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Manipulating Audio

Manipulating Audio

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Why Digital AudioWhy Digital Audio

Analogue electronics are always prone to noise

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The Digital DomainThe Digital Domain

Based on numbersDigital representation of analogue

signal:

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Digital ElectronicsDigital Electronics

Less expensive to designLess expensive to manufactureOffer high noise immunityAge immunityTemperature immunity Increased reliability

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The Digital DomainThe Digital Domain

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0 s

6.3 7.2 6.4 4.8 3.2 1.9 1.3 2.2

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0 6 7 6 5 3 2 1 2

s

Analogue signal

6, 7, 6, 5, 3, 2, 1, 2

Digital stream

Digital waveform

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NyquistNyquist

The highest frequency which can be accurately represented is one-half of the sampling rate CD: Sample Rate =

44,100 HzNyquist Frequency =

SR/2 = 22,050 Hz

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AliasingAliasing

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AliasingAliasing

Bach trumpet

SR=22050 - highest frequency in music is about 7000 Hz (no aliasing)

SR=11025 - (some aliasing; adds a little dullness and a metallic quality)

SR=4410 - (lots of aliasing; sounds like bad video game)

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Low Pass FilteringLow Pass Filtering

The original signal must be low-pass filtered to remove signals higher than 0.5 of the sampling rate

CD: SR = 44,100Hz thus original signal must not exceed 22,050Hz to be completely sampled

Low-pass filtering avoids frequency fold-over

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FiltersFilters

low-pass filter band-pass filter high-pass filter

White noise (unfiltered)Filtered white noise (low pass, band pass, high pass)

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FiltersFilters

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OversamplingOversampling

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Sampling realitySampling reality

Critical sampling is not attempted

Lowpass filters can not attenuate the signal precisely at the Nyquist frequencyDVD audio – 96 KHz?CD – 44.1KHzTelephone – 8KHz

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QuantizationQuantization

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0 s

6.3 7.2 6.4 4.8 3.2 1.9 1.3 2.2

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0 6 7 6 5 3 2 1 2

s

Analogue signal

6, 7, 6, 5, 3, 2, 1, 2

Digital stream

Digital waveform

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QuantizationQuantization

The number of quantization levels (N) is dependant on binary word length

N = 2n

n = number of bits• 28 = 256• 216 = 65536 (CD)• 224 = 16777216 (DVD)

The more bits the better the approximation

Worst error is 0.5 LSB

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Quantization ErrorQuantization Error

Difference between the actual analogue value and the selected quantization interval value

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DitheringDithering

A small amount of noise that is uncorrelated with the input signal is added

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DitheringDithering

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DitheringDithering

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A to D Principal elementsA to D Principal elements

MultiplexerProcessing

(error correction)

Dither generator

Sample and Hold

Anti-aliasing

filter

A to D Converter

Sample and Hold

Anti-aliasing

filter

A to D Converter

Analogue input (L)

Analogue input (R)

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SummarySummary

Sampling and Quantization are the two fundamental criteria for a digitisation system

Aliasing occurs when sampling theory is not observed

Sampling is losslessQuantisation is lossyDither can substantially reduce

quantization distortion

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FinFin

Fin