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

Abstract: The low-pass filter is a fundamental building block from which digital signal-processing systems (e.g. radio and radar) are built. Signals in the electromagnetic spectrum extend over all timescales/frequencies and are used to transmit and receive very long or very short pulses of very narrow or very wide bandwidth. Time/Frequency agility is the key for optimal spectrum utilization (i.e. to suppress interference and enhance propagation) and low-pass filtering is the low-level digital mechanism for manoeuvre in this domain. By increasing and decreasing the bandwidth of a low-pass filter, thus decreasing and increasing its pulse duration, the engineer may shift energy concentration between frequency and time. Simple processes for engineering such components are described and explained below. These lecture notes are part of a short course that is intended to help recent engineering graduates design low-pass digital filters for this purpose, who have had some exposure to the topic during their studies, and who are now interested in the sending and receiving signals over the electromagnetic spectrum, in wireless communication (i.e. radio) and remote sensing (e.g. radar) applications, for instance. The best way to understand the material is to interact with the spectrum using receivers and or transmitters and software-defined radio development-kits provide a convenient platform for experimentation. Fortunately, wireless communication in the radio-frequency spectrum is an ideal application for the illustration of waveform agility in the electromagnetic spectrum. In Parts I and II, the theoretical foundations of digital low-pass filters are presented, i.e. signals-and-systems theory, then in Part III they are applied to the problem of radio communication and used to concentrate energy in time or frequency.