If we substitute the equation \(x_l (t)= u_c (t)+j u_s (t)\) in equation x (t) + j ẋ (t) = xl(t) ej2πFct and equate real and imaginary parts on side, then what are the relations that we obtain?

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Sampling and Reconstruction of Signals topics include: A/D Converters and their oversampling, band pass signal sampling and representation, sample and hold concepts and quantization and coding techniques. Sampling and reconstruction are processes that convert continuous-time signals into a sequence of numbers and back again.  Sampling converts continuous-time signals, like sound, into a sequence of numbers that can be stored, manipulated, and transmitted by computers. Reconstruction converts the samples back into a continuous-time format for physical presentation. For example,... Show more

If we substitute the equation \(x_l (t)= u_c (t)+j u_s (t)\) in equation x (t) + j ẋ (t) = x<sub>l</sub>(t) e<sup>j2πF<sub>c</sub>t</sup> and equate real and imaginary parts on side, then what are the relations that we obtain?