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enter image description here enter image description here

I have to find yn/xn ratio.

From the circuit analysis i found out transfer function Uout//Uin =enter image description here . I am having hard time trying to isolate two coefficients of two complex fourier Series. Any help is highly appreciated. Thank you.

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    \$\begingroup\$ One of your images say \$\hat{y}_n = \frac{\hat{x}_n}{1+jn\omega_0 R C}\$. Doesn't that already give you the ratio \$\frac{\hat{y}_n}{\hat{x}_n}\$ ? \$\endgroup\$
    – AJN
    Commented Sep 23, 2020 at 15:45
  • \$\begingroup\$ thats what answer should be \$\endgroup\$
    – TeilZeitGott
    Commented Sep 23, 2020 at 21:17
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    \$\begingroup\$ Since you are referring to a transfer function, I assume the circuit is a linear time invariant system. Then, it has the property that the output for the sum of a set of signals is same as the sum of the outputs of the individual signals. Your U_in is the sum of certain signals. Can you take it from here? \$\endgroup\$
    – AJN
    Commented Sep 24, 2020 at 1:32

1 Answer 1

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For LTI systems, use the linearity property. $$ \begin{align} H(s) \cdot \left(\sum X_i (s)\right) \mapsto{} & \sum H(s)\cdot X_i (s) & {}={} & \sum Y_i(s) \\ h(t) \circledast \cdot \left(\sum x_i (t)\right) \mapsto{} & \sum h(t)\circledast x_i (t) & {}={} & \sum y_i(t) \end{align} $$

From the above, \$\frac{y_i}{x_i}\$ or \$\frac{Y_i}{X_i}\$ can be found by comparing like terms.

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