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a)
![As sgn(n) = lim[e-at ult) - eatu(-+)]](http://img.homeworklib.com/questions/29da4c10-52f9-11eb-95bb-273d9ed7b289.png?x-oss-process=image/resize,w_560)
![So, F[sgn(n)] = F[lim[e-at u(t) - eatu(-t)]]](http://img.homeworklib.com/questions/2a246f60-52f9-11eb-be4c-21b69585dd77.png?x-oss-process=image/resize,w_560)
![= lim F [e-atu(t)] – lim F[eatu( -t)] 040](http://img.homeworklib.com/questions/2a70e720-52f9-11eb-8604-dd7b0aa2e814.png?x-oss-process=image/resize,w_560)
![F[sgn(t)] = lim – a0a+w a +0a – jw](http://img.homeworklib.com/questions/2b071b80-52f9-11eb-85cb-3d5bc2a98dfe.png?x-oss-process=image/resize,w_560)
Therefore, Fourier Transform of sgn(t) is 2/jw.
b)
![So, F[u(t)] = F(0.5 +0.5sgn(t)](http://img.homeworklib.com/questions/2bedbbe0-52f9-11eb-9112-490d2e0851f8.png?x-oss-process=image/resize,w_560)
![= F(0.5] +0.5F|sgn(t)](http://img.homeworklib.com/questions/2c3b7800-52f9-11eb-b577-1523bdf1dbde.png?x-oss-process=image/resize,w_560)
![So, F[u(t)] = (0.5)275(w) + (0.5)](http://img.homeworklib.com/questions/2cd9fa10-52f9-11eb-801e-69bd6e3d7f4c.png?x-oss-process=image/resize,w_560)
![or F[u(t)] = 1.5(w) +](http://img.homeworklib.com/questions/2d1d7d20-52f9-11eb-949b-27734ed2cae8.png?x-oss-process=image/resize,w_560)
Therefore the Fourier Transform of u(t) is
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