h2 (t) = u(t- 6) + 2u(t – 6) + 3u(t - 6)
%3D
Assume the Fourier transform of a function v(t) is V(@). The expression of
v(t) in the time domain is
d)
v(t) = 1
1.
and t>:
Deduce the waveform v'(t) if its Fourier transform is V(w - 6).
Transcribed Image Text:(iii) Comparing the amplitude spectra of f(t) [in Q4-a)] and g(t), explain the relationship between Fourier series and Fourier transform. Assume the Fourier transform of a function u(t) is U(w) = 6tsinc. Deduce the Fourier transforms H, (ao) and H, (w) of the following two waveforms constructed from u(t). c) %3D h,(t) = u(t + 6) h2 (t) = u(t- 6) + 2u(t – 6) + 3u(t - 6) %3D Assume the Fourier transform of a function v(t) is V(@). The expression of v(t) in the time domain is d) v(t) = 1 1. and t>: Deduce the waveform v'(t) if its Fourier transform is V(w - 6).
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