Let me express my agreement with the nice choice of subject: the simulation of tube amps. Of course during and before the advent of solid state systems, some people may have laughed about the idea alone (because tubes sound so annoying after while), but in the context of guitars, it's usually nice.

Of course there's the question as to what is nice to simulate about them, such as it is often suggested that a tube stage will mostly add second harmonic distortion, but of course certain transients, multi-pole filter and multiplicative effects are there as well. Probably for a guitar, the added harmonics, which are a function of the tones and volume you play, can be best generated by a mild (non-resonant) band pass with at least a true high-pass (zero DC component remaining), and possibly you want the average the result, maybe with a potent at least multi-coupled impulse cabinet simulation.

About delay: clearly, it's important to acknowledge the existence of delay in just about every digital system, while it is possible to get rid of it altogether (except for the speed of light) like I've worked on with digitally controlled analog parts, in a full digital system and current clock rates: it's always there. The character of the delay has been mentioned, sure that's important too, and it's not a ad idea to think that in most current practical cases, there's a certain form of limited reconstruction filter in the DA converter, that certainly has a character (try feeding the sound round and round a few times, you''ll get a good idea of that character). To be sure to know the difference between a general delay and a digital one, use a speaker at big distance, or a tape echo. The constancy of the delay is another factor that is important to players and singers, with as possible exception of naturally sounding equalization (which also introduces some phase delay): the more constant the delay is, for my personal preference to the accuracy of a mid frequency wave length easily, the better. Finally, there's the "digital hole" in the sound you get when a (reconstruction error containing) digital system amplifies a microphone and is heard back "live": probably it can be instantaneously spotted for it's unnaturalness, compared with an analog system, which is something to think about.

Concerning the sources having created the advent of the h(z) things, from what I recall from my university text-books, the main idea was simply the congruence of the h9z0 with the h(s) or H(1/(2 PI jW)). Of course the undergrad EE student will have the understanding that the digital signal will be a sequence of impulses, which in principle can be reconstructed into and analog signal, and of course we also know the idea of a z-1 delay is in principle an infinite order system, so tht it's a bit different transform than a perfect digital form of the Linear System Theory and its very complicated complex plane analysis.

T.

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