8. Critical sampling
• When a signal is sampled at exactly twice its highest frequency
• Never done in audio
9. Sampling Rate
• High
• Large guard band
• Allows varispeed
• Low
• Reduce transmission and storage BW
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. 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. 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.
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
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. 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. 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. 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. 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. 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. Distortion, not noise
• Peak to peak = ±1/2 Quantization interval (Q)
• An ideal quantizer is by definition non-linear and will cause
distortion!!
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
26. Metering
• 0dBFS (reference is when all codes are being used – Full Scale)
• Overload
• Output is at full scale for many consecutive samples
27. Dither
• Noise added to the signal to de-correlate the signal from the
quantizer
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!
30. ADC Process
• Analog-to-Digital conversion
• Anti-alias filter
• sample & hold
• quantizer (with Dither)
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. Oversampling
• gentle analog anti-alias filter
• High Fs
• Digital filter (anti-alias) and downsample
• Digital filter easier than analog
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
