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# 365 digital basics before

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• (Pohlmann pg. 27)
Proof in Couch pg. 90-91

• Pohlmann pg. 35

• ### 365 digital basics before

1. 1. MUSC 365 Basics of Digital Audio Module (original)
2. 2. Analog = continuous • continuous time and amplitude
3. 3. Digital = discrete • is discrete time and amplitude
4. 4. Sampling Theory
5. 5. Sampling • making discrete Time • A signal of bandwidth BW may be LOSSLESSLY sampled if the sampling rate Fs >= 2BW
6. 6. Sampling • Amplitude is held (sampled) only at certain times • Input must be bandlimited to half the sampling rate
7. 7. Nyquist Frequency • half the sampling frequency • Fs/2
8. 8. Critical sampling • When a signal is sampled at exactly twice its highest frequency • Never done in audio
9. 9. Sampling Rate • High • Large guard band • Allows varispeed • Low • Reduce transmission and storage BW
10. 10. Sampling • A band limited waveform amplitude modulates an impulse train. • The spectrum of an impulse train is sinewaves @ multiples of Fs • Modulated spectrum is waveform spectrum (bandlimited) repeated around multiples of Fs (with upper and lower sidebands) • If impulses have some width, then the total spectrum is superimposed with the |Sin (x)/x| curve
11. 11. Aliasing • Input signal must be bandlimited • If it is not, sampling will cause the ﬁrst lower sideband to fold back into the signal • Inputs frequencies above Fs/2 are folded back into audio band • Wagon wheel analogy in ﬁlm • A 7 kHz wave sampled @ 10kHz looks just like a 3 kHz wave
12. 12. Sample & Hold • Must acquire analog input amplitude at sample time and hold it long enough for it to be quantized • Sampled analog waveform has greater bandwidth than original input. This is inefﬁcient, so amplitude is Quantized and Coded.
13. 13. Encoding/Modulation
14. 14. Pulse Code Modulation (PCM) • Binary Code is transmitted
15. 15. Quantization • making discrete Amplitude • Peak S/E(dB) = 6.02n + 1.76 • 1.76 factor based on sinusoidal input • Adding bit increases S/N by 6dB • Number of bits determines resolution
16. 16. Dynamic Range • 8 bits = 28 = 256 = 48dB • 12 bits = 212 = 4,096 = 72dB • 16 bits = 216 = 65,536 = 96dB • 20 bits = 220 = 1,048,576 = 120dB • 24 bits = 224 = 16,777,216 = 144dB
17. 17. Dynamic Range • S/E power ratio increases exponentially with data bandwidth • (one additional bit is double the accuracy) • assumes equal distribution (large signal)
18. 18. Incredible accuracy • Image a stack of paper 22 feet high. The thickness of a sheet of paper is the accuracy of a 16bit quantization interval! • Image a stack of paper a mile high. The thickness of a sheet of paper is the accuracy of a 24bit quantization interval!
19. 19. Quantization Error • Distortion power relative to number of intervals, independent of amplitude of signal • No input, no error • Perceptively changes with input type and level • Error is +/- 1/2 Q with a rectangular PDF (equal chance) • High level signal has un-correlated error
20. 20. Types of error • Overload Noise (If input > MSB) • Over lights on equipment • Random Noise (large input) • White noise (rectangular, not Gaussian p.d.f), masked by signal • Granulation distortion (Very low level input)
21. 21. Quantization Error • Quantization noise is not random, but based on signal. • Distortion produces harmonics which can alias • Multiple input freq. can cause intermodulation distortion • Quantization error can create Aliasing (frequencies not present in source) even though it occurs after the sample process
22. 22. Idle channel Noise/Hunting noise • Input signal below LSB, but low freq. information (rumble) moves it across quantizing intervals, the signal (and noise) will come and go
23. 23. Distortion, not noise • Peak to peak = ±1/2 Quantization interval (Q) • An ideal quantizer is by deﬁnition non-linear and will cause distortion!!
24. 24. Quantizing • Held amplitude is measured and assigned the closest number • 2n steps, where n = number of bits • approximately 6dB of dynamic range per bit
25. 25. Transmission • AES/EBU • S/PDIF • TDIF
26. 26. Metering • 0dBFS (reference is when all codes are being used – Full Scale) • Overload • Output is at full scale for many consecutive samples
27. 27. Dither • Noise added to the signal to de-correlate the signal from the quantizer
28. 28. Pro • Randomizes granulation distortion, changing it to white noise • encodes low-level signals via PWM • ear averages PWM signal to resolve signal • With dither, resolution is below least signiﬁcant bit!
29. 29. Con • Raises noise ﬂoor slightly
30. 30. ADC Process • Analog-to-Digital conversion • Anti-alias ﬁlter • sample & hold • quantizer (with Dither)
31. 31. Oversampling • to ease the requirements • of the anti-alias ﬁlter and • the accuracy of the quantizer • we trade amplitude accuracy for time accuracy • sample crude, but fast
32. 32. Oversampling • gentle analog anti-alias ﬁlter • High Fs • Digital ﬁlter (anti-alias) and downsample • Digital ﬁlter easier than analog
33. 33. Dynamic Range • S/N = 6.02(#of bits + 0.5* #of octaves oversampling) + 1.76
34. 34. Analog vs. Digital Deterioration • In Analog, noise steadily deteriorates the signal-to-noise ratio • In Digital, we reach a point of catastrophic failure, when the data can no longer be received correctly
35. 35. Analog vs. Digital Deterioration