(1) (a) (6) (c) CALCULATE THE FOILUWING [ {t² Sin (Tit)} LAPLACE TRANSFORM FOR THE L {(e-²-2e³²) (4 x ² + (²²²) } [ {246¹ (√3 cos (√2+) + √2 Sin (√3+ ) ) }
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- Suppose that f(t) is periodic with period [-n, n) and has the following complex Fourier coefficients: Co = -3, 1 = -3+3i, C2 = 3, C3 = -4 + 2i, ... ... (A) Compute the following complex Fourier coefficients. C3 = (B) Compute the real Fourier coefficients. (Remember that et kt = cos(kt) + i sin(kt).) %3| ao = > a2 = > az = bi bz = %3D (C) Compute the complex Fourier coefficients of the following. (1) The derivative f (t). Co (ii) The shifted function f(t +) Co C2 Ca= (iii) The function f(3t). Co C1 = %3D2) Derive an expression for the x(t) and Determine the Fourier transform of the signal x(t) shown in Figure 2. x(t) cos at Şekil 2Sketch the following waveform f(t)= Vo = 0 -t/2≤t≤t/2 otherwise and show that its Fourier transform is F (1) 2sin Varsine ( Votsinc (0) 2 ωτ Use this result to sketch a fully labelled graph of the amplitude spectrum of a single square voltage pulse, of amplitude 24V and pulse width 1.4μs, using units of Hz for the frequency axis. (Note: graph paper is not required - a clear, fully-labelled sketch is adequate).
- A function f(x) is given by (in the picture). Find the Fourier transform of f(x) with hint (in the picture to)16. Find the Fourier transform of f(x), show the details. f(x) = |x|e¹x1 (-∞0(b) Determine the Z-transforms of the following expressions (ii) (cos 0 + i sin 0)"Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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