A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C) elements, connected all in series or all in parallel, limits_k = 1^3 a_kcos ( k _0t ), where ak ≠ 0, ω0 ≠ 0. The source has nonzero impedance. Which one of the following is a possible form of the output measured across a resistor in the network?

limits_k = 1^3 b_kcos ( k _0t + _k ), where b_k a_k, k

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Signal Processing

A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C) elements, connected all in series or all in parallel, $$\sum\limits_{k = 1}^3 {{a_k}\cos \left( {k{\omega _0}t} \right),} $$ where a_k ≠ 0, ω₀ ≠ 0. The source has nonzero impedance. Which one of the following is a possible form of the output measured across a resistor in the network?

A) $$\sum\limits_{k = 1}^3 {{b_k}\cos \left( {k{\omega _0}t + {\phi _k}} \right),} {\text{ where }}{b_k} \ne {a_k},\,\forall k$$ B) $$\sum\limits_{k = 1}^3 {{b_k}\cos \left( {k{\omega _0}t + {\phi _k}} \right),} {\text{ where }}{b_k} \ne 0,\,\forall k$$ C) $$\sum\limits_{k = 1}^3 {{a_k}\cos \left( {k{\omega _0}t + {\phi _k}} \right)} $$ D) $$\sum\limits_{k = 1}^2 {{a_k}\cos \left( {k{\omega _0}t + {\phi _k}} \right)} $$

Answer & Solution

Correct Answer: Option A

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