Gratitude Day 12: A-law & µ-law Audio Companding

Our first foray into lossy compression will be in the audio realm, looking at a pair of companding algorithms (short for "compressing and expanding") used extensively in telecommunications: A-law and µ-law. Now, these algorithms don't exactly belong to the same category of the more well-known audio codecs, such as MP3, AAC, Opus, or ATRAC (eww). Actually, companding algorithms aren't technically codecs at all, they're more like reversible audio filters that help preserve audio quality (particularly aiming at human voice) when it is being compressed by other means. In particular, A-law and µ-law are used to preserve audio quality when a signal is being reduced from 16-bit audio (CD-quality) down to 8-bit audio (telephone quality). From a bird's-eye perspective, the mechanism is a little bit like Dolby Noise Reduction, which was an analog system used to reduced tape noise. The basic idea* behind Dolby NR is that tape noise or tape hiss was limited to a certain set of audio frequencies,…