Digital Audio

Nyquist theorem

1.For periodic functions, if you sample at a rate that is at least twice as fast as the signal of interest, then no information (data) will be lost upon reconstruction.

2.If you restrict the input signal's bandwidth to less than one-half the sampling frequency, then no errors due to aliasing are possible.

my defintion

The Nyquist Theorem explains when turning a sound wave into digital audio, if you sample fast enough you will not lose information. For every periodic functions, if you sample at a rate that is at least twice as fast as the signal, then no information or data will be lost when it is reconstructed into digital. You must sample at least 2x the highest audio frequency, so then the digital system gets enough "snapshots" to recreate the original wave accurately. If it's slower than that, the system does not construct the acoustic waveform accurately and this is called aliasing. 

what does sampling rate determine

The sampling rate deteremines frequency response of a digital audio signal

what does the number of bits determine

The number of bits determine the dynamic range of a digital audio signal

Dither

Dither is a small amount of noise that is added to audio at the least significant bit. It is necessary because it prevents quantization distortion. With this added noise, it linearizes the quantization process and greatly reduces distortion. When audio has a lower bit depth, the system has fewer vertical steps to go off of and it is forced to round values that can create repeating quantization errors that create distortion. Dither does not get rid of quantization error, but it allows the digital system to encode amplitudes smaller than the least significant bit.  So by adding dither, those rounded errors are randomized so the distortion is so soft we can not hear it.  

dither konrad

Dither is noise added at the level of the least significant bit. it is necessary to reduce quantization noise. It works by decorrelating the quantization noise from the audio signal which transforms it from a harsh modulated distortion to a more noise-like signal. The noise in the signal slightly randomizes the amplitude levels of the original signal, thereby removing the distortion and actually retaining very low signal levels which otherwise would be quantized as pure silence.

Dither Simple terms

Noise added at the level of the least significant bit to eliminate quantization noise and decorrelate it from the signal. It slightly randomizes the amplitude levels of the original signal which removes the distortion. It can increase dynamic range by 2 - 3 bits.

bit calculation

dB/ 6 (6 dB per bit)

dynamic range of a 16 bit system

96.33 dB/16 bits = 6.02 dB per bit

What are the advantages of oversampling in digital audio?

The corner frequency of the anti-alias filter is moved above 20 kHz and Quantization noise is reduced in the audio range

dBFS scale

dBFS refers to decibels in reference to full scale. It is a measure of amplitude levels in digital systems where 0 dBFS equals the maximum possible level. Above 0 it will clip. The rest of the numbers are negative values.

nominal operating level

Nominal operating level is 20 dB below full scale, or -20 dBFS

Sampling

When a digital audio system takes regular snapshots of the sound over time; Sampling rate determines how high of frequencies you can record

Quantization

Process of mapping continuous infinite values to a smaller set of discrete finite values. Each sample’s amplitude is rounded to the nearest digital value. Bit depth determines dynamic range and accuracy of those loudness values

Aliasing

'Phantom' frequencies created when a signal above half the sample rate is allowed into, or created within, a digital system. The frame rate is too low for frequencies and the waveform recorded does not accurately represent the acoustic waveform

Quantization distortion

The difference between the actual voltage and the quantized voltage. The signal is softer than the least significant bit so it can’t be digitized and instead distortion is created.