fundamentals of...fundamentals of... fundamentals of digital audio

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  • Fundamentals of ...Fundamentalsof

    Digital Audio

  • Analog vs. DigitalAnalogDigitalAMPLIFIERSOUND PRESSUTRE WAVEMICROPHONESOUND PRESSUTRE WAVEVOLTAGE IN WIREANALOG TO DIGITAL CONVERTERCOMUTERMEMORYDIGTAL TO ANALOG CONVERTERAMPLIFIERAnalog vs. Digital

  • Idealized ModelSampling / Reconstructionf(t)f*(t)quantizerf(nT)computerg(nT)zero-orderholdg(t)smoothingfilter(low-pass)g(t)A/D converterD/A convertersamplerModel of the sampling and desampling processIdealized Model...

  • Deconstruction of SamplingDeconstruction of Samplingf(t)analog(a)quantized inamplitude(b)(c)quantized intimef*(t)f(nT)(d)digitalGraphic representation of types of signals:

    a) analog signal

    b) quantized (continuous time) signal

    c) sampled data signal

    d) digital signal

  • FidelityFidelitydepends on:

    sampling rate

    bit depth

    (encoding scheme)

  • Sampling rateSampling RateHuman hearing: 20-20,000 HzSampling Theorem:

    Must sample twice as high as highest componentTypical rates:8 K11 K22 K44.1 K48 Kdark / dullbright / clean

  • Intensity

    10-2

    10-4

    10-6

    10-8

    10-10

    10-122 x 10

    2

    2 x 10-1

    2 x 10-2

    2 x 10-3

    2 x 10-4

    10-5Watt/m2Newton/m4Fletcher & MunsonFletcher & Munson

  • Foldover in time domainOriginalsignalOriginalsignalSampling pulseSampling pulseResultantDigitizedWaveformResultantDigitizedWaveformFoldover in time domain

  • Positive and negative FrequencyPositive and Negative Frequencyanalog|H(f)|f-f0Nyquist frequency

  • Digital Spectraquantization in time0

    |H(f)|digitalsampling rateSRNyquist FrequencySR2Digital Spectra

  • folderover in freq...foldoversampling ratefoldover frequency =1/2 sampling ratefoldover in frequencydomain

  • quantization in amp.4

    3

    2

    1

    0

    -1

    -2

    -3

    -4errorquantization levelsdigitalanalogQuantization in Amplitude

  • distribution of error0-11maximum errorof 1/2Distribution of Error

  • Computing S/N

    IdealdB = 20 log2N12N-10.5or6 dB / bitComputing S/N ideal

  • Bit DepthExample S/Nbits

    248121624dB

    1224487296144

    voice

    CDproaudioBit depth Example S/N

  • 96 dB24 dB16 bits16 bits4 bits4 bitsDynamic Range ProblemDynamic range problem

  • Low-level Signal Problem+2+10-1-2intendedresultFolding Frequencyfoldedalow-level signal problem

  • Dither+2+10-1-2FFafDither

  • Signal ReconstructionSR/2SRfaIdeal reconstruction filterhasnt been foundSignal reconstructionReconstruction Filter

  • Oversampling Converters Multibit oversamplingconvert 44.1 K to176.4 K (4x)352.8 K (8x)

    1-bit oversampling1 bit at high ratesigma-deltaMASH128 x 1-bit =8 * 16-bits

    Oversanpling Converters

  • Multibit OversamplingSR2SRfa3 SR2faatMultibit Oversampling

  • Actual Converters Combine oversamplingfirst with 1-bit streamsecond

    Resulting noise lower4x 6dB8x 12dB

    In computers ground isolation of digital noise overwhelms everything else!Actual Converters

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