For each of the following Fourier transforms, use Fourier transform properties (Table 4.1) to determine whether the corresponding time-domain signal is (i) real, imaginary, or neither and (ii) even, odd, or neither. Do this without evaluating the inverse of any of the given transforms. - - (a) X₁(jw) = u(w) – u(w − 2) (b) X2(jw) = cos(2w) sin(1/2) (c) X3(jw) = A(w)ej B(w), where A(w) == (sin 2w)/w and B(w) = 20 + 1/2 (d) X(jw) = Σ%=-∞(½)|*| 8(w — *) -
For each of the following Fourier transforms, use Fourier transform properties (Table 4.1) to determine whether the corresponding time-domain signal is (i) real, imaginary, or neither and (ii) even, odd, or neither. Do this without evaluating the inverse of any of the given transforms. - - (a) X₁(jw) = u(w) – u(w − 2) (b) X2(jw) = cos(2w) sin(1/2) (c) X3(jw) = A(w)ej B(w), where A(w) == (sin 2w)/w and B(w) = 20 + 1/2 (d) X(jw) = Σ%=-∞(½)|*| 8(w — *) -
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This is a practice question from the Signal and Systems course of my Electrical Engineering Program.
Could you please walk me through the steps for solving this?
Thank you for your assistance.
Transcribed Image Text:For each of the following Fourier transforms, use Fourier transform properties (Table
4.1) to determine whether the corresponding time-domain signal is (i) real, imaginary,
or neither and (ii) even, odd, or neither. Do this without evaluating the inverse of any
of the given transforms.
-
-
(a) X₁(jw) = u(w) – u(w − 2)
(b) X2(jw) = cos(2w) sin(1/2)
(c) X3(jw) = A(w)ej B(w), where A(w)
==
(sin 2w)/w and B(w)
=
20 + 1/2
(d) X(jw) = Σ%=-∞(½)|*| 8(w — *)
-
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