05)(5 marks)The Fourier transform of the signal x(t) is given below Find $\int_{-\infty}^{\infty} |x(t)|^2 dt$
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The Fourier transform of a signal x(t) is denoted as X(ω), where ω is the angular frequency. Show more…
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Given that x(t) has the Fourier transform X(jw), express the Fourier transforms of the signals listed below in terms of X(jw). You may find useful the Fourier transform properties listed in Table 4.1. (a) x1(t) = x(1 - t) + x(-1 - t) (b) x2(t) = x(3t - 6) (c) x3(t) = d^2/dt^2 x(t - 1)
Consider the signal x(t) = { 0, |t| > 1; (t + 1)/2, -1 <= t <= 1 (a) With the help of Tables 4.1 and 4.2, determine the closed-form expression for X(jw). (b) Take the real part of your answer to part (a), and verify that it is the Fourier transform of the even part of x(t). (c) What is the Fourier transform of the odd part of x(t)?
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