Dr. AIX

Mark Waldrep, aka Dr. AIX, has been producing and engineering music for over 40 years. He learned electronics as a teenager from his HAM radio father while learning to play the guitar. Mark received the first doctorate in music composition from UCLA in 1986 for a "binaural" electronic music composition. Other advanced degrees include an MS in computer science, an MFA/MA in music, BM in music and a BA in art. As an engineer and producer, Mark has worked on projects for the Rolling Stones, 311, Tool, KISS, Blink 182, Blues Traveler, Britney Spears, the San Francisco Symphony, The Dover Quartet, Willie Nelson, Paul Williams, The Allman Brothers, Bad Company and many more. Dr. Waldrep has been an innovator when it comes to multimedia and music. He created the first enhanced CDs in the 90s, the first DVD-Videos released in the U.S., the first web-connected DVD, the first DVD-Audio title, the first music Blu-ray disc and the first 3D Music Album. Additionally, he launched the first High Definition Music Download site in 2007 called iTrax.com. A frequency speaker at audio events, author of numerous articles, Dr. Waldrep is currently writing a book on the production and reproduction of high-end music called, "High-End Audio: A Practical Guide to Production and Playback". The book should be completed in the fall of 2013.

11 thoughts on “Filters: Part II

  • November 28, 2014 at 5:16 pm
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    As I read the opening of Anderton’s reply, I sensed the good Baron JBJ Fourier spinning at 2f rpm in his grave. Anderton’s “. . and a simple sinusoidal signal at that” evokes the presence of overtones, so his illustrative waveform contains higher frequencies that analysis would capture, and Fourier could pass the sampling baton to Nyquist. Dr Aix, our Doctor Mirabilis, thanks for your site. I open it each dawn to wake my sleepy cerebri. Cheers, James Marchment in Darkest Australia

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  • November 28, 2014 at 7:22 pm
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    Hi, Mark!

    The sampling theorem states if a function contains no frequencies higher than B cps it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart. I look at that in context of Fourier’s theorem which states a periodic function if sufficiently continuous can be expressed as sum of a series of sine or cosine terms… . The square wave is a complex function. I figure it is a good substitute for for the complex output of a musical instrument. Fourier’s theorem says that a square wave consists of an infinite set of odd order harmonics. My electronics instructor told me up to the 9th harmonic was enough to approximate a square wave. Let’s say we want to pass a 5,000 cps square wave through the sampling theorem. If the sample rate is 10,000 cps I think the output will look like a sine wave. If the sampling frequency is 90,000 cps, I bet it will approximate a square wave. That’s because the 5 kHz square wave is really the sum of the following sine waves: 5 kHz, 15 kHz, 25 kHz, 35 kHz, and 45 kHz. We must successfully sample all of those sine waves to accurately make the 5 kHz square wave. And isn’t that the goal of high resolution audio? To approximate complex musical events to create accurate output? Take a second look at what Craig is saying…I think it supports our cause.

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    • November 29, 2014 at 9:45 am
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      Thanks for the comment. Your analysis is correct. We need to be able to accurately capture and reproduce frequencies up to our hearing threshold…including complex waveforms like square waves. Craig, I believe has got it…it’s the Tonto commenter that is messing with the facts.

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  • November 28, 2014 at 9:17 pm
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    Also these words of Anderton’s: “The actual figure of 96Khz is used due to the mathematical nature of binary expansion.”.

    [a] What’s a sampling frequency got to do with binary expansion?

    [b] Even if it did, binary expansion would lead us to sampling frequencies of 65.5 kHz or 131 kHz! Not 96.

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    • November 29, 2014 at 9:46 am
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      Actually, these are not Anderton’s words…they are one of his readers comments, which is why I pushed back.

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  • November 28, 2014 at 10:35 pm
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    Nyquist theorem says that at least two samples are needed to accurately reconstruct a signal, as mentioned above. Only two samples per period only happen at Nyquist frequency, which is half of sampling rate (fs/2). However, there is no complex signal at this frequency, as the signal has to be bandlimited, according to the Nyquist theorem – here we are at your filter topic Mark. There is no a complex signal at exactly Nyquist frequency, only a sine wave as all other frequencies above fs/2 are filtered, respectively have to be filtered, in order to avoid aliasing. For all other signals below fs/2, more than two, better much more than two samples are given per period. The signal will be 100% reconstructed by multiplying the sample with sinc function. Therefore, in order to decide what sampling frequency and word length is necessary to capture and reconstruct the entire frequency spectrum, waveforms and dynamic of music signal, frequency bandwidth and dynamic are the parameters we have to look at. There is a lot of misunderstanding and wrong statements in the industry and further with music lovers at the end of the chain, simply by not knowing and/or understanding the sampling theory e.g. Nyquist-Shannon theorem.

    Craig Anderton is right: you need more than two samples to reconstruct a complex sound and also with two samples only a sine wave can be reconstructed. He only does not come to the simple point that Nyquist exactly describes this, by saying that the very highest frequency in the music signal must be sampled at least twice – which means all others below fs/2 are sampled more than twice -, but the very highest frequency (overtone / harmonic) is a sine wave.

    Given these facts, 24/96 is a perfect frame to capture the entire spectrum music provides. We can record ultrasonics till 48kHz (and there is quite nothing above this point) with dynamic of 144dB. Also transients are no problem to reconstruct accurately. Transients are tailored by very high frequency elements in the music signal. We have a relation between frequency spectrum and raise time (e.g. transients) of a signal. With other words, if we see transients, we also see the corresponding high frequencies in a spectrum analyzer. Thus, we have to check: does the chosen sample rate allow to capture these frequencies according to the Nyquist theorem.

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    • November 29, 2014 at 9:48 am
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      This is very well put…thanks very much for the additional clarification. The essence for everyone to understand is that Nyquist-Shannon is dealing with the highest partials of a sound (that was allowed through the LPF at the ADC stage), which turns out to be a sine wave NOT a complex wave.

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  • November 29, 2014 at 5:08 am
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    Once again the confusion arises because of the assumption that more samples per waveform equals more accurate interpolation (and therefore reconstruction) of the waveform. There’s just a complete misunderstanding (well actually no understanding) of the mathematics behind waveform reconstruction. I recommend this article to get a better understanding of how audio sampling works.

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    • November 29, 2014 at 9:49 am
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      Thanks Dave…good read.

      Reply

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