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Should the Square Wave Test be Mandatory?

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I usually enjoy audio reviews that have clear analysis measurements and realistic listening conclusions. I tend to quickly gloss over measurement charts and tables that are either difficult to understand or not comprehensive. At the same time reviews that tend to say that everything is good makes me feel that the reviewer has sold his soul to the prevailing dollars. Of course the other extreme that everything (except for the one product the reviewer believes in) is crap, often leaves me feeling that the review is not without prejudice or bias.


Anyway, I came across this test, a so-called torture test, for a DAC’s ability to output correctly a square wave input signal. It seems reasonable and easy to understand, but is it a valuable measure of a DAC’s accuracy? And does the extreme accuracy come at the expense of a melodic sound?




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The torture test is nothing more than a manifestation of the total misunderstanding of digital sampling theory. A perfect square wave consists of a fundamental frequency and an infinite number of odd harmonics and requires infinite bandwidth which is impossible to achieve. For higher sampling frequencies the second wave will look closer and closer to a square wave. For audio the square wave at 44.1 Khz sampling frequency (almost sinusoid looking) is perfectly adequate. Most basic textbooks on Digital Signal Processing would be able to shed more light than my limited attempt at an explanation.


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This is exactly one of the problems I have with certain measurements.


I used to be familiar with Fourier analysis and I know that any periodic signal can be represented as a sum of sinusoids. I know that a square wave can be formed by adding together sinusoids of the appropriate amplitude, frequency, and phase. I know that using only the odd-numbered harmonics, you can construct a square wave and to achieve the shape of a true square wave with no ripples in the stationary parts would require the summation of an infinite number of sinusoids.


I know that to generate a square wave you need to alternate between two values representing the high and low voltage of the waveform. If you try to run the DAC faster than it can respond to the new voltage, however, the output waveform may not appear to be square due to the limited bandwidth or slew rate of the converter.

I also know that when you look at a square wave with an oscilloscope, the scope's input bandwidth may limit your ability to see the correct waveform. In the frequency domain a square wave consists of a succession of odd harmonics of the fundamental frequency. If your scope cuts off below the third harmonic you will see a sine wave even if the actual signal is a square wave.


What I don’t understand is why this torture test is nothing more than a manifestation of the total misunderstanding of digital sampling theory. Why isn’t it a case of the output not equaling the input? If we go from A/D and then D/A (or D/A and then A/D), we should be able to trace what is lost through each stage of the conversions.


If this test is misleading, especially to the average reader, then one can assume that the average person can easily be misled by measurements, especially if competing experts don’t agree, which leads me to my last question.


What clear measurements based on standard, accepted tests should all reviews of DACs include? I remember the useless total harmonic distortion wars of the early 70s and I don’t what history to repeat itself.



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Total harmonic distortion is a much more useful test to see if input equals output than the square wave test that you referenced. If you understand what a square wave, sine wave, Fourier Series etc is and you don't understand why this is not a good indicator of audio performance I don't know how I could help you.

Although I find high-end magazine reviews of dubious value, Atkinson's tests in Stereophile contain a pretty good set of measurements (of most devices). There is no single measurement that can tell you if something is good or bad and it requires technical understanding that requires reading and time spend.


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The posted input and output waveforms were part of a highly respected product efforts to explain why DSD is better than 24/192 and lower resolutions. If you buy into these graphs, you would also conclude that 24/192 is much better than 24/96. It may not be a thousand words but the picture is pretty clear, even if you disagree with what is being portrayed.


I will look into the Atkinson's tests of DACs in Stereophile. I am obviously hoping to find some meaningful and discriminating tests that can be used to evaluate DACs and whose results will be accepted by most. I fully expect manufacturers to create or use tests to demonstrate the superiority of their product which is why I value independent tests from objective reviewers that can be verified, instead of those reviewers who simply re-publish the manufacturers test results.


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What is being displayed is the bandwidth limitation of the system. If you thing that linear frequency response in the Megahertz region is important for audio then this is important. I cannot discern the specifics of the signals involved due to the poor resolution of the pictures in the link but something does not sit well with the engineer in me. Comparing 16bit/44.1, 24bit/96Khz, 24bit/192Khz to 1bit/5.6Mhz is like comparing apples to oranges and without being able to see the details of the signals it's definitely misleading.

Also, maybe this can be of some help



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