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This Classroom 77 BMW at 80 MPH 94 Blender at 3 110 Rock Concert (OSHA limits workers to 30 minutes) 120 Loud thunder, Jackhammer at 3 (discomfort) 140 Jet on takeoff at 100 JP0PP0'Understanding the decibel:We will review the highlights Questions from the reading? ;;@*Understanding the decibelDecibel is a ratio: Hence is dimensionless! Is logarithmic Recall: y = log10(x) is equivalent to 10y=x dB=10log10(I2/I1) Plugging in I2=2, I1=1 we get 10log10(2/1) or roughly 3 &',0'       A+Understanding the decibelStandard reference pressure for dB SPL 20 microPascals Threshold of hearing of a 1000 Hz tone dB SPL = 20log10(p/20) For a pressure p in microPascalsx'N!'EB,Understanding the decibelPDynamic range of an n-bit system is the ratio of the largest representable value and the quantization error n-bit system can represent 2n values discrete levels are always within one unit of the correct value Dynamic Range(dB)=20log10(2n/1) H" 6n Hence the 96dB dynamic range of 16 bit (CD) audio l2VF  2  ,= H( Digital AudiovWhat do we mean by: Digital? (vs Analog) To Digitize? Why do we do it? What advantages does it have? What weaknesses? 6bbWF/Analog vs. Digital G0 Digital AudioWe really only care about Analog Audio Digital audio exists to: Capture an Analog Signal Manipulate an Analog Signal Reconstruct (synthesize) an Analog Signal 6@_@_H1 Digital AudioUltimately we do digital audio because Our computers are digital (anybody remember analog computers?) We are better at building fast DSPs than precise analog circuits that don t drift with age/temperature '%B&'%B&  GI2 Digital AudioMany ways to represent an analog signal as digital For now, we only care about PCM Pulse code modulation Representing signal by a series of pulses Developed in 1937 2SRSSJ3 Digital AudioAn analog signal may be represented by Sampling the amplitude of analog signal at a regular interval (sampling rate) Quantizing each sample into a fixed range of values&''KB Digital AudioConverting A/D  Sampling Requires low pass filtering analog signal Converting D/A  Reconstruction Requires low pass (reconstruction) filter Creating a Digital signal not sampled from analog - Synthesis t* *>* *>  L4 Digital AudioCD Audio: 44100 frames per second (each frame contains 2 samples) Count in Frames (not samples or bytes) Can represent a 22050 Hz signal 16 bit (signed) samples 96 dB dynamic range (6*16bit)  g g   M5 Digital AudioProfessional Digital Audio 48000 Frames/Second Multiple of film s 24 frames per second (film is actually double shuttered 48 times/s) Phillips/Sony s 1980 Red-book CD spec. 44100 Frames/Second Physical tradeoff made to fit Beethoven's 9th onto the 120mm CD Solid state laser frequency in the near infra-red 780nm Purposefully incompatible to make sample rate conversion more difficult ZZWZ'ZZZZW'  + N6 Digital AudioRTime/Amplitude Quantization n bits represent 2n values Recall: Sound is a periodic displacement Hence encode values of nominal 0 +/- 1/2n Range set by practical analog constraints Values above/below range clip Usually additional bits add precision not range Precision adds dynamic range over the digital noise floor (quantization error)  X *  O7 Digital AudioTime/Amplitude Quantization 16 bit 2 s compliment used in CD Audio and is most common 8 bits used in voice CODECs and places where quality isn t required Noisy environments Signals guaranteed to be normalized (use all bits) Gotcha: PC s use unsigned 8 bit 24 bits catching on as new quality standard Typically will process 16 bit samples in 24 bit pipeline to provide headroom xZ~ZfZzZZ~fz  k P8 Digital Audio@Popular Sampling rates: 44100 used in CD audio and most high end PC applications 48000 used in professional audio and some high end PC applications 22050 CD rate used in games and applications where the ultimate in quality not deemed necessary 8000 typically used for voice where frequencies above 4000Hz not critical *))Q? Digital AudioSampling Theory A signal may be perfectly represented provided it is sampled at a rate twice the highest frequency component of the signal This rate is known as the nyquist rate A signal thus sampled may be perfectly reconstructed &<R@ Digital AudioSampling Theory Practically this means: Analog signal must be band limited to the sample rate before digitization Must be performed in the analog space before digitization This must be performed in the analog space Sharper the filter the more expensive it gets Energy from frequency components exceeding the Nyquist rate will be aliased Perfect reconstruction not possible due to quantization error Viif  T g z o h   p o d   |   <|    m    J ܶ    T ܶ   |   l      dUSA Digital Audio)Quantizing an Analog Signal Equivalent to converting from a real to n-bit integer value Real value must be rounded or truncated It is infinitely unlikely that the real value will ever be precisely a whole number (representable by an integer) Resulting difference is called the quantization error VZdZsZ7Zds7 H[D$Sampling/Quantizing an Analog Signal%%( T9 Assignment 12SineSynth.c A silent prelude to Audio Hello World Warm-up to get us in the spirit of digital audio Microsoft interview problem To be written in C Provide handwritten (2-line?) Makefile to build the program Due Tuesday 1/20 before class Deposit in csx245\submit folder Email me, keng@sworks.com, if problemsF ZZ'Z '"   0%U< Assignment 1Synthesize a sinewave of specified frequency, frame-rate, and quantization Output to be printed to standard out, one line per sample, left justified, no padding printf( %d\n , value); (correctness will be automatically verified) >D.,  9V= Assignment 1void SineSynth(double frequency, int frameRate, int bitsPerSample) main should use getopt to get parameters from command line in order argv[1] frequency argv[2] frameRate argv[3] bits quantization main should call SineSynth() which should not return PZ8Z>Z6ZZG -             H   W> Assignment 1 Questions? (  X. 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S XContinuous in time @` < <.? m` ODigital @` < <28?m  NAnalog @``B < 0o ?m`mZB < s *1 ?`ZB < s *1 ?S`SZB < s *1 ?7 `7 ZB < s *1 ? ` ZB < s *1 ? ` `B < 0o ?``B < 0o ?mZB < s *1 ? m `B < 0o ?`m`ZB '< s *1 ?`H < 0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 0L0(  Lx L c $B `P   x L c $t! `  H L 0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 @P0(  Px P c $, `P   x P c $  `  H P 0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 PT0(  Tx T c $ `P   x T c $ `  H T 0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 `X0(  Xx X c $$ `P   x X c $ `  H X 0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 `0(  x  c $t$ `P   x  c $8 `  H  0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 p\0(  \x \ c $d `P   x \ c $T `  H \ 0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 `0(  `x ` c $ `P   x ` c $ `  H ` 0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 d0(  dx d c $n `P  8 x d c $L `  H d 0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 h0(  hx h c $ `P   x h c $` `  H h 0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 l0(  lx l c $ `P   x l c $ `  H l 0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0  0(  x  c $xi `P   x  c $ `  H  0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 00(  x  c $z `P   x  c $Xx `  H  0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 @0(  x  c $ `P   x  c $X `  H  0޽h ? +T3f3f___PPT10i._+D=' = @B +b  0L0 aY(  x  c $\8 `P  8 |  T " A?P@  0\p W U!Illustration thanks to Bob Stuart" 2"H  0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 p0(  px p c $ `P   x p c $ `  H p 0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 |0(  |x | c $h `P   x | c $(C `  H | 0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 0(  x  c $  `P   x  c $ `  H  0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 0(  x  c $ `P   x  c $4 `  H  0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 80(  8x 8 c $!8 `P  8 x 8 c $&8 ` 8 H 8 0޽h ? +T3f3f___PPT10i._+D=' = @B +  0L0 40(  4x 4 c $( `P  8 x 4 c $do `  H 4 0޽h ? +T3f3f___PPT10i._+D=' = @B +r@M9W][g&0iw/<plo9rt4z|D_9b؄e` [Vd _d=[wD(Oh+'0T hp   , 8DL4CS245 Introduction to Interactive Sound SynthesisKen Greenebaum TexturedKen Greenebaum19Microsoft Office PowerPoint@ ;+@bEnU@$1GSg  )'    """)))UUUMMMBBB999|PP3f333f3333f3ffffff3f̙3ff333f333333333f33333333f33f3ff3f3f3f3333f33̙33333f333333f3333f3ffffff3f33ff3f3f3f3fff3ffffffffff3ffff̙fff3fffff3fff333f3f3ff3ff33f̙̙3̙ff̙̙̙3f̙3f333f3333f3ffffff3f̙3f3f3f333f3333f3ffffff3f̙3f3ffffffffff!___www``4'A x(xKʦ """)))UUUMMMBBB999|PP3f3333f333ff3fffff3f3f̙f3333f3333333333f3333333f3f33ff3f3f3f3333f3333333f3̙33333f333ff3ffffff3f33f3ff3f3f3ffff3fffffffff3fffffff3f̙ffff3ff333f3ff33fff33f3ff̙3f3f3333f333ff3fffff̙̙3̙f̙̙̙3f̙3f3f3333f333ff3fffff3f3f̙3ffffffffff!___wwwlllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllew0TTܖ 0ܖ1 A .  @n?" dd@  @@`` D<Xj""$123456784," 2MNO1STUVWXYZ[\_`abcdfh?R$.Kb|MR$W^%{H:M2$$)WJUߍ! 0AA@8 xʚ;Bv3ʚ;g4,d,d 0ppp@ <4dddd k 0Tȵ <4dddd l 0T<4!d!d l 0T80___PPT10 ?  %;IIntroduction to Interactive Sound Synthesis Lecture 3: Fundamentals cont..J+Ken Greenebaum&%TSound Pressure Levels: "Mine Goes to 11! ++(Human hearing is more sensitive to some frequencies than others This sensitivity changes based on Loudness of sound Age of listener Fletcher-Munson equal loudness curves<c"&c"&<&TSound Pressure Levels: "Mine Goes to 11! ++( ='TSound Pressure Levels: "Mine Goes to 11! ++(Fletcher-Munson equal loudness curves Most sensitive 2000-5000Hz Sensitivity falls off for low frequency sounds especially at low sound levels Sensitivity also falls off for high frequencies >&&>(TSound Pressure Levels: "Mine Goes to 11! ++(.C-Weighted dB SPL Models uneven human perception of frequency by discounting high and low frequency s contribution Measured with an inexpensive device <a%a%?)TSound Pressure Levels: "Mine Goes to 11! ++(Common dB SPL values 0 Hearing threshold 18 Whisper at 5 30 Library, very quiet country home 51 My BMW at idle (from inside) 55 Average Office XX? This Classroom 77 BMW at 80 MPH 94 Blender at 3 110 Rock Concert (OSHA limits workers to 30 minutes) 120 Loud thunder, Jackhammer at 3 (discomfort) 140 Jet on takeoff at 100 .P0P0'Understanding the decibel9We will review the highlights Questions from the reading?::@*Understanding the decibelDecibel is a ratio: Hence is dimensionless! Is logarithmic Recall: y = log10(x) is equivalent to 10y=x dB=10log10(I2/I1) Plugging in I2=2, I1=1 we get 10log10(2/1) or roughly 3',0'       A+Understanding the decibelStandard reference pressure for dB SPL 20 microPascals Threshold of hearing of a 1000 Hz tone dB SPL = 20log10(p/20) For a pressure p in microPascalsx'N!'EB,Understanding the decibelNDynamic range of an n-bit system is the ratio of the largest representable value and the quantization error n-bit system can represent 2n values discrete levels are always within one unit of the correct value Dynamic Range(dB)=20log10(2n/1) H" 6n Hence the 96dB dynamic range of 16 bit (CD) audiol2VF  1  ,= G( Digital AudiouWhat do we mean by: Digital? (vs Analog) To Digitize? Why do we do it? What advantages does it have? What weaknesses?&bbVF/Analog vs. Digital G0 Digital AudioWe really only care about Analog Audio Digital audio exists to: Capture an Analog Signal Manipulate an Analog Signal Reconstruct (synthesize) an Analog Signal&@_@_H1 Digital AudioUltimately we do digital audio because Our computers are digital (anybody remember analog computers?) We are better at building fast DSPs than precise analog circuits that don t drift with age/temperatureb'%B&'%B&  EI2 Digital AudioMany ways to  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~<      !"#$%&()*+,-./0123456;=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxy{|}~Root EntrydO)`L1Pictures,(Current UserJSummaryInformation(,UPowerPoint Document(2DocumentSummaryInformation88 / 00DArialr New0TT3ܖ 0ܖDTahoma New0TT3ܖ 0ܖ" DWingdingsw0TT3ܖ 0ܖ0DCourier New0TT3ܖ 0ܖ1 A .  @n?" dd@  @@`` <4Pi""$123456784," 2MNO1STUVWXYZ[\_`abcdfh?R$.Kb|MR$W^%{H:M2$$)WJUߍ! 0AA@8 xʚ;Bv3ʚ;g4,d,d&&>(TSound Pressure Levels: "Mine Goes to 11! ++(.C-Weighted dB SPL Models uneven human perception of frequency by discounting high and low frequency s contribution Measured with an inexpensive device <a%a%?)TSound Pressure Levels: "Mine Goes to 11! ++(Common dB SPL values 0 Hearing threshold 18 Whisper at 5 30 Library, very quiet country home 51 My BMW at idle (from inside) 55 Average Office XX? This Classroom 77 BMW at 80 MPH 94 Blender at 3 110 Rock Concert (OSHA limits workers to 30 minutes) 120 Loud thunder, Jackhammer at 3 (discomfort) 140 Jet on takeoff at 100 .P0P0'Understanding the decibel9We will review the highlights Questions from the reading?::@*Understanding the decibelDecibel is a ratio: Hence is dimensionless! Is logarithmic Recall: y = log10(x) is equivalent to 10y=x dB=10log10(I2/I1) Plugging in I2=2, I1=1 we get 10log10(2/1) or roughly 3',0'       A+Understanding the decibelStandard reference pressure for dB SPL 20 microPascals Threshold of hearing of a 1000 Hz tone dB SPL = 20log10(p/20) For a pressure p in microPascalsx'N!'EB,Understanding the decibelNDynamic range of an n-bit system is the ratio of the largest representable value and the quantization error n-bit system can represent 2n values discrete levels are always within one unit of the correct value Dynamic Range(dB)=20log10(2n/1) H" 6n Hence the 96dB dynamic range of 16 bit (CD) audiol2VF  1  ,= G( Digital AudiouWhat do we mean by: Digital? (vs Analog) To Digitize? Why do we do it? What advantages does it have? What weaknesses?&bbVF/Analog vs. Digital G0 Digital AudioWe really only care about Analog Audio Digital audio exists to: Capture an Analog Signal Manipulate an Analog Signal Reconstruct (synthesize) an Analog Signal&@_@_H1 Digital AudioUltimately we do digital audio because Our computers are digital (anybody remember analog computers?) We are better at building fast DSPs than precise analog circuits that don t drift with age/temperatureb'%B&'%B&  EI2 Digital AudioMany ways to represent an analog signal as digital For now, we only care about PCM Pulse code modulation Representing signal by a series of pulses Developed in 1937&SRSRJ3 Digital AudioAn analog signal may be represented by Sampling the amplitude of analog signal at a regular interval (sampling rate) Quantizing each sample into a fixed range of values&''KB Digital AudioConverting A/D  Sampling Requires low pass filtering analog signal Converting D/A  Reconstruction Requires low pass (reconstruction) filter Creating a Digital signal not sampled from analog - Synthesis`* *>* *>L4 Digital AudioCD Audio: 44100 frames per second (each frame contains 2 samples) Count in Frames (not samples or bytes) Can represent a 22050 Hz signal 16 bit (signed) samples 96 dB dynamic range (6*16bit)n g g   M5 Digital AudioProfessional Digital Audio 48000 Frames/Second Multiple of film s 24 frames per second (film is actually double shuttered 48 times/s) Phillips/Sony s 1980 Red-book CD spec. 44100 Frames/Second Physical tradeoff made to fit Beethoven's 9th onto the 120mm CD Solid state laser frequency in the near infra-red 780nm Purposefully incompatible to make sample rate conversion more difficultZZWZ'ZZZW'  + N6 Digital AudioQTime/Amplitude Quantization n bits represent 2n values Recall: Sound is a periodic displacement Hence encode values of nominal 0 +/- 1/2n Range set by practical analog constraints Values above/below range clip Usually additional bits add precision not range Precision adds dynamic range over the digital noise floor (quantization error) X *O7 Digital AudioTime/Amplitude Quantization 16 bit 2 s compliment used in CD Audio and is most common 8 bits used in voice CODECs and places where quality isn t required Noisy environments Signals guaranteed to be normalized (use all bits) Gotcha: PC s use unsigned 8 bit 24 bits catching on as new quality standard Typically will process 16 bit samples in 24 bit pipeline to provide headroom^Z~ZfZyZ~fykP8 Digital Audio?Popular Sampling rates: 44100 used in CD audio and most high end PC applications 48000 used in professional audio and some high end PC applications 22050 CD rate used in games and applications where the ultimate in quality not deemed necessary 8000 typically used for voice where frequencies above 4000Hz not critical*((Q? Digital AudioSampling Theory A signal may be perfectly represented provided it is sampled at a rate twice the highest frequency component of the signal This rate is known as the nyquist rate A signal thus sampled may be perfectly reconstructed&;R@ Digital AudioSampling Theory Practically this means: Analog signal must be band limited to the sample rate before digitization Must be performed in the analog space before digitization This must be performed in the analog space Sharper the filter the more expensive it gets Energy from frequency components exceeding the Nyquist rate will be aliased Perfect reconstruction not possible due to quantization error@iif  T g z o h   p o d   |   <|    m    J ܶ    T ܶ   |   l      dTSA Digital Audio(Quantizing an Analog Signal Equivalent to converting from a real to n-bit integer value Real value must be rounded or truncated It is infinitely unlikely that the real value will ever be precisely a whole number (representable by an integer) Resulting difference is called the quantization errorVZdZsZ6Zds6 G[D$Sampling/Quantizing an Analog Signal%%( T9 Assignment 1SineSynth.c A silent prelude to Audio Hello World Warm-up to get us in the spirit of digital audio Microsoft interview problem To be written in C Provide handwritten (2-line?) Makefile to build the program. ZZ  U< Assignment 1Synthesize a sinewave of specified frequency, frame-rate, and quantization Output to be printed to standard out, one line per sample, left justified, no padding printf( %d\n , value); (correctness will be automatically verified) >D.,  9V= Assignment 1void SineSynth(double frequency, int frameRate, int bitsPerSample) main should use getopt to get parameters from command line in order argv[1] frequency argv[2] frameRate argv[3] bits quantization main should call SineSynth() which should not return PZ8Z>Z6ZZG -             H , W> Assignment 1 Questions? (  X. 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Digital AudioSampling Theory A signal may be perfectly represented provided it is sampled at a rate twice the highest frequency component of the signal This rate is known as the nyquist rate A signal thus sampled may be perfectly reconstructed&;R@ Digital AudioSampling Theory Practically this means: Analog signal must be band limited to the sample rate before digitization Must be performed in the analog space before digitization This must be performed in the analog space Sharper the filter the more expensive it gets Energy from frequency components exceeding the Nyquist rate will be aliased Perfect reconstruction not possible due to quantization error@iif  T g z o h   p o d   |   <|    m    J ܶ    T ܶ   |   l      dTSA Digital Audio(Quantizing an Analog Signal Equivalent to converting from a real to n-bit integer value Real value must be rounded or truncated It is infinitely unlikely that the real value will ever be precisely a whole number (representable by an integer) Resulting difference is called the quantization errorVZdZsZ6Zds6 G[D$Sampling/Quantizing an Analog Signal%%( T9 Assignment 1SineSynth.c A silent prelude to Audio Hello World Warm-up to get us in the spirit of digital audio Microsoft interview problem To be written in C Provide handwritten (2-line?) Makefile to build the program. ZZ  U< Assignment 1Synthesize a sinewave of specified frequency, frame-rate, and quantization Output to be printed to standard out, one line per sample, left justified, no padding printf( %d\n , value); (correctness will be automatically verified) >D.,  9V= Assignment 1void SineSynth(double frequency, int frameRate, int bitsPerSample) main should use getopt to get parameters from command line in order argv[1] frequency argv[2] frameRate argv[3] bits quantization main should call SineSynth() which should not return PZ8Z>Z6ZZG -             H , W> Assignment 1 Questions?  X. 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