Does the reduction in sampling rate causes compression of the signal? If yes, can you please provide me some specific example?
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\$\begingroup\$ Reduction of sampling rate is reducing the number of samples thus reducing the amount of information transferred per time unit. Can you call it "compression"? I don't think so. \$\endgroup\$– Eugene Sh.Sep 29, 2015 at 18:03
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\$\begingroup\$ Right, you can call it a lossy "compression"... \$\endgroup\$– AlexxxSep 29, 2015 at 18:05
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\$\begingroup\$ Well, it would be very bad "lossy compression" as the ratio between the loss and the compression is 100%. \$\endgroup\$– Eugene Sh.Sep 29, 2015 at 18:16
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\$\begingroup\$ Define what you mean by compression. It means different things here I believe. \$\endgroup\$– Andy akaSep 29, 2015 at 19:54
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Reducing the sample rate of a signal certainly reduces the data rate, all else held constant. However, I wouldn't call this "compression".
Without pre-filtering the signal to remove frequencies above 1/2 the sample rate, lowering the sample rate will cause aliasing.
For example, let's say you take a HiFi audio signal of a concert or something where there are significant frequencies above 10 kHz. This sounds fine when appropriately filtered and sampled at, let's say 44 kHz (the sampling frequency used by CDs). Now if you decided you only cared about frequencies up to 3 kHz, you don't just lower the sampling rate to 6 kHz. If you did, all the frequencies above 3 kHz (half the sampling rate) would turn into aliases. The result would be a mess with all kinds of squeals and weird sounds. To get just the lower data rate 3 kHz signal, you have to filter the full signal to eliminate content above 3 kHz. Only then can you sample at 6 kHz and avoid aliasing.
In any case, even if you did the filtering to avoid aliasing, I wouldn't call this "compression".
answered Sep 29, 2015 at 18:29
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\$\begingroup\$ Yes, I got your point. What if the initial sampling rate is W and reduced sampling rate is R, such that W/R is some integer n. Can we achieve compression by using the reduced sampling rate R, where each sample is some sort of combination of n samples? And, can we reconstruct the original signal from the reduced sampling rate? \$\endgroup\$– J CianSep 29, 2015 at 19:15
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\$\begingroup\$ Of course, for audio signals, "compression" has a precise meaning, reducing the dynamic range, and it is unrelated to the sampling rate. \$\endgroup\$– TEMLIBSep 30, 2015 at 1:10
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\$\begingroup\$ @JCian: What you are describing is called dessimation, and is commonly done. However, it's not so simple as just averaging N original samples down to 1. A box filter like that still lets thru significant frequencies that will cause aliasing. Ideally you want to run the input samples thru a sinc filter, as these have sharp frequency cutoffs. \$\endgroup\$ Sep 30, 2015 at 10:55
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\$\begingroup\$ @TEMLI: There are various ways to compress a audio signal. What you describe is one of them, but certainly not the only one, or the definition of what "compression" means to audio. You seem to be confusing compressing and companding. \$\endgroup\$ Sep 30, 2015 at 10:57