A network consisting of a finite number of linear resistor (R), inducer (L), and capacitor (C) elements, connected all in series or all in parallel, is excited with a source of the form limits_k = 1^3 a_xcos ( k _0t ),rmwerea_k 0, _0 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 a_xcos ( k _0t + _k )

This question belongs to Electronics And Communications Engineering Signal Processing

Signal Processing

A network consisting of a finite number of linear resistor (R), inducer (L), and capacitor (C) elements, connected all in series or all in parallel, is excited with a source of the form
$$\sum\limits_{k = 1}^3 {{a_x}\,\cos \left( {k{\omega _0}t} \right),{\rm{were}}\,{a_k} \ne 0,} \,{\omega _0} \ne 0.$$
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) $$\sum\limits_{k = 1}^3 {{b_x}\,\cos \left( {k{\omega _0}t + {\phi _k}} \right),{\rm{were}}\,{b_k} \ne {a_k},} \,\forall K$$ B) $$\sum\limits_{k = 1}^3 {{b_x}\,\cos \left( {k{\omega _0}t + {\phi _k}} \right),{\rm{were}}\,{b_k} \ne 0,} \,\forall K$$ C) $$\sum\limits_{k = 1}^3 {{a_x}\,\cos \left( {k{\omega _0}t + {\phi _k}} \right)} $$ D) $$\sum\limits_{k = 1}^2 {{a_x}\,\cos \left( {k{\omega _0}t + {\phi _k}} \right)} $$

Answer & Solution

Correct Answer: Option C

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