Quote:

Originally Posted by

**groovyd**

sorry but this argument is not worth my time...

Your previous explanations are confusing and unclear what exactly you are talking about, especially when you don't include any graphics to illustrate the point you are trying to make, nor do you link or cite any sources where folks can go for a more in-depth understanding.

If I understand correctly, the issue at hand is regarding discrete-time sampling rates and the reconstruction of band-limited signals (and finite energy---like all real signals). In this case, in the xiph.org video, monty (correctly) explains how a real band limited signal is mathematically perfectly defined by sampling above the signal's nyquist frequency. In other words, given a set of discrete samples, there is exactly one and only one band-limited signal which perfectly intersects all of the sample points. This concept was clearly illustrated in monty's video. He further clarifies the point by demonstrating how the phase of the signal is perfectly captured by discrete time sampling. Again, this is the case because there is a one-to-one relationship between a discrete-time sampled waveform and its corresponding band-limited continuous waveform.

You need to define what you mean by "near sine waves" and relate the difference between a actual sine wave and whatever this other thing is that you are talking about, and then relate what additional Fourier coefficients your near sine waves have in addition to the fundamental. Then you need to relate how those harmonics relate to the concept of a band-limited signal. If you've added Fourier components that exceed one half of the sampling frequency, you have violated the Nyquist criterion and you are now discussing a different topic than covered in the video.

The logical flow of the arguments is:

1) there is a reasonably well defined frequency range of human hearing ( e.g., 20Hz -- 20kHz ). There may be exceptions, but by a few % of the Hz one way or another, and certainly not by a factor of 2 in either direction.

2) neither subsonic nor ultrasonic frequencies contribute to the audibility of sounds (this is by definition, "subsonic" meaning lower than what can be heard, etc.)

the corollary here is that all sound that can be heard fits neatly into the band-limited frequency range defined by human hearing (e.g., 20Hz--20kHz).

3) discrete-time sampled sound at frequencies of 44.1kHz or more is sufficient to mathematically define all the energy in a signal band-limited in the human audible range. [1]

Therefore, sampling above twice the highest frequency in the band-limited signal is mathematically sufficient to fully define the continuous time waveform.

[1] - http://en.wikipedia.org/wiki/Sampling_theorem

If the wikipedia source is wrong, I encourage you to use your master's degree-level knowledge on the topic to corrected or amend the article. However, in this case, I don't anticipate that you will overturn the fundamental concept of the Nyquist-Shannon sampling theorem. Perhaps others can chime in with sources of the other bullet points on the list as I am quite busy at work now. Maybe I can fill it in later if there is interest, but the sources are already linked in other parts of the forum, so you can use your googlefu to find it.

Cheers