Introduction to Random Signals and Noise

5

Bandpass Processes

Bandpass processes often occur in electrical engineering, mostly as a result of the bandpass filtering of white noise. This is due to the fact that in electrical engineering in general, and specifically in telecommunications, use is made of modulation of signals. These information-carrying signals have to be filtered in systems such as receivers to separate them from other, unwanted signals in order to enhance the quality of the wanted signals and to prepare them for further processing such as detection.

Before dealing with bandpass processes we will present a summary of the description of deterministic bandpass signals.

5.1 DESCRIPTION OF DETERMINISTIC BANDPASS SIGNALS

There are many reasons why signals are modulated. Doing so shifts the spectrum to a certain frequency, so that a bandpass signal results (see Section 3.4). On processing, for example, reception of a telecommunication signal, such signals are bandpass filtered in order to separate them in frequency from other (unwanted) signals and to limit the amount of noise power. We consider signals that consist of a high-frequency carrier modulated in amplitude or phase by a time function that varies much more slowly than the carrier. For instance, amplitude modulation (AM) signals are written as

where A is the amplitude of the unmodulated carrier, m(t) is the low-frequency modulating signal and ω₀ is the ...