View stunning SlideShares in full-screen with the new iOS app!Introducing SlideShare for AndroidExplore all your favorite topics in the SlideShare appGet the SlideShare app to Save for Later — even offline
View stunning SlideShares in full-screen with the new Android app!View stunning SlideShares in full-screen with the new iOS app!
High fs: Large guard band, Allows varispeed Low fs: Reduces transmission and storage BW Critical Sampling: When a signal is sampled at exactly twice its highest frequency. Never done in audio
High fs: Large guard band, Allows varispeed Low fs: Reduces transmission and storage BW Critical Sampling: When a signal is sampled at exactly twice its highest frequency. Never done in audio
High fs: Large guard band, Allows varispeed Low fs: Reduces transmission and storage BW Critical Sampling: When a signal is sampled at exactly twice its highest frequency. Never done in audio
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.
http://www.youtube.com/watch?v=C8_6NRXfRVE
http://www.youtube.com/watch?v=C8_6NRXfRVE
giving a &#x2018;quantity&#x2019;
giving a &#x2018;quantity&#x2019;
giving a &#x2018;quantity&#x2019;
6dB of dynamic range per bit
6dB of dynamic range per bit
6dB of dynamic range per bit
6dB of dynamic range per bit
6dB of dynamic range per bit
Error is +/- 1/2 Q with a rectangular PDF (equal chance)
Error is +/- 1/2 Q with a rectangular PDF (equal chance)
Error is +/- 1/2 Q with a rectangular PDF (equal chance)
Error is +/- 1/2 Q with a rectangular PDF (equal chance)
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
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
encodes low-level signals via PWM ear averages PWM signal to resolve signal With dither, resolution is below least significant bit!
encodes low-level signals via PWM ear averages PWM signal to resolve signal With dither, resolution is below least significant bit!
Transcript
1.
MUSC 365
Basics of Digital Audio Module (revised)
7.
Digital = discrete
• time and amplitude are discrete
8.
Digital = discrete
• time and amplitude are discrete
• only certain values are allowed
9.
Continuous vs. Discrete
Continuous Discrete
All numbers (including fractions) Only integers
distance down my street number of houses on my street
time it takes to cook an egg number of eggs a chicken lays
volume of applesauce number of apples in a basket
11.
Sampling
• the process of making discrete time
12.
Sampling
• the process of making discrete time
• Amplitude of a waveform is captured (sampled) at regularly spaced
intervals
13.
Sampling
• the process of making discrete time
• Amplitude of a waveform is captured (sampled) at regularly spaced
intervals
• the rate of repeat of this regularly spaced interval is called the sample
rate
15.
Sampling Rate (ƒs)
• The sample rate determines the bandwidth of the system
16.
Sampling Rate (ƒs)
• The sample rate determines the bandwidth of the system
• A signal of bandwidth BW may be LOSSLESSLY sampled if the
sampling rate ƒs ≥ 2 • BW
17.
Sampling Rate (ƒs)
• The sample rate determines the bandwidth of the system
• A signal of bandwidth BW may be LOSSLESSLY sampled if the
sampling rate ƒs ≥ 2 • BW
• Input must be bandlimited to half the sampling rate
20.
Sampling Rate (ƒs)
• Common sample rates:
• 44.1kHz for audio only (CD, MP3, etc)
21.
Sampling Rate (ƒs)
• Common sample rates:
• 44.1kHz for audio only (CD, MP3, etc)
• 48kHz for video/ﬁlm (DVD, etc)
22.
Sampling Rate (ƒs)
• Common sample rates:
• 44.1kHz for audio only (CD, MP3, etc)
• 48kHz for video/ﬁlm (DVD, etc)
• double (2x) and quadruple (4x) those rates
38.
Sampling Process
• There is only waveform
that satisﬁes 2 conditions:
39.
Sampling Process
• There is only waveform
that satisﬁes 2 conditions:
• it passes thru all the
sample points, and
40.
Sampling Process
• There is only waveform
that satisﬁes 2 conditions:
• it passes thru all the
sample points, and
• it does not have
frequencies above ƒs / 2
42.
Aliasing
• Input signal must be bandlimited (frequencies above ƒs / 2 removed)
43.
Aliasing
• Input signal must be bandlimited (frequencies above ƒs / 2 removed)
• If it is not, frequencies above ƒs / 2 are folded back into audio band
44.
Aliasing
• Input signal must be bandlimited (frequencies above ƒs / 2 removed)
• If it is not, frequencies above ƒs / 2 are folded back into audio band
• This artifact is called aliasing
58.
Quantization
• the process of making discrete Amplitude
59.
Quantization
• the process of making discrete Amplitude
• the amplitude range is broken up into a ﬁxed number of level, also
called quantization intervals
60.
Quantization
• the process of making discrete Amplitude
• the amplitude range is broken up into a ﬁxed number of level, also
called quantization intervals
• amplitude is measured and assigned to the closest interval
69.
Quantization Process
• the smaller the intervals, the smaller the error will be
70.
Quantization Process
• the smaller the intervals, the smaller the error will be
• since the range (maximum to minimum) is ﬁxed,
71.
Quantization Process
• the smaller the intervals, the smaller the error will be
• since the range (maximum to minimum) is ﬁxed,
• more levels will mean smaller levels
73.
Quantization
• number of levels based on word length (number of bits per sample)
74.
Quantization
• number of levels based on word length (number of bits per sample)
• # of levels = 2 # of bits
75.
Quantization
• number of levels based on word length (number of bits per sample)
• # of levels = 2 # of bits
• Adding bit doubles the number of levels,
76.
Quantization
• number of levels based on word length (number of bits per sample)
• # of levels = 2 # of bits
• Adding bit doubles the number of levels,
• which cuts the error in half
77.
Quantization
• number of levels based on word length (number of bits per sample)
• # of levels = 2 # of bits
• Adding bit doubles the number of levels,
• which cuts the error in half
• reduces error by 6dB
88.
Incredible accuracy
• Imagine a stack of paper 22 feet high.
89.
Incredible accuracy
• Imagine a stack of paper 22 feet high.
• The thickness of a sheet of paper is the accuracy of a 16-bit
quantization interval!
90.
Incredible accuracy
• Imagine a stack of paper 22 feet high.
• The thickness of a sheet of paper is the accuracy of a 16-bit
quantization interval!
• Now imagine a stack of paper a mile high. The thickness of a sheet of
paper is the accuracy of a 24-bit quantization interval!
92.
Quantization Error
• Distortion power relative to number of intervals, independent of
amplitude of signal
93.
Quantization Error
• Distortion power relative to number of intervals, independent of
amplitude of signal
• Error changes perceptively with input level
94.
Quantization Error
• Distortion power relative to number of intervals, independent of
amplitude of signal
• Error changes perceptively with input level
• High level signal has un-correlated error (random noise)
95.
Quantization Error
• Distortion power relative to number of intervals, independent of
amplitude of signal
• Error changes perceptively with input level
• High level signal has un-correlated error (random noise)
• Low level signal has correlated error – distortion, not noise-like
107.
Analog vs. Digital Deterioration
• In Analog, noise steadily deteriorates the signal-to-noise ratio
108.
Analog vs. Digital Deterioration
• In Analog, noise steadily deteriorates the signal-to-noise ratio
• In Digital, audio quality is independent of transmission/storage quality
109.
Analog vs. Digital Deterioration
• In Analog, noise steadily deteriorates the signal-to-noise ratio
• In Digital, audio quality is independent of transmission/storage quality
• Until we reach a point of catastrophic failure, when the data can no
longer be received correctly
Thank you so much or this material :)
Views
Actions
Embeds 0
Report content
Proof in Couch pg. 90-91
Proof in Couch pg. 90-91
Proof in Couch pg. 90-91
Low fs: Reduces transmission and storage BW
Critical Sampling: When a signal is sampled at exactly twice its highest frequency. Never done in audio
Low fs: Reduces transmission and storage BW
Critical Sampling: When a signal is sampled at exactly twice its highest frequency. Never done in audio
Low fs: Reduces transmission and storage BW
Critical Sampling: When a signal is sampled at exactly twice its highest frequency. Never done in audio
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
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
ear averages PWM signal to resolve signal
With dither, resolution is below least significant bit!
ear averages PWM signal to resolve signal
With dither, resolution is below least significant bit!