There seems to be a fair bit of confusion about trying to reproduce square waves using bandwidth-limited systems (and face it, all audio systems are bandwidth-limited), so I decided to try to write up some basic things that hopefully will help clear some of the confusion.
As we know, a square wave is the sum of all odd harmonics, according to the formula
By the way, that formula has nothing to do with Fourier analysis -
Edge.org[/URL], the website of the science and technology think thank [URL="http://en.wikipedia.org/wiki/Edge.org"]Edge Foundation[/URL], has a great collection of answers from various experts to their "[URL="http://www.edge.org/q2011/q11_index.html"]Edge Question 2011[/URL]", "What Scientific Concept Would Improve Everybody's Cognitive Toolkit?"[/LEFT]
Here are the results of the listening test. Unfortunately I only got 6 submissions before I decided to stop collecting entries, so it is not really a statistically relevant sample, and I would not draw any profound conclusions from the results.
As has been pointed out, anyone handy with a program such as Audacity could have cheated by looking at the spectrum plots, and just looking at file sizes would already have provided a lot of guidance. Fortunately the results seem to indicate
As some posters have doubted the benefit of resolutions and sample rates higher than 16 bit and 44.1 kHz, I set up a listening test.
Robert von Bahr of BIS has very kindly arranged for the permission to use a track from BIS-SACD-1949, "endBeginning" by New York Polyphony (available from eClassical).
I made available 8 versions of the track "Lamentationes Jeremiae - IV. Mem.". In addition to the original 24/96 track, there are versions that have been