 of negative frequencies.

This is called a *one-sided* bandpass filter.  An example of a two-sided bandpass filter would be

`\[ g(t) \cos(\omega_o t) \Longleftrightarrow [G(\omega-\omega_o)+G(\omega+\omega_o)]/2. \]`

Note that a one-sided bandpass is necessarily complex-valued, because it will be something like a complex exponential with a localizing envelope.

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