THE SCOTTY WHO KNEW TOO MUCH

Transcription

1 A fable THE SCOTTY WHO KNEW TOO MUCH JAMES THURBER Several summers ago there was a Scotty who went to the country for a visit. He decided that all the farm dogs were cowards, because they were afraid of a certain animal that had a white stripe down its back. You are a pussycat and I can lick you, the Scotty said to the farm dog who lived in the house where the Scotty was visiting. I can lick the little animal with the white stripe too. Show him to me. Don t you want to ask any questions? Nah, said the Scotty. You ask the questions. So the farm dog took the Scotty into the woods and showed him the white-striped animal and the Scotty closed in on him, growling and slashing. It was all over in a moment and the Scotty lay on his back. When he came to, the farm dog said, What happened? He threw vitriol, * said the Scotty, but he never laid a glove on me. A few days later the farm dog told the Scotty there was another animal all the farm dogs were afraid of. * Vitriol is sulfuric acid, which also is used in car batteries. 1

2 Lead me to him, said the Scotty. I can lick anything that doesn t wear horseshoes. Don t you want to ask any questions about him said the farm dog. Nah, said the Scotty. Just show me where he hangs out. So the farm dog led him to the place in the woods and pointed out the little animal when he came along. A clown, said the Scotty, a pushover, and he closed in, leading with his left and exhibiting some mighty fancy footwork. In less than a second Scotty was flat on his back, and when he woke up the farm dog was pulling quills out of him. What happened? said the farm dog. He pulled a knife on me, said the Scotty, but at least I have learned how you fight out here in the country, and now I am going to beat you up. So he closed in on the farm dog, holding his nose with one front paw to ward off the vitriol and covering his eyes with the other front paw to keep out the knives. The Scotty couldn t see his opponent and he couldn t smell his opponent and he was so badly beaten that he had to be taken back to the city and put in a nursing home. Moral: It is better to ask some of the questions than to know all the answers. 2

3 Introduction to Audio and Music Engineering Lecture 23 Topics: From simple filters to echo and reverb Variable single tap FIR filter Variable single tap IIR filter Plucked string filters Karplus - Strong plucked string models Waveguide modeling of wind musical instruments 3

4 Revisit the simple FIR filter Y = X + a n z n X + input X output Y H (z) = 1 + a n z n n = 1 n sample a n 5 H (ω) = 1 + a n e jnω Magnitude Response (db) Pole/Zero Plot Real Part Normalized Frequency ( π rad/sample) 4

5 The FIR filter Y = X + a n z n X + input X output Y H (z) = 1 + a n z n n sample a n H (ω) = 1 + a n e jnω n = 6 Pole/Zero Plot 5 Magnitude Response (db) Real Part Normalized Frequency ( π rad/sample) 5

6 The FIR filter Y = X + a n z n X + input X output Y H (z) = 1 + a n z n n sample a n H (ω) = 1 + a n e jnω n = 1 5 Magnitude Response (db) Pole/Zero Plot Real Part Normalized Frequency ( π rad/sample) 6

7 Revisit the simple IIR filter input X + output Y Y = X + b n z n Y H (z) = ( 1 + b n z n ) 1 b 1 Z -1 H (ω) = ( 1 + b n e jnω ) 1 n = 1 Pole/Zero Plot 14 Magnitude Response (db) Real Part Normalized Frequency ( π rad/sample) 7

8 IIR filter input X + output Y Y = X + b n z n Y H (z) = ( 1 + b n z n ) 1 n = 1 b 1 Pole/Zero Plot Z H (ω) = ( 1 + b n e jnω ) 1 Magnitude Response (db) Real Part Normalized Frequency ( π rad/sample) 8

9 Plucked string simulation Pluck the string Makes high harmonics decay faster Fine tune the frequency Karplus Strong Model Makes string decay Delay sets the frequency 9

10 Musical Instrument Physical Modeling Combine filters and lines, plus a model of the excitation mechanism, to generate musical instruments sounds by simulating the physics of the instrument. Clarinet Physical Model Reed Bore Bell Blowing pressure Nonlinear valve Digital Delay Line Digital Delay Line Cross-over network Output sound (physical modeling is used widely in commercial synthesizers, e.g., Yamaha VL 7M) 1

11 Clarinet Physics P p End View Greater Embouchure Force Reed begins to close Embouchure Force flow bias region reed Pressure Impulse bell Blowing P - internal p P - p Each time the pressure increases in the mouthpiece the reed opens and lets in more air positive feedback. 11

12 Clarinet Waveguide Model Blowing Pressure p + (n) Unit Unit Unit Output Filter (HP) Nonlinear Scattering Junction + p(n) Bi-directional line Reflection Filter (LP) Unit Unit Unit p - (n) Reed Bore Bell 12

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14 Using Physical Models to encode musical performances Simple Waveguide Model Maximum Likelihood Estimation Estimate parameters ~ 45/sec Compress ~ 1x Orig Sound Mb/min Greater Embouchure Force Lesser Embouchure Force Extracted Parameters -.1 Mb/min 12 flow "a - red" "d - blue" Blowing P - internal p Time (samples) 14

15 Original Resynthesized 15

16 Even more compact Employ measured acoustic parameters of a clarinet to begin with a more accurate model. 1 time varying parameter 2/sec (16 bits/sec) Compress ~ 7 x Original Resynthesized 16

17 Current Results Analysis Re-synthesis Uncompressed Audio 1X Music 1X Parameter Estimation Physical Model 7X PM Parameters History Physical Modeling Music Representation 7 x smaller Continuing Work Physical Model Music Refine models: include tonguing, vocal tract, exciter (reed, lips) dynamics Extend to other wind, bowed, plucked instruments Encode recordings of multiple instruments Source separation Wav MP3 Synthetic PM Empirical PM 17