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if we don't apply a sinusoidal signal at the input s may become a complex number $$$$ All real-world signals exist only on the $j\omega$ axis. Consider that a complicated signal can be broke...
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#1: Initial revision
> _if we don't apply a sinusoidal signal at the input s may become a complex number_ $$$$ **All real-world signals exist only on the \$j\omega\$ axis.** Consider that a complicated signal can be broken down into a fundamental sinewave and its harmonics. The harmonics are still sinusoidal and, for a linear filter circuit, they can be treated as individual sinewaves.