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  1. Fundamentals of ... • Fundamentals • of • Digital • Audio

  2. Analog vs. Digital Analog vs. Digital Analog AMPLIFIER MICROPHONE SOUND PRESSUTRE WAVE SOUND PRESSUTRE WAVE VOLTAGE IN WIRE Digital DIGTAL TO ANALOG CONVERTER ANALOG TO DIGITAL CONVERTER COMUTER MEMORY AMPLIFIER

  3. Idealized Model... Idealized Model Sampling / Reconstruction smoothing filter (low-pass) zero- order hold g(nT) g(t) f(t) f(nT) g(t) f*(t) quantizer computer sampler A/D converter D/A converter Model of the sampling and desampling process

  4. Deconstruction of Sampling f(t) Deconstruction of Sampling f(t) analog (a) Graphic representation of types of signals: a) analog signal b) quantized (continuous time) signal c) sampled data signal d) digital signal quantized in amplitude (b) f*(t) quantized in time (c) f(nT) digital (d)

  5. Fidelity Fidelity • depends on: • sampling rate • bit depth • (encoding scheme)

  6. Sampling rate Sampling Rate Human hearing: 20-20,000 Hz Sampling Theorem: Must sample twice as high as highest component Typical rates: 8 K 11 K 22 K 44.1 K 48 K dark / dull bright / clean

  7. Fletcher & Munson Intensity 10-2 10-4 10-6 10-8 10-10 10-12 2 x 10 2 2 x 10-1 2 x 10-2 2 x 10-3 2 x 10-4 10-5 Watt/m2 Newton/m4 Fletcher & Munson

  8. Foldover in time domain Foldover in time domain Original signal Original signal Sampling pulse Sampling pulse Resultant Digitized Waveform Resultant Digitized Waveform

  9. Positive and negative Frequency Positive and Negative Frequency |H(f)| analog f -f 0 Nyquist frequency

  10. Digital Spectra Digital Spectra quantization in time |H(f)| digital 0 sampling rate SR Nyquist Frequency SR 2

  11. folderover in freq... foldover in frequency domain foldover sampling rate foldover frequency = 1/2 sampling rate

  12. quantization in amp. Quantization in Amplitude digital analog 4 3 2 1 0 -1 -2 -3 -4 error quantization levels

  13. distribution of error Distribution of Error 0 -1 1 maximum error of ± 1/2

  14. Computing S/N ideal Computing S/N “Ideal” 2N 1 dB = 20 log 2N-1 0.5 or 6 dB / bit

  15. Bit depth Example S/N Bit Depth Example S/N bits 2 4 8 12 16 24 dB 12 24 48 72 96 144 voice CD proaudio

  16. Dynamic range problem Dynamic Range Problem 16 bits 96 dB 24 dB 4 bits 4 bits 16 bits

  17. low-level signal problem Low-level Signal Problem intended result +2 +1 0 -1 -2 a folded Folding Frequency

  18. Dither Dither +2 +1 0 -1 -2 a f FF

  19. Signal reconstruction Signal Reconstruction a Reconstruction Filter f SR/2 SR Ideal reconstruction filter hasn’t been found

  20. Oversanpling Converters Oversampling Converters • Multibit oversampling • convert 44.1 K to • 176.4 K (4x) • 352.8 K (8x) • 1-bit oversampling • 1 bit at high rate • sigma-delta • MASH • 128 x 1-bit = • 8 * 16-bits

  21. Multibit Oversampling Multibit Oversampling a t a f 3 SR 2 SR 2 SR a f

  22. Actual Converters Actual Converters • Combine oversampling • first with 1-bit stream • second • Resulting noise lower • 4x 6dB • 8x 12dB • In computers ground isolation of • digital noise overwhelms everything else!