If we wish to take samples of some analog waveform, as in doing analog to digital conversions at some specific conversion charge, there may be an absolute decrease restrict to the speed of doing conversions versus the very best frequency element of the analog sign. That restrict should not be violated if the sampling course of is to yield legitimate outcomes. We don’t wish to encounter the phenomenon referred to as “aliasing”.
The time period “aliasing” as we use it right here has nothing to do with spy thrillers or crime novels. Aliasing is an undesirable impact that may come up when some analog waveform is being sampled for its instantaneous values at common time intervals which might be longer than half the reciprocal of a sampling frequency. If we had been to pattern some waveform as soon as each microsecond, the sampling interval is half of that one microsecond for which we’d have a sampling frequency restrict of two MHz or sooner.
Aliasing will happen if the sampled waveform has frequency element(s) which might be larger in frequency than 50% of the sampling frequency. To show that assertion round, aliasing will happen if the sampling frequency is simply too low. Aliasing will happen at any sampling charge that’s decrease than twice the very best frequency element of the waveform being sampled.
The following query is: Why?
The late comic Professor Irwin Corey as soon as posed an identical query: “Why is the sky blue?” His reply was one thing like “It is a query which have to be taken in two elements. The primary half is ‘Why?’ ‘Why’ is a query Man has requested for the reason that starting of time. Why? I don’t know. The second half is ‘Is the sky blue?’ The reply is ‘Sure!’”
Happily, we will do some higher than that as follows.
The sampling course of may be considered multiplying the waveform being sampled by a really slim responsibility cycle pulse waveform of zero worth for more often than not and of unity worth for the very slim sampling time interval. That sampling waveform will probably be wealthy in harmonics. There will probably be a spectral line on the sampling frequency itself plus spectral traces at every of the sampling frequency’s harmonics as nicely. Every spectral line could have sidebands as proven in Determine 1 which is able to prolong from these sampling frequency spectral traces up and down the frequency spectrum in step with the sampled waveform’s bandwidth.
Determine 1 Sampling versus aliasing the place spectral line could have sidebands that can prolong from these sampling frequency spectral traces up and down the frequency spectrum in step with the sampled waveform’s bandwidth.
The sampling waveform is amplitude modulated by the sampled waveform and so I’ve chosen to name that sampled waveform’s highest frequency element, Fmod. Every bandwidth is 2 * Fmod.
If the sampling frequency is excessive sufficient as with Fs1, the illustrated sidebands don’t overlap. There’s a respectable guard band between them, and no aliasing happens.
If the sampling frequency begins getting decrease as with Fs2, the sidebands begin getting nearer collectively and there’s a much less comfy, if I’ll use that phrase, guard band.
If the sampling frequency will get too low as with Fs3 which is lower than twice Fmod, the sidebands overlap, and we have now aliasing. Sampling integrity is misplaced. The sampled waveform can’t be reconstructed from the undersampled output of this now unsatisfactory system.
Think about this an homage to Claude Shannon (April 30, 1916 – February 24, 2001) and his sampling concept.
John Dunn is an electronics marketing consultant, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York College (MSEE).
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