where we have defined
sinusoid's phasor, and its carrier wave.
For a real sinusoid,
When working with complex sinusoids, as in Eq.(4.11), the phasor representation of a sinusoid can be thought of as simply the complex amplitude of the sinusoid. I.e., it is the complex constant that multiplies the carrier term .
Linear, time-invariant (LTI) systems can be said to perform only four operations on a signal: copying, scaling, delaying, and adding. As a result, each output is always a linear combination of delayed copies of the input signal(s). (A linear combination is simply a weighted sum, as discussed in §5.6.) In any linear combination of delayed copies of a complex sinusoid
Since every signal can be expressed as a linear combination of complex sinusoids, this analysis can be applied to any signal by expanding the signal into its weighted sum of complex sinusoids (i.e., by expressing it as an inverse Fourier transform).
Importance of Generalized Complex Sinusoids
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