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The low-pass filter is a fundamental building block from which digitalsignal-processing systems (e.g. radio and radar) are built. Signals in theelectromagnetic spectrum extend over all timescales/frequencies and are used totransmit and receive very long or very short pulses of very narrow or very widebandwidth. Time/Frequency agility is the key for optimal spectrum utilization(i.e. to suppress interference and enhance propagation) and low-pass filteringis the low-level digital mechanism for manoeuvre in this domain. By increasingand decreasing the bandwidth of a low-pass filter, thus decreasing andincreasing its pulse duration, the engineer may shift energy concentrationbetween frequency and time. Simple processes for engineering such componentsare described and explained below. These lecture notes are part of a shortcourse that is intended to help recent engineering graduates design low-passdigital filters for this purpose, who have had some exposure to the topicduring their studies, and who are now interested in the sending and receivingsignals over the electromagnetic spectrum, in wireless communication (i.e.radio) and remote sensing (e.g. radar) applications, for instance. The best wayto understand the material is to interact with the spectrum using receivers andor transmitters and software-defined radio development-kits provide aconvenient platform for experimentation. Fortunately, wireless communication inthe radio-frequency spectrum is an ideal application for the illustration ofwaveform agility in the electromagnetic spectrum. In Parts I and II, thetheoretical foundations of digital low-pass filters are presented, i.e.signals-and-systems theory, then in Part III they are applied to the problem ofradio communication and used to concentrate energy in time or frequency.

Lecture notes on the design of low-pass digital filters with wireless-communication applications