I'm talking about ALIASING.
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What is Aliasing?
A nice, concise definition from 1996:
Make sense?earlevel.com wrote:
What is aliasing?
It’s easiest to describe aliasing in terms of a visual sampling system we all know and love—movies. If you’ve ever watched a western and seen the wheel of a rolling wagon appear to be going backwards, you’ve witnessed aliasing. The movie’s frame rate isn’t adequate to describe the rotational frequency of the wheel, and our eyes are deceived by the misinformation!
The Nyquist Theorem tells us that we can successfully sample and play back frequency components up to one-half the sampling frequency. Aliasing is the term used to describe what happens when we try to record and play back frequencies higher than one-half the sampling rate.
Consider a digital audio system with a sample rate of 48 KHz, recording a steadily rising sine wave tone. At lower frequency, the tone is sampled with many points per cycle. As the tone rises in frequency, the cycles get shorter and fewer and fewer points are available to describe it. At a frequency of 24 KHz, only two sample points are available per cycle, and we are at the limit of what Nyquist says we can do. Still, those two points are adequate, in a theoretical world, to recreate the tone after conversion back to analog and low-pass filtering.
But, if the tone continues to rise, the number of samples per cycle is not adequate to describe the waveform, and the inadequate description is equivalent to one describing a lower frequency tone—this is aliasing.
In fact, the tone seems to reflect around the 24 KHz point. A 25 KHz tone becomes indistinguishable from a 23 KHz tone. A 30 KHz tone becomes an 18 KHz tone.
In music, with its many frequencies and harmonics, aliased components mix with the real frequencies to yield a particularly obnoxious form of distortion. And there’s no way to undo the damage. That’s why we take steps to avoid aliasing from the beginning.
Here's another, more in-depth explanation:
The Audio Fool blog wrote:
Sampling a continuous waveform into discrete digital samples results in lost information. Discrete samples can only tell what the wave is doing at periodic instants in time, and not what's happening between them. The continuous sampled wave could be doing anything between samples. We simply don't know.
The problem here is that when we want to get back the data that we threw away and turn samples back into a continuous wave, we must interpolate between samples to find the lost information. Unfortunately, there are an infinite number of signals that could have produced the samples that we want. Fortunately, if we accept a small restriction on our continuous waveform, we can get back to one unique signal.
I think an example is in order. Consider the 7kHz sine wave below, shown over a 1ms interval.
If we sample this sine wave with a sampling rate of 10kHz, we get 11 samples in this interval (counting the endpoints), as shown below.
But when we play back these samples, you won't get 7kHz out of the speaker. What you hear is the 3kHz wave described by the red curve below.
So what happened? Notice that both curves produce exactly the same samples, when sampled at 10kHz. At this sample rate, there is no way to tell the difference between 3kHz, 7kHz, or even the 13kHz wave below.
This effect is known as aliasing, and these frequencies are aliases of each other. In fact, for any frequency f and sample rate S, all frequencies of the form (N*S ± f) for some integer N are aliases.
There is hope, though. For given f and S, there is one unique frequency of the type (N*S ± f) that is between 0 and S/2. Looking at the samples in the example above, the 3kHz wave is between zero and half the sampling rate. No other frequency between 0 and 5kHz can be produced from those samples, and the wave is unique. The frequency S/2, called the Nyquist frequency, is the upper limit of alias-free signal frequency.
All of the information lost from sampling a continuous waveform has a frequency higher than S/2. Therefore, the process of sampling is lossless, as long as all of the frequencies you're interested in are below half the sample rate.
But wait, you may ask. What if you're interested in preserving higher frequencies? Just increase the sample rate to more than twice the highest frequency you're interested in. The human ear can hear frequencies of up to about 20kHz, and it's no coincidence that CD Audio samples at 44.1kHz, providing bit-perfect representation of any frequency humans can hear.
There is one more problem when sampling. Sampling just your frequencies of interest isn't always enough. High frequencies don't just go away when you sample. This out-of-band noise (Noise because it's not part of the signal we want to preserve) in your continuous signal will still be sampled, only now it will alias down below S/2 and contaminate the digital signal you want to keep.
For this reason, any time you sample a continuous signal, you must first band-limit the signal with a low-pass filter to block (attenuate) all frequencies above the Nyquist frequency, so that there is no out-of-band noise at the sampling stage. More on what that means in another post.
Truthfully, I didn't read all that up there, as I think I have a grip on what is going on here. But I assume the quotes explained it pretty well. It's not about what the human ear can hear, per se, it is about where the math is happening, which ultimately ends up influencing frequency ranges that the ear can hear.
