Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!mnetor!seismo!columbia!heathcliff.columbia.edu!zdenek From: zdenek@heathcliff.columbia.edu (Zdenek Radouch) Newsgroups: sci.math,sci.physics Subject: Re: Analog/Digital Distinction Message-ID: <3783@columbia.UUCP> Date: Wed, 5-Nov-86 20:47:23 EST Article-I.D.: columbia.3783 Posted: Wed Nov 5 20:47:23 1986 Date-Received: Thu, 6-Nov-86 00:51:22 EST References: <116@mind.UUCP> <267@apple.UUCP> Sender: nobody@columbia.UUCP Reply-To: zdenek@heathcliff.columbia.edu.UUCP (Zdenek Radouch) Followup-To: net.physics Distribution: net Organization: Columbia University CS Department Lines: 55 Keywords: Sampling, quantization, and dimensionality Xref: mnetor sci.math:133 sci.physics:117 In article <267@apple.UUCP> turk@apple.UUCP (Ken "Turk" Turkowski) writes: > >As a practical consideration, all analog signals are band-limited. False. For a PARTICULAR purpose we can consider property A to be of interest only if it is in an interval . The property is ANY property, not just the frequency - see below! >...By the >Sampling Theorem, there is a sampling rate at which a bandlimited signal can >be perfectly reconstructed. *Increasing the sampling rate beyond this >"Nyquist rate" cannot result in higher fidelity*. False. The Nyquist Theorem assumes that the band of the signal REALLY IS limited. It in fact isn't, we are just not interested in the sound we cannot hear. It is a common misconception that you don't have to worry about the frequency you cannot hear. As far as hearing is concerned - yes. But the sampling works ONLY if the signal IS bandlimited. You need a low pass filter to LIMIT the band of the signal. Such a filter is easy to describe mathemati- cally (Fx < Fn -> A=1; Fx > Fn -> A=0) but it cannot be build. Hence the real sampling rate has to be higher than the Nyquist rate. >What can affect the fidelity, however, is the quantization of the samples: >the more bits used to represent each sample, the more accurately the signal >is represented. False. Either you are interested in unlimited range i.e. the original analog signal, or you assume a particular application and corresponding set of ranges of all the properties involved. In the first case (of no practical importance) you would need infinite sampling frequency as well as infinite number of the bits for each sample. Once you limited the frequency range according to the mechanism of hearing you should do the same to the dynamic range. You said: According to our experience, we are interested only in the frequencies up to N Hz. Therefore (according to Nyquist) the sampling rate can be 2N Hz. Similarly: According to our experience, we are interested only in dynamic levels up to N dB. Therefore (using simple math) we need only N/6 bits of resolution. zdenek ------------------------------------------------------------------------- Men are four: He who knows and knows that he knows, he is wise - follow him; He who knows and knows not that he knows, he is asleep - wake him; He who knows not and knows that he knows not, he is simple - teach him; He who knows not and knows not that he knows not, he is a fool - shun him! zdenek@CS.COLUMBIA.EDU or ...!seismo!columbia!cs!zdenek Zdenek Radouch, 457 Computer Science, Columbia University, 500 West 120th St., New York, NY 10027