Find the Fourier transform of the function shown in the figure if A = 15 and B = 50. g(t) B A 2 G(w) is calculated as (- jw + 1 jwe jw + e JW _ e- 2 jay / w2.The function g(t ) given in the diagram appears to be a piecewise function. Here's how it looks: . From t = 0 to t = 1, the function is constant at B. . From t = 1 to t = 2, the function linearly decreases from B to A. . After t = 2, the function becomes 0. Fourier Transform Steps To find the Fourier transform G(w). we need to calculate the transform over the two intervals: 1. For the interval t E [0, 1] : The function g(t) = B. Fourier transform for a constant function B over this range is: [ \\int_0^1 B e^{-j\\omega t} dt = B \\left[ \\ frac(e*{-j\\omega t}} {-j\\omega} \ ight]_0^1 = B \\left( \\frac(1 - e^{-j\\omega}} (j\\omega} \ ight) ] 2. For the interval t E [1, 2] : The function g(t) is linearly decreasing, so we can express it as: [ g(t) = A + (B - A) (2 - t) ] For this interval, we compute the Fourier transform similarly: [ \\int_142 (A + (B-A) (2 - t) ) e^{-j\\omega t} dt ] This will lead to a more complex expression, which needs to be simplified step by step. Final Expression After calculating and simplifying the integrals, the Fourier transform will be expressed in the form as shown in the