Wide bandwidth = necessary?
Eldartford: that is an interesting phenomenon. Do you think we humans can appreciate more of the sound if the gear is capable of reproducing frequencies above 20kHz even if the recording itself doesn't contain any frequency above 16kHz? With other words: would the music sound more "natural"? If that is the case, then I have to have this super tweeter also --> it will superficially create naturalness (sounds like contradictio in terminis). Chris |
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I found out that I could hear the introduction/removal of a low pass filter at a frequency well above the frequency at which I became stone-deaf to a sine wave (the usual test signal). That is quite normal from many sharp low pass or brick wall filters which will introduce a ripple on what passes through - you can indeed hear the ripple. Essentially any box function applied to a signal will introduce ripple within the band. There are phase effects to. You don't have to resort to the idea that we can hear ultrasonics (like a bat) to believe that a filter can be audible. Here is an example of a chebyshev filter |
humans also have a type of wavefront detection mechanism that is independent of our freqency perception. The pre ripple trips this wavefront detector and is perceived as diminishing the detail in the music. I have long believed that our sense of hearing includes a "waveform steepness" factor quite independent of frequency response. Those are excellent points (and excellent posts), and I suspect that what is behind this is the Haas Effect, which causes our hearing mechanisms to "latch on" to the leading edge of closely spaced sound arrivals. We evolved that capability to aid localization of the source of sounds that may arrive at our ears via both a direct path and (slightly later) via reflections. See the following: http://en.wikipedia.org/wiki/Haas_Effect Also, a few comments re the Nyquist rate and the Sampling Theorem and why sampling at twice the highest frequency that may be present is valid in theory but not in practice. Counter-intuitive though it may seem (as Viridian indicated, sampling at the minimum Nyquist rate provides only two samples per period of the highest input signal frequency), that sample rate (of twice the highest possible signal frequency) maintains 100% of the information in the original waveform, regardless of the complexity of the waveform (sinusoidal or not), provided that two things are true: 1)No out-of-band spectral components are present (which would alias down to lower frequencies following the sampling process). 2)The sample record is of infinite length. I believe that follows from the fact that any arbitrary waveform (in the time domain) is mathematically equivalent to a summation of sine waves at various frequencies and amplitudes, but determination of that equivalency requires that an entire sample history covering all time is available. The equation defining the Fourier Transform, which mathematically converts between the time domain and the frequency domain, involves an integration from -infinity to +infinity. The relevant distinction between a pure sine wave and a complex musical waveform, which ElDartford referred to, is that for the pure sine wave we essentially know its entire past and future history -- it's always the same. That's in theory. In practice, we need an anti-aliasing filter in front of the a/d, to filter out-of-band frequencies, and the steeper the filter slope the worse its side-effects will be, everything else being equal. And of course, item 2 can only be satisfied in the real world to some approximation. The idea seems to be that the sample record need only be "long," relative to the changes that occur in the content. All things considered, it's remarkable that redbook cd (sampling at just about 10% above the Nyquist rate) works as well as it does. Regards, -- Al |
