A PyDataGlobal 2020 talk focuses on digitizing and converting to spectra. A simple python module DEEPS shows the errors of signals having frequencies lower than Nyquist frequencies, which is verified on open datasets and indicates YouTube sounds are distorted.
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Basic Pitfalls in Waveform Analysis
1. Signal Frequency FSig, FSR, and FNyq
Summary
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Nyquist frequency FNyq:= 0.5FSR, Historical upper limit
FSR =16kHz
FSig
0.1 FSR
0.5 FSR=FNyq
0.9 FSR
November 15, 2020
2. Basic Pitfalls in Waveform Analysis
- Introduce DEEPS -
Yukio Okuda
sf.yukio@gmail.com
an independent, Atsugi, Japan
November 2020
3. Me = Industrial Soft Hard +40 Years Introduction
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Soft+Hard, 2 Years:
Mechanical Vibration of Mother Machines
4. Sensor Selection , Waveform Failure Analysis
Soft, 8 Years: OSS
Soft+Hard, 15 Years: Digital LSI Testing and Failure
Analysis
5. based on Data Analysis IEEE-ITC Papers
Soft, 17 Years: Developing LSI Design CAD tools
Soft, 6 Years: Developing Information Retrieval
Hard, 3 Years: Color TV Production
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
6. Outline Introduction
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Digitizing Error at lower than Nyquist Frequency FNyq
Digitize
(interpolate)
No-Repeatability
Pseudo Amplitude Modulation AM
FNyq
DCASE-2
DCASE-4
• Models
• Error signatures
Verified by DEEPS
Digitize Error Estimation (Prediction) by (Spectrum)
Improve
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
8. ADC: Analog to Digital Converter
ADC
No error
Extractor
Feature
Analysis
Digitizing
Time
Time
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
9. Outline of Models Models
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Show errors at lower than Nyquist Frequency
Rarely reported
Improving applications is the next stage
– Low Sampling Rate
— # of Signal Repeats
Systematic Error
Shape Spectrum
Random Error
DEEPS
˜ Clock Skew
Show errors
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
10. What is ADC Models
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Sampling at the predefined intervals of TS
11. Sampling Rate FSR := 1/TS
ADC = Sampling
Distortions at high frequency
Deterministic error ¬ Repeatable
Start time is uncontrollable
Random error ¬ No-Repeatable
18. Un-Controllable Start Time Models
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Errors between measurements in a measurement
Errors depend on FSig ? Robustness
ADC
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
19. Estimate Error Variance caused by Start Time Variance Models
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At a Start Time variance of Clock offsets Co=[0, 0.3, 0.6]
Repeat number NR= 4, FSig= 6.1kHz, ∆ FSp := FSp− FSig
Wave
FFT
Spectrum
FSp
Estimation
∆ FSp
Amp.:Summarize,Normalize
Freq.:∆from6.1kHz
Heat Map
∆ FSp
6.1kHz
∆FSp
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
20. Compare Error Variances of FSigs at NR= 4 Models
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Clock offsets Co= 0, 0.1, 0.2, .., 0.9 Assume random uniform
FSig= 6, 6.1, 6.2, .., 7.5 kHz, NR= 4
FSig
– —
∆FSp
– 6.4kHz shows the own frequency
— 7.1kHz shows the own frequency
Others show:
Different one frequency
Different two or three frequencies
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
21. Compare Error Variances of FSigs at NR= 8 Models
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Clock offsets Co= 0, 0.1, 0.2, .., 0.9 Assume random uniform
FSig= 6, 6.1, 6.2, .., 7.5 kHz, NR= 8
FSig
– —˜
∆FSp
– 6.4kHz shows the own frequency
Same as at NR= 4
— 7.1kHz shows the own frequency
Same as at NR= 4
˜ 6.1kHz shows the own frequency
Three frequencies at NR= 4
Others show two or three frequencies
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
22. A Magic Signal of 6.4 kHz Models
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Differently distorted waves yield a FSp of 6.4 kHz!
NR= 4
FFT
Spectrum
NR= 8
FFT
Spectrum
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
23. Summary of Models Models
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DEEPS estimates error signatures at a FSR of 16 kHz
Signals higher than 4 kHz are distorted
No error signatures
Except, the Signals of 6.4 kHz, 7.1 kHz
• Show the FSp of the FSig
• Signals of 7.1 kHz show AM modulation waves
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
24. Outline of Verification Verification
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A/B Testing is difficult for an independent
Challenge post-mortem analysis on DCASE Challenge Datasets
25. DCASE: Detection Classification of Acoustic Scenes Events
Task2 ĸ
• Obtained by the one tool Statistical analysis of spectra
• 13,000 nominal sounds
• 10 sec • FSR= 16 kHz • four device types
Task4 ĸ
• From Used by several Voice Recognition Activities
• 12,000 unlabeled sounds, non-controllable measurements
• 10 sec • FSR= 16 kHz, 44.1 kHz
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
26. Averaged Spectra of Task2 Verification
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Compare tails of spectra from 4kHz
– All 6.4kHz peaks — Slider/Valve 7.1kHz peaks
– –
–
–
—
—
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
27. How to locate error signals Verification
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Apply Low-Pass Filter-Bank
Spectrum has no time information, i.e. Non-temporal
Reversed signals show the same spectra
FFT
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
28. Task2 Ex1: 6.4kHz Verification
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Spectrum peaks around 6.4 kHz
Ex1: slider/train/normal id 06 00000075
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
29. Task2 Ex1: 7.1kHz Verification
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Spectrum peaks around 7.1 kHz
Ex1: slider/train/normal id 06 00000075
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
30. Spectrum Endpoints of Task4 Verification
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All sounds may include distortions
– 70% sounds are digitized by FSR=16 kHz, upconverted to 44.1 kHz
— 30% sounds are digitized by FSR=44.1 kHz
–
–
—
—
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
31. AM Signatures at a FSR of 44.1 kHz Verification
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Peak count (2, 3, 4, 5) identifies AM signatures FSig
19.9 kHz
— ˜ ™ š
˜ ™ ˜ ˜ ˜ ˜
— ˜
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
32. Summary of Verification Verification
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Demonstrated
1 Digitizing error at lower than FNyq
2 DEEPS estimations
3 sounds include distortions
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
33. Discussion for Improvements Discussion
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Application policies set Max FSig Max Error
Feature error predictions set FSR
ADC + Waves
Waveform Variations
Controllable
Non-Controllable
Max FSig
Max Error
FSR
Correct
Feature Extraction
Error Prediction
FFT Statistics
Time Series
Wavelet Cepstrum
Human Ear Eq.
. . .
DA
DataAnalysis
Appli.
Science
Medical
Industry
Home
. . .
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
34. Feature Error Predictions by DEEPS Discussion
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Feature extractor decide error from waveform variations
Wave Gen Drive Extractor
Features
FSig-N
Wave Gen Drive Extractor
Features
FSig-1
Sum
Indicator
FSig
Already FFT with spectrum
Challenging predictions: • Characteristics of waves
• References to Metrics • Parameters • Window size • FSig
dependancy • . . .
May be effective on non-controllable systems
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
36. Error Metrics for FFT: FSp
Discussion
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Ghost FSp, FSig of 4.2, 4.3, 4.4 kHz show FSp of 4.0, 4.3, 4.6 kHz
Co= 0, 0.1, 0.2, .., 0.9, FSig= 1, 1.1, .. 7.9, NR= 4
FSig
FSp
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
37. Aliasing Drops at near FNyq
Discussion
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Unremovable error signals ¬ Reject FSig ≥ FNyq by H/W filters
Co= 0, 0.1, 0.2, .., 0.9, FSig= 8.0, 8.5, 15.5, NR= 20
FSig
FSp
FNyq
Drops
FSp
Spectrum
Task2-Ex1
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
38. Waves are Noises or Signals Discussion
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Amplitude Ratio RAmp := AmpFSig
/Amp
Task2-Ex1, high pass filter of 7kHz ¬ Highly destorted signals
Amplitude
absRAmp
Time Time
Spectrum is a poor indicator of waveform amplitudes
Waves with different amplitudes show the same spectrum amplitude
FFT
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
39. Basic H/W Requirements Discussion
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MUST-1 Reject FSig ≥ FNyq by
– Mics or — Low-pass filters(LPFs)
MUST-2 Apply ADCs with enough high FSR
Option Reject FSig Max-FSig If need
– Mics or ™ digital LPFs, Not˜LPFs
MaxFSig
–
Low-Pass Filter
MaxFSig
—˜
ADC Low-Pass Filter
™
MaxFSig
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
40. Low-Pass Filter Distortions Discussion
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Phase Shifts of analogue low-pass filter(LPF) cause
distortions
Phase Shifts depend on Circuit Frequency
By Brews ohare ĸ
FFT ¬ Spectrum + Phase
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
41. Audio Recording Discussion
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Low FSR standard
1982 CD(Compact Disc) FSR= 44.1 kHz ¬ Challenging at ’80
• Poor Human Hearing, Ear Frequency Curve
1984 PC-AT Intel 80286 clock= 6, 8 MHz
2003 Pro audio standard AES3: 88.2, 96, 176.4, 192 kHz
Mics of up to 20kHz ¬ 90% FNyq of FSR= 44.1 kHz
Ear Frequency Curve ¬ Voice recognition unique features
EarGain
FSigɀ ĸ
Pre-emphasis
Gammatone
Spectrograms
Cepstrum
Mel Spectrogram
MFCCs
Chroma
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
42. Conclusion 33/ 34
DEEPS demonstrated
Existence of digitizing error at lower than FNyq
sounds include distortions
Indicated
Apply FSRs obtained from
Max FSig Max Error Feature error predictions
Check Audio recording for Data Analysis
Y. Okuda Basic Pitfalls in Waveform Analysis PyData Global 2020 talk-38
43. Thank you, the supporting staffs of
DCASE, PyData Global,
Your
Questions Comments