1. Copyright 2004 Ken Greenebaum Introduction to Interactive Sound Synthesis Lecture 18:Noise Ken Greenebaum

2. Copyright 2004 Ken Greenebaum That sound What are we listening to? What are we listening to?

3. Copyright 2004 Ken Greenebaum Assignment 6 Any questions? Any questions? Understand: Understand: Sound file format? Sound file format? SustainIn/SustainOut? SustainIn/SustainOut? Everybody Everybody Comparing interpolation for extra credit? Comparing interpolation for extra credit?

4. Copyright 2004 Ken Greenebaum Noise Random numbers Random numbers

5. Copyright 2004 Ken Greenebaum Types of Noise White Noise White Noise Pink Noise Pink Noise Perlin Noise Perlin Noise

6. Copyright 2004 Ken Greenebaum White Noise Every Frequency in human hearing Every Frequency in human hearing 20Hz – 20kHz 20Hz – 20kHz Equal Energy in each Frequency Equal Energy in each Frequency Perceived as having more high Frequency energy Perceived as having more high Frequency energy Each successive octave has twice the frequencies Each successive octave has twice the frequencies 100 Hz – 200 Hz have 100 discrete frequencies 100 Hz – 200 Hz have 100 discrete frequencies 200 Hz – 400 Hz have 200 discrete frequencies 200 Hz – 400 Hz have 200 discrete frequencies

7. Copyright 2004 Ken Greenebaum White Noise Why is it called White? Why is it called White?

8. Copyright 2004 Ken Greenebaum White Light White Light White Light Contains all perceptible frequencies of light Contains all perceptible frequencies of light Each frequency has equal energy Each frequency has equal energy Then how can the RGB monitor produce white? Then how can the RGB monitor produce white?

9. Copyright 2004 Ken Greenebaum White Noise Johnson Noise Johnson Noise Sound of turbulent noise: Sound of turbulent noise: Lots of fans, People talking, etc. Lots of fans, People talking, etc. Not necessarily unpleasant Not necessarily unpleasant Useful for masking unwanted sounds Useful for masking unwanted sounds This is the dither we apply to ‘hide’ quantization noise This is the dither we apply to ‘hide’ quantization noise

10. Copyright 2004 Ken Greenebaum Pink Noise Also called 1/f noise Also called 1/f noise Equal Energy per octave Equal Energy per octave Logarithmic amplitude Logarithmic amplitude Power reduced by 3db (half) per octave Power reduced by 3db (half) per octave (Equalized for human perception) (Equalized for human perception) Why is it called Pink? Why is it called Pink?

11. Copyright 2004 Ken Greenebaum Pink Noise Most common sound in nature? Most common sound in nature? Waves, Wind Waves, Wind Used for measuring the response of audio gear Used for measuring the response of audio gear

12. Copyright 2004 Ken Greenebaum Less common noise colors Brown noise Brown noise Simulated Brownian motion Simulated Brownian motion -6dB/Octave reduction -6dB/Octave reduction Purple noise Purple noise +6dB/Octave increase +6dB/Octave increase

13. Copyright 2004 Ken Greenebaum Synthesizing White Noise (Pseudo) Random Number Generator (Pseudo) Random Number Generator Usually implemented as: Usually implemented as: long shift registers long shift registers Feedback involving exclusive or Feedback involving exclusive or Accept a seed Accept a seed Produce long string of values Produce long string of values (same seed, same values) (same seed, same values)

14. Copyright 2004 Ken Greenebaum Linear Congruential Generator // Generator x[n+1] = a * x[n] mod m double random () { static unsigned int a=1588635695, static unsigned int a=1588635695, m=4294967291U, q=2, r=1117695901; m=4294967291U, q=2, r=1117695901; SEED = a*(SEED % q)-r*(SEED / q); SEED = a*(SEED % q)-r*(SEED / q); return ((double)SEED / (double)m); }

15. Copyright 2004 Ken Greenebaum Random Number Generation See Knuth for details! See Knuth for details!

16. Copyright 2004 Ken Greenebaum Synthesizing Pink Noise Theoretically can filter White noise Theoretically can filter White noise Unfortunately we don’t know how to construct the correct filter! Unfortunately we don’t know how to construct the correct filter!

17. Copyright 2004 Ken Greenebaum Synthesizing Pink Noise Solutions Solutions In Analog Domain In Analog Domain A bank of parallel filters are used A bank of parallel filters are used Digitally Digitally Apply ‘pinking’ filters to white noise Apply ‘pinking’ filters to white noise Add a series of white noise Add a series of white noise

18. Copyright 2004 Ken Greenebaum Weighted sum of low pass filters white=rand(); buf0=0.997 * buf0 + 0.029591 * white; buf1=0.985 * buf1 + 0.032534 * white; buf2=0.950 * buf2 + 0.048056 * white; buf3=0.850 * buf3 + 0.090579 * white; buf4=0.620 * buf4 + 0.108990 * white; buf5=0.250 * buf5 + 0.255784 * white; pink=buf0 + buf1 + buf2 + buf3 + buf4 + buf5;

19. Copyright 2004 Ken Greenebaum Sample and hold Add together a series of sample and hold values Add together a series of sample and hold values Frequencies related by a factor of two: Frequencies related by a factor of two: High Quality Random Number + Hold Random Number 2 samples + Hold Random Number 4 samples + Hold Random Number 8 samples…

20. Copyright 2004 Ken Greenebaum 1/f synthesizers Optimized solutions exist Optimized solutions exist Gardener Method Gardener Method Voss Method Voss Method

21. Copyright 2004 Ken Greenebaum Really a family of noises:

22. Copyright 2004 Ken Greenebaum Perlin Noise Noise: Noise: Continuous interpolated fn: Continuous interpolated fn:

23. Copyright 2004 Ken Greenebaum Sum of noise = rich noise

24. Copyright 2004 Ken Greenebaum Readings Audio Anecdotes Volume 2 Audio Anecdotes Volume 2 Infinite Impulse Response Filters Infinite Impulse Response Filters Finite Impulse Response Filters Finite Impulse Response Filters

25. Copyright 2004 Ken Greenebaum Next Class Assignment 6 Due! Assignment 6 Due! Subtractive Synthesis Subtractive Synthesis