for the x(t) = 3e2*u(t) + 4e3tu(t) signal; a-) Is the Fourier transform of the signal defined, that is, does it converge? b-) For which of the following 'values' is the Fourier transform of x (t) e¯ot "defined? i. o = 1 ii. o = 2.5 iii. o = 3.5 c-) Find (s) 'which is the Laplace transform of x (t)'. Mark the region (ROC) where it is defined with the pole and zeros.

1-Find the Fourier-transform (FT), for the following signals: (a) x1(n) = -8(n + 1) + 8(n –- 1). As this is an odd function, show that the FT is a pure imaginary function of frequency. (b) x2(n) = -8(n)+8(n – 2). Calculate it in two ways, first directly, and second by relating it to the signal in the previous part, and then using the properties of the Fourier transform. (c) x3(n) = 8(n + 1) + 5 + 8(n – 1). As this is an even function, show that the FT is a real function of frequency. (d) vi(n) = (–0.9)"-lu(n – 1), (e) v2(n) = (-0.9)"u(n – 1), (f) h(n) = 2[u(n) – u(n – 80)].

Which of the following characteristics must a signal have in order to be expressed in terms of a Fourier transform?You must indicate all valid optionsA) None is correctB) It must be continuous and have finite energyC) It must be periodic and have finite energy.D) All are correctE) To be periodic and to have infinite energy