Consider a signal f (t) with Fourier transform F(@). Suppose we are given the following clues about the signal. Clue 1: The signal f (t) is positive and real-valued. Clue 2: The inverse Fourier transform of (3+ jw) F (@) is A e-St u(t), where A is a constant. Clue 3: The Fourier transform F(w) obeys IF (? do = 6n. -8 Using these clues, ) Determine the expression for f (t). (ii) Compute the energy of f (t). (iii) Compute the constant A.

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Consider a signal f(t) with Fourier transform F(@). Suppose we are given the
following clues about the signal.
Clue 1: The signal f (t) is positive and real-valued.
Clue 2: The inverse Fourier transform of (3+ jw) F (@) is A e-St u(t), where A is
a constant.
Clue 3: The Fourier transform F(w) obeys
8.
IF (@)? do = 6n.
-8
Using these clues,
1) Determine the expression for f (t).
(ii) Compute the energy of f (t).
(iii) Compute the constant A.
Transcribed Image Text:Consider a signal f(t) with Fourier transform F(@). Suppose we are given the following clues about the signal. Clue 1: The signal f (t) is positive and real-valued. Clue 2: The inverse Fourier transform of (3+ jw) F (@) is A e-St u(t), where A is a constant. Clue 3: The Fourier transform F(w) obeys 8. IF (@)? do = 6n. -8 Using these clues, 1) Determine the expression for f (t). (ii) Compute the energy of f (t). (iii) Compute the constant A.
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