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.

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13 Responses to What is aliasing?

  1. Firlefonz says:

    A human ear can hear until a frequency up to 20kHz. So why do we have a bit rate by 44.1 and not 40kHz?

    “The Nyquist Theorem tells us […] one-half the sampling frequency”

    • Nigel Redmon says:

      Because our lowpass filter will start to roll off the response at 20 kHz, and it will still take a very steep filter to have the response down as far as we’d like by 22.05 kHz.

    • Dan says:

      Because of broadcast television and being a multiple of framerates including drop-frame broadcast standards.

      • Nigel Redmon says:

        Yes, that’s why it’s the exactly number 44.1 kHz (and similar reasons for 48 kHz for DAT), but I think the question was, in essence, why is it more than 40 kHz. The main criteria for choosing the sample rate was to be high enough to be twice the accepted range of human hearing, plus a “stop band” to give room for the reconstruction filter to roll off adequately, but still be as low as practical within those constraints (to maximize the recording time). The exact number of 44.1 kHz was chosen because it fit those constraints, and gave some potential initial advantage to converting video gear for CD manufacturing. But that is secondary and not critical. They had to decide on a number; that one was in the acceptable range, and had a potential benefit at the time.

        • darryl says:

          it could so easily have been any value twice that of 20khz to be in line with nyquist theorem, but as Dan says, it was born out of using video tape, when cd came along ‘there was no other practical way of storing digital sound than by a PCM Converter & video recorder combination.’
          http://en.wikipedia.org/wiki/PCM_adaptor

  2. Chris Clark says:

    Why 44.1kHz

    We were asked to answer this question for a client recently!

    http://www.cs.columbia.edu/~hgs/audio/44.1.html

    • Francis Hicks says:

      have a look at oversampling, thats why we sample over 40 KHz at 41.1 …. its because it helps to increase the resolution and digital reproduction of an analogue signal. over sampling reduces noise, increases the audio bandwidth. all of this means that when converting analogue to digital and back, the binary numbers when sampling each bit can do it more accurately. there fore representing the analogue wave in digital more accurately meaning higher quality. Im still learning as well so if this is wrong i apologise but i think its almost correct 🙂

  3. paul says:

    thank 4 helping a Nigerian student

  4. joe says:

    As I understand this, the point to take away about aliasing is: avoid it, as it will create distortion. So why don’t explanations of this give come right out w/that important info first, then the long-winded technical details? Am I not understanding this correctly?

  5. Samaga says:

    I have few request;
    1. can any one explain what is the meaning of high resolution audio when human being cant here more than 20kHZ? why 96khz, 192 khz?
    2. can any one provide complete windows based source including sample application for 3band parametric equalizer

    Thank you very much.
    regards,
    Samaga

    • Cybil says:

      Samantha, I can offer one reason to consider the high-frequency resolution, because it is correlated to the amount of aliasing the signal undergoes at initial digitization, and during further processing through the soundcard and the software in the process of editing.
      Aliasing introduces “wrong” frequencies (often very close to original frequencies present in the signal) into the usual range of human hearing, at the Nyquist frequency and below. Aliasing can sound like extra harmonic content in the mid-upper end of the signal’s frequency domain.
      If you see aliasing on a spectral graph you see that the more aliasing, the more each component of the signal (each partial or harmonic) tends to be “doubled” by a very close nearby “alias”. This is more a property of strongly harmonic signals (pitched instruments). This sound isn’t easily apparent. It is a measurable phenomenon, however.
      The doubling of frequencies is approximately the phenomenon called “folding”, which is what happens to analog frequencies above the system’s Nyquist when they get sampled by the system. They get folded.

    • Nigel Redmon says:

      For #2, you can search the web; for #1, there is much disagreement. Some claim to hear the difference, but I don’t know of any double-blind test that has shown that they can. Personally, I don’t use the higher sample rates, despite owning equipment capable of it.

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