Welcome to this video on digital audio aliasing.

As we have already learnt, Nyquist theory helps determine the minimum acceptable sample rate to ensure good analogue to digital audio conversion for the range of frequencies that humans can hear.

Aliasing is an unwanted audible side effect of an insufficient sample rate and occurs when the sample rate is less than that required by Nyquist theory.

Caption - Aliasing noise

The audible effects of aliasing include random noise or unpleasant and unwanted lower harmonics within the sound. These artifacts are known as Aliasing Noise. Aliasing noise become apparent when a digital signal is converted back to analogue by a DAC.

Caption - Complex sound waves

A complex sound wave, such as a piano recording or a completed music mix, will contain multiple harmonics at different frequencies spread across the audio spectrum. Nyquist theory dictates that the sample rate must be sufficient for the highest audible frequency harmonic in the sound wave, which for humans will be 20kHz.

Caption - Low frequency sound waves and harmonics

Consider a sound wave harmonic at 20Hz. There will be 20 cycles of its waveform every second. This means that if it is recorded at a sample rate of 44.1kHz, each cycle will be represented by 2,205 samples.

44,100 divided by 20 = 2,205

We can see that each cycle is measured comprehensively and the shape of the waveform is recorded accurately.

Caption - Hi frequency sound waves and harmonics

Now consider a sound wave harmonic at a high frequency of 20kHz. There will be 20,000 cycles of its waveform every second. This means each cycle will be represented by 2.205 samples.

44,100 divided by 20,000 = 2.205

So each cycle of a high frequency sound wave harmonic is measured barely enough times to retain its basic shape. It is adequate but not very accurate.

When the digital data is converted back into an an analogue electrical sound wave by a D to A converter at playback, there will be just enough information to re-create the original wave but not very accurately. Digital wave shaping filters are used to smooth the wave back into the best possible shape. The difference between the sampled and replayed signal is heard as distortion. As humans are less sensitive to high frequencies above 15kHz, for most people this distortion will be inaudible.

Caption - How does insufficient sample rate cause aliasing?

There is an effect in film making, caused by its fixed frame rate of 24 frames per second, that can lead to odd visible effects. The most common effect is that of a speeding car wheel appearing to revolve backwards. This happens because 24 frames per second is insufficient to capture fast motion.

Aliasing in digital audio produces the effect of a hi frequency harmonic being reconstructed as an unwanted lower one.

In a complex sound wave containing many harmonics, only the harmonics for which the sample rate is insufficient will be altered. Harmonics for which the sample rate is adequate will reproduced accurately.

Consider a sound wave harmonic at 20,000Hz being recorded at a sample rate of 32kHz. This would mean 1.5 samples per cycle of the waveform, clearly inadequate.

If we look at the sound wave harmonic reconstructed by a D to A converter we can see that the wave shape has changed dramatically into a lower frequency one, introducing aliasing noise into the complex sound wave.

Caption - Anti-aliasing filters

To prevent aliasing, analogue to digital converters pass the incoming signal through a low pass filter in order to remove any harmonics above the highest frequency that the sample rate can accommodate. Thus, an anti-aliasing filter in a A to D converter set at a 44.1kHz samaple rate will remove any harmonics above 20kHz. The design of these filters is critical for good sound quality.

Caption - Thanks for watching

The script for this video, with accompanying images, can be found at projectstudiohandbook.com 

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