By now you have reached the most challenging part of this tutorial, namely the DSP section. This is by far the longest and most difficult part. Not than we are going to be engaging in any die hard Bourbakian gymnastics, but in its own peculiar way, math tends to be a bit dense. And make no mistake about it, some math is absolutely essential before we can really understand sound. There are lots of interesting phenomena, technology and signal processing algorithms which are a bit impossible to cover without. There are also some which necessarily entail real rigor. Getting superficially acquainted with the basics is really the least painful way, then. Often one can do without extensive mathematical background, however, since most DSP is really quite intuitive after the essential concepts have been grasped. This chapter aims at just that—giving a strong intuitive background and a bunch of real world examples and procedures to help in implementing audio DSP. To keep the readership interested, some advanced topics are passingly mentioned. Most of these have been confined to their own sections or put into sidebars.
Eventhough we nowadays have computers everywhere and just about all you will ever want to do with sound is doable digitally, you should make no mistake about it: we are very much continuous time beings. Digital signal processing is really an aberration brought on by the discreteness of digital computers. The sampling theorem is the linkage that connects these two quite incompatible domains and hence affects every perceptually significant calculation we are about to perform in the digital domain. Sooner or later.
‐discrete time filters. ‐Finite Impulse Response (FIR) vs. Infinite Impulse Response (IIR) filters. ‐Convolution.
Analogspectra: Fourier series and transformations. The Laplace transformation.
‐Poles and zeroes. ‐pStability in pole/zero lingo. ‐Z vs. Laplace transforms. ‐Frequency and phase response.
‐Linearity ‐differentiation ‐connection to convolution ‐linear vs. circular convolution.
‐whitening ‐inverse filtering
‐time vs. frequency duality/resolution ‐the uncertainty principle
‐filter banks ‐QMFs ‐MDCTMIDI:MDCT. ‐This is really a can of worms whence ‐filter banks ‐critical sampling ‐perfect reconstruction ‐continuous wavelets ‐overcompleteness ‐and so on, ad nauseam crawl out. ‐Alas, enough for a treatise in itself.