ABSTRACT
All bandpass waveforms, whether they arise from modulated signals, interfering signals, or noise, may be represented in a convenient form given by the following theorem. The usefulness of the complex envelope representation for bandpass waveforms cannot be overemphasized. The spectrum of the bandpass signal is the translation of the spectrum of its complex envelope. The modulated signal is just a special application of the bandpass representation. Modulation is the process of encoding the source information modulating signal (m(t)) into a bandpass modulated signal. Consequently, the modulated signal is just a special application of the bandpass representation. Phase modulation and frequency modulation are special cases of angle-modulated signaling. Digitally modulated bandpass signals are obtained when m(t) is a digital baseband signal—for example, the output of a transistor–transistor logic transistor–transistor logic (TTL) circuit. In communication problems, the information source signal is usually a baseband signal—for example, TTL waveform from a digital circuit or an audio signal from a microphone.
