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: <3803@columbia.UUCP> Date: Sun, 9-Nov-86 15:26:33 EST Article-I.D.: columbia.3803 Posted: Sun Nov 9 15:26:33 1986 Date-Received: Sun, 9-Nov-86 20:59:56 EST References: <105@mind.UUCP> <6654@think.COM> <22067@rochester.ARPA> <521@ptsfd.UUCP> <277@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: 96 Summary: Do you have to post the drivel to three groups? Xref: mnetor sci.math:166 sci.physics:139 In article <277@apple.UUCP> turk@apple.UUCP (Ken "Turk" Turkowski) writes: > > ... The steps seen >on signals coming directly from an A/D converter are due to aliases in the >frequency domain; a lowpass filter with a sharp cutoff at half the Nyquist >rate will eliminate these steps or aliases. > Nonsense. Discrete nature of the digital signal has NOTHING to do with alias distortion. (It's about equivalent to saying: There is a relation between the digital representation of the numbers in my program and the bus error I got.) Also note that aliasing can only be PREVENTED. Once it occurs, there is NO WAY to eliminate it. If you want to post something, anybody can find in any introductory text for signal processing, why don't you read it first? You would learn something and in addition you might find some interesting problem, we could disscuss. It's boring to keep correcting the drivel. Anyway, let me say something about A/D, D/A, aliasing and related subjects. The standard analog-digital-analog chain looks like this: 2. ADC analog signal -> 1. LP filter -> -> 4. signal processing engine 3. sampling -> 5. DAC -> 6. LP filter -> analog signal 1. LP filter (low pass) limits the frequency range of the input signal to <0, Fsampling/2> in order to eliminate aliasing (see 3.) Note that 2. and 3. can be in any order 2. ADC ("analog to digital converter") 1. Converts continuous amplitude of input signal to discrete levels 2. Represents discrete amplitude levels as numbers 3. sampling Conversion of continuous-time signal f(t) into sequence x(n) with values x(n) = f(nT) by periodic sampling. T is sampling period. This is the critical part of the chain because sampling process is many-to-one mapping. In general, if F(f) is the sampling function, F(f1) = F(f2) DOESN'T imply f1 = f2! F(f) becomes one-to-one only if f is from <0,Fs/2> where Fs = 1/T. Sampling process is the only place in the chain with possibility of many-to-one mapping. In plain words if you sample an "illegal" frequency f>Fs/2 you will get different frequency on the output. The output frequency will be fFs/2) components from the spectrum. These frequencies are inherent to discrete-time signal. In addition please note: 1. "Analog to digital converter" does only part of the conversion from analog to digital. 2. "Digital to analog converter" DOESN'T perform the digital to analog conversion. 3. The mathematics in signal processing uses DISCRETE-TIME signals as opposed to STEP signals engineers like to draw. The original signal can be reconstructed only if the pulses fed to the output LP filter have zero width. If the pulsewidth is finite (equal to T in step function) there will be decrease in amplitude of the high frequencies that has to be corrected elsewhere. 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