Question

A cascaded system that consists of an LTI system and a delay system is shown in Figure Q4(b). The input signal X(t) and impulse response of the LTI system, h(t) are given as the following: x(t) = 6-2&u(t) h(t) = e-fu(t) Determine: The Fourier transform of y(t). (3 marks) The Fourier transform of z(t). (3 marks) A basic modulator circuit is shown in Figure Q4(c). Modulation is a multiplication between input signal, m(t), and a carrier signal, c(t). The process yields a modulated signal, y(t). Frequency of carrier signal is higher than frequency of the input signal (wc >wn). (1) Analyze the Fourier Transform of signal y(t) by using modulation properties. (4 marks) Sketch the amplitude spectrum signal of Y(w). (2 marks) (11)

Answer 1

Given X(t) ۸(t) et ult) - at e FT ا a tjw او ۔ می -2 Pa et ult) It jw ۶ (1) = ) ( د )۸ & FT انه) 4 . (بها) * ان - 2 tów 2t j wat diwaw² 2 يما - من 3 + ( 1 ) 2 (t) ay (t-2) FT ما ه ل - ها - ا) * ما2 - 2 ( ) = 2 با - فه 3 2 (4 ) 7(E) Cos wat. Coswet cos we twaste cos (ww.)t} 6-j6 e te 2 coso + 2 4 ( ها ) و انیمه ها) 5- ا(ها) في ايه ها ) - ,ملا' 36 te F.T & Et) 1 L را به FTے نماز FT 1. e 1 (س) ۶ ها » + ها ) 18 ( 4 ما +نها ) + (ما- ہما - مها )8 » ) - به) + به لا ز) 74 1/ 1/4 We can wetom ما - ما انا - ناسا ۔