1) Prove Lecture 1, equation 11: fasulerse. I ove Sinc (t) dt -0 00 -8 f sine ² (1) dt. Use Fourier analysis to do so, Use the EE definition Sinc (t) = sin It I, reet (w.) = 1/7 7 R at 2

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1) Prove Lecture 1, equation 11:
00
f
-∞
sinc (t)dt = f sinc² (1) dt
-0
Use Fourier analysis to do so,
Use the EE definition
Sinc (t) = sinit, & rect (w) = +1
d
7
#
at
2) Prove that
Parsevel's Theorem is a Corollary
the Convolution Theorem,
f(n)• g(n)
7
J
25
are
show they
Wolfram Alpha for integral.
.e.
implies that
8
Σ f(n) = = = SIF(W) | " du
∙n 5.00
-T
of
F(W) * G(w)
Parseval's Th
3) Calculate the signal energy of S(n) = (K₂) u(n)
in both the time-domain and the w-domain and
equal. You may use a calculator or
Transcribed Image Text:1) Prove Lecture 1, equation 11: 00 f -∞ sinc (t)dt = f sinc² (1) dt -0 Use Fourier analysis to do so, Use the EE definition Sinc (t) = sinit, & rect (w) = +1 d 7 # at 2) Prove that Parsevel's Theorem is a Corollary the Convolution Theorem, f(n)• g(n) 7 J 25 are show they Wolfram Alpha for integral. .e. implies that 8 Σ f(n) = = = SIF(W) | " du ∙n 5.00 -T of F(W) * G(w) Parseval's Th 3) Calculate the signal energy of S(n) = (K₂) u(n) in both the time-domain and the w-domain and equal. You may use a calculator or
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