Question

You have been given a 10 seconds recording of a sinusoid function Acos(wot) starting at time=0. As you listen to this tone you noticed that there is an echo in the recording and you have been told that the echo is an added tone delayed by 1 second with the same frequency and that is attenuated by 50%. a) Please write an expression x(t) that mathematically models this recording. RU) b) Please calculate X(w)

Answer 1

Solution - The girm sinusoidal function' Alor(wit). The echo is an added tone delayed by 1 second with the name frequenuj, wo allenated by so% a)- An expression for this recording that can mathematically model this is alt = A costerot) + A costwo(t-1) 1 6- XW) 2 Salt ejut at As popularly, the Fourier Transform, Xlow for a cosimisci dal signal, cesu, t'Xiw = n (SCW-word & Sluend) Hence, the required Founder Transferm will be - X(w) = 24 (Slove) + S1w4wd) + nA e-ju (<10-04 Slutwe) xw5 = (14 ¢din) na (slow-vo) 4 6Cwt vous)