edhall@rand-unix.UUCP (Ed Hall) (06/21/84)
+ One thing first: since square waves (and indeed all waveforms with symmetrical peaks, like triangle waves and so forth) contain only odd harmonics, the lowest non-fundamental harmonic in a 20KHz square wave is 60KHz, not 40KHz. Anyone here who can hear up to 60KHz? :-) Human ears (and probably all biological ears) seem to respond to frequency spectra, not waveform. This is quite fortunate, as small movements of sound source or sound receiver cause huge changes in waveshape, and (usually) little change in the frequency spectrum. (Standing-wave effects are the exception, but aren't very signifigant except in extremely reverberant environments or other artificial conditions. Our perceptual system seems to ignore them unless they are very obvious.) It appears that the ear does the biological equivalent of a continuous fourier transform on the sound it receives, and responds to the relative amplitudes of the various frequencies. It is quite possible (by introducing phase shifts) to create waveforms that look completely different, yet are essentially indistiguishable by ear. And it is quite possible (by introducing low levels of higher harmonics) to produce waveforms that look essentually identical to the eye but sound quite different. The bottom line is that waveform purity of square-waves (or any other specific waveform) is a poor measure of sound fidelity. (And before someone starts arguing about the ability to perceive phase, let me remind you that introduction of any non-linearity into the reproduction chain, and I'm thinking specifically of speakers or headphones, can create a phase-dependent change in the frequency spectra. This can easily explain the differences heard by those who claim a need to preserve ``absolute phase'', i.e. whether polarity is preserved from microphone to speaker, since differences between tops and bottoms of the recorded waveshapes would cause different spectra if passed through a device with non-linearities. And differences between the top and bottom waveshape halves are quite the norm for natural sound. Note that I've said nothing about relative phase between ears or between stereo channels. This type of phase difference is quite audible. Also, there may be a certain amount of ability to hear phase shifts at low (<500Hz) frequencies, but it is a fairly subtle effect.) -Ed Hall decvax!randvax!edhall
newton2@ucbtopaz.CC.Berkeley.ARPA (06/23/84)
Here's another contribution to the discussion of square-wave response that seems evergreen among audiophiles. First, in comparing the perceived sound from reproducing 20 kHz sine and square waves, it seems to me that equal rms amplitudes is precisely what you *don't* want- you want the audible components equal (a little question- begging here, I'm afraid). If the rms values are equal, then 10% or so of the energy of the square wave is in higher harmonics, versus 100% of the sine wave concentrated at 20 kHz. You're trying to demonstrate that the so-called ultrasonic components are audible, so shouldn't they be present *in addition* to the 20 kHz component? Second, as someone earlier pointed out, for a symmetrical waveform, the first higher harmonic present is at 60 kHz, not 40 kHz. We're talking BATS here, forget about Fido. Only tiny flying rodents (and golden-eared audiophiles unconstrained by double-blind experiments) can hear this stuff; only hunter-killer submarines and Polaroid cameras can emit it. The Nyquist argument seems definitive to me-- the whole point of the anti- imaging or reconstruction filter is to eliminate the ambiguity inherent in the sampled data. Just asserting that alternating maxes and mins are written "by a computer" on the disk doesn't show that a "square" was written-- *every* sinusoidal component of the audio spectrum recorded on a CD could be interpreted as a poorly-reproduced squarewave, and images-without-end (within the slewrate limit of the DAC) would be reproduced absent the smoothing filter. Speaking as an erstwhile audio designer (and only for myself), I find squarewave testing the world's most wonderful shortcut in *quickly* assessing what's going on phase/amplitude wise *in those well-behaved circuits where it's useful*. Examples of such are DC-coupled amplifiers and such, equalizers that are alleged to have "flat" positions and so on. Examples of circuits that everyone either puts up with, assumes are "perfect" or simple doesn't realize are ubiquitous are transformer- coupled mic preamps, transformer-output mics, virtually all FM exciters, "classic" tube amps, crossover networks (active or passive) and so on-- square wave testing is often uninformative for these circuits, which nevertheless seem to perform sufficiently transparently (when well-designed) to allow golden-earniks to hear right through to the special beeswax Georg Neumann used to coat the capacitors in those priceless prewar tube mics...:-)
sjc@mordor.UUCP (06/25/84)
Quotes from two different postings: >But you missed the point... >If the CD logic is sound it must reproduce a perfectly square wave >given a properly generated square wave test disk. >As for the validity of testing auudio equipment with 20 khzsquare waves, >Charles is RIGHT ON. *I* can hear the difference between a 20 Khz >square wave, and a 20 Khz sine wave. The only difference is due to sine >wave components at frequencies > 20 Khz. Therefore, extended frequency >range is VITAL to accurate reproduction of very high frequency sounds, >esp. percussion. This includes having speakers that are capable of >reproducing the high frequencies, too. (My Infinity Quantum-2's are >flat to 30 Khz, and gradually roll off beyond that. My Kenwood High Speed >amp is flat to > 100 Khz. Even my Ortofon MC-20FL cartridge is fairly flat >to about 25 Khz.) A test disk may provide a series of samples which (when viewed as unsigned integers) alternate between 0 and 65535, but a correctly functioning CD player must not produce from that a perfect square wave, because the Nyquist theorem says that a series of samples at 2*N Hz will contain only invalid information at frequencies at or above N Hz. The CD player must filter out such frequencies, and as a result will produce from that test disk a sine wave. This has nothing to do with whether a CD player uses purely analog or partly digital filtering. No matter how ideal the filter--whether made by Kyocera or Sears Roebuck--its purpose is to attenuate frequencies above (44)/2 kHz as completely as it can. I will not only admit that a CD player cannot reproduce a perfect 20kHz square wave, I will claim that the more nearly ideal the antialiasing filter is, the more nearly it will turn a 20kHz square wave into a 20kHz sine wave. The CD system will give you >90dB dynamic range, remarkably low added-harmonic- and IM-distortion, complete freedom from wow and flutter, and disks that will last indefinitely--but it will not give you 20kHz square waves. If you require 20kHz square waves, CDs are not for you. (Neither, of course, are analog tape recorders, FM broadcasts, or vinyl records that have been played numerous times.) Clearly people vary in ability to hear high frequencies (particularly with age and exposure to Mick Jagger at 120dB). Note that there is no difference between a 20kHz square wave and a 20kHz sine wave until you get to 40kHz. When comparing sinusoids with square waves by ear, one must be careful to use a signal generator which produces the same RMS magnitude for each. --Steve Correll sjc@s1-c.ARPA, ...!decvax!decwrl!mordor!sjc, or ...!ucbvax!dual!mordor!sjc