Search results

No, the Fourier Transform and the Sampling theorem are not applicable everywhere. Formally, they are only applicable to signals with unlimited duration, sampled with unlimited precision. There is a classic theorem in LTS Theory, proving that every time-limited signal has infinite, that is...

I was in the top 5%, per finals results, in both university classes I took that dealt, among other things, with Linear Time-Invariant Systems Theory (LTS), of which Fourier transform is a part. Not to mention other university math education needed to get a graduate degree in Physics. Compared...

I literally wrote "most real-life music fragments are not just sums of long-running perfect sinusoids with unchanging amplitudes". If mammalian cochlea behaved like a Fourier transformer operating in bursts of constant duration, it could indeed represent any signal as a deterministic set of...

Yes, I agree that distortions in a decently-priced low-power electronics (e.g. DACs) are all but sorted out by now. Mainstream high-power electronic devices (e.g. amplifiers) are still dicey: you'd need to spend significantly more to buy something well-behaved on a variety of music genres. As to...

One problem here is that one can create a number of such models. For instance, by changing sampling rate and transformation window width. Or, in mathematical terms, by switching the orthogonal base of functions over which the linear transform operates. This is a trivial fact actually. Analogous...

Several writers on this thread already alluded to the fact that distortions along the sound reproduction chain "stack up". Sometimes in simple ways, e.g. like several white noise generators do. Sometimes in much more complicated ways. An otherwise insignificant distortion in one element of the...

If a person had vitamin and mineral deficiency before he or she started taking the supplements, they may help, mainly through improving cardiovascular health. Mammal cochlea is an organ which requires substantial blood supply when active, yet blood vessels going there are not wide. If a person...

I'd recommend to just go to 5.1 configuration for movies. And buying a good 3-way center speaker or studio monitor (I use https://www.adam-audio.com/en/ax-series/a77x/). Such configuration will ensure that: (1) There are no interference and combing effects from typical 5.1 or 7.1 movie audio...

The three lineages of Layers (MPEG-1/2/2.5 Audio Layer I,II,III) were developed by different consortiums. Instead of trying to integrate them, or to give a preference to a single one, it was more practical to just let them all be, and for the consortiums to cross-license their patents protecting...

Thank you for the effort to generate and post the graphs. Let's discuss now what they really represent. First, let's start with yet another experiment. Let's render exactly same sequence of samples, but at 48 KHz sampling rate. Thus, the audio signal would be at 12 KHz. If we follow the...

From https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem: "Strictly speaking, the theorem only applies to a class of mathematical functions having a Fourier transform that is zero outside of a finite region of frequencies." "Shannon's version of the theorem states: If a...

Could you please write here the definition of the the theorem you use.

That's helpful. Thanks!

It appears we have different definitions of "audible range". Let me try explaining once again what I mean, from another angle. Apologies if you already know all of it - what follows could be still interesting to others. Imagine a PCM file at 192KHz with this sequence of four repeating values...

This is interesting consideration indeed. Even though, there appears to be some confusion. WXA-50 uses ICEpower 125asx2, right? Which, according to https://icepower.dk/products/amplifier-power-modules/asx-series/, is "based on ICEpower’s HCOM class D topology". Which, according to the HCOM...

Nope. I considered such behavior a bug in my DSP code - long since fixed. One man's garbage ... :) If you want to do something like this intentionally, you may play with parameters in any number of plugins removing/transforming transients (e.g...

It does apply the smoothing effect, yet it is too small to be noticed all by itself. You'd need a system which happens to be just below the edge of the transient front detection threshold, to notice the effect when substitution of one of the components pushes the overall system over the edge...

Depends on the definition of "commonplace" I guess. It is an active area of research, which, while anatomically known since 1960s, only came into prominence after 2012, when better neural simulation models became commonplace: https://www.frontiersin.org/articles/10.3389/fncom.2018.00036/full

I like that. Nicely illustrates my point. If you stretch the first graph in time, you will see that the responses are qualitatively similar, yet not exactly the same. On the second graph, same deal - similar yet not exactly the same. In addition, it shows the ramp-up to about 10% of amplitude...

I think that in the context of this conversation some of us are mixing three facets of music audio signals into one. The three: sinusoidal (aka harmonic), impulse (aka transient), and noise. The paradigm of Linear Time-Invariant systems deals elegantly with the first one, while treating the...