tags: music mus-407 signal-processing sampling

Aliasing

Aliasing (or foldover) is the phenomenon where frequencies greater than the [Nyquist Frequency] $N$ are still digitally represented within the range $[0, N]$.

• input [frequency] will "reflect" off of zero and $N$ if boundary is exceeded
• similar to "negative frequencies" in [modulation synthesis]

Imagine a [sampled] analog input with [spectral] content above $N$.

• Foldover occurs as the [waveform] is sampled
• Results in unnecessary and/or unwanted interference (either constructive or destructive)
• Alias frequencies interfere/sum with sub-$N$ frequencies, altering the spectrum

ADC/DAC Conversion Process

An ADC includes an [anti-alias filter], which removes analog frequency components that would cause aliasing.

A DAC includes a smoothing filter.

• reconstruction of an analog signal from raw digital data results in [waveform] discontinuities ("staircase" shape)
• without smoothing, these artifacts produce audible high frequency content

Both classify as [low-pass filter] whose [cutoff frequency] is at or near the [Nyquist Frequency].

Aliasing in general does not exist just in audio, but in anything digital.

• think: pixels on a screen
• in this case, resolution of a digital image is similar to sample rate of digital audio