Sound Ampliude and Loudness Audio DSP Dr. Deepa Kundur Universiy of Torono Sound: vibraion ransmied hrough a medium (gas, liquid, solid and plasma) composed of frequencies capable of being deeced by ears. Noe: sound canno ravel hrough a vacuum. Human deecable sound is ofen characerized by air pressure variaions deeced by he human ear. The ampliude, frequency and relaive phase of he air pressure componens deermine (in par) he way he sound is perceived. Dr. Deepa Kundur (Universiy of Torono) Audio DSP 1 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP / 56 Ampliude and Loudness Ampliude and Loudness Sinusoids and Sound: Ampliude Sound Volume A fundamenal uni of sound is he sinusoidal. A volume x a () = A cos(πf 0 + θ), F0 pich (more on his... ) θ phase (more on his... ) R Volume = Ampliude of sound waves/ s quoed in db, which is a logarihmic measure; 10 log(a ) no sound/null is db Loudness is a subjecive measure of sound psychologically correlaing o he srengh of he sound. he volume is an objecive measure and does no have a one-o-one correspondence wih loudness perceived loudness varies from person-o-person and depends on frequency and duraion of he sound Dr. Deepa Kundur (Universiy of Torono) Audio DSP 3 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 4 / 56
Music Volume Dynamic Range Ampliude and Loudness Sinusoids and Sound: Frequency Tess conduced for he musical noe: C6 (F 0 = 1046.50 Hz). Dynamic Level Decibels Threshold of hearing 0 ppp (pianissimo) 40 p (piano) 60 f (fore) 80 fff (forississimo) 100 Threshold of pain 10 A fundamenal uni of sound is he sinusoidal. x a () = A cos(πf 0 + θ), R A volume F0 pich θ phase (more on his... ) Dr. Deepa Kundur (Universiy of Torono) Audio DSP 5 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 6 / 56 Pure Frequency Tuning Forks Q: Wha ype of sound does a pure frequency produce? A: A pure one wih a single pich. Q: Can any insrumen produce a pure one by playing a single noe? A: No. A uning fork is a wo-pronged insrumen ha is an acousic resonaor. I is usually made ou of seel and resonaes a a specific consan pich which is a funcion of he lengh of he prongs. Sriking he uning fork will produce he required sounds alhough iniially here may be overones ha die ou quickly. A very common uning fork used by musicians produces he A noe (F 0 = 440 Hz), which is inernaional concer pich used o une orchesras. Dr. Deepa Kundur (Universiy of Torono) Audio DSP 7 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 8 / 56
Harmonically Relaed Frequencies and Pich Sinusoids can be represened eiher as: x a () = A cos(πf 0 + θ), R or for mahemaical convenience when inerpreing as Fourier componens as: x a () = Ae j(πf 0+θ), Pich is direcly relaed o he frequency F 0. R To be able o hear a frequency F 0, i has o be in he human audible range. Scienific Designaion Frequency (Hz) k for F 0 = 8.176 C1 3.703 4 C 65.406 8 C3 130.813 16 C4 (middle C) 61.66 3 C5 53.51 64 C6 1046.50 18 C7 093.005 56 C8 4186.009 51 C1 C C3 C4 C5 C6 C7 C8 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 9 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 10 / 56 Harmonically Relaed Frequencies Recall harmonically relaed sinusoids have he following analyic form for k Z: Signaure Sounds or x a,k () = A cos(πkf 0 + θ) x a,k () = Ae j(πkf 0+θ) They are used in he conex of he Fourier Series o build periodic s: Q: If wo differen people sing he same noe or wo differen insrumens play he same noe, why do hey sound differen? The noes are no pure ones. There are naural overones and underones ha provide disinguishing signaures ha can be viewed in he associaed specra. x() = X (k)e j(πkf 0) k= Dr. Deepa Kundur (Universiy of Torono) Audio DSP 11 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 1 / 56
Fourier Transforms of he Same Noe Tuning Fork Human Audible Range 0 f Insrumen A 0 f Insrumen B Hearing is usually limied o frequencies beween 0 Hz and 0 khz. The upper limi decreases wih age. The audible frequency range is differen for animals 0 f Dr. Deepa Kundur (Universiy of Torono) Audio DSP 13 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 14 / 56 Animal Audible Range Sinusoids and Sound: Phase Species Approx Range (Hz) human 0-0,000 dog 67-45,000 rabbi 360-4,000 ba,000-110,000 goldfish 0-3,000 Reference: R.R. Fay (1988), Hearing in Verebraes: A Psychophysics Daabook. A fundamenal uni of sound is he sinusoidal. x a () = A cos(πf 0 + θ), R A volume F0 pich θ phase Dr. Deepa Kundur (Universiy of Torono) Audio DSP 15 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 16 / 56
Consider a general sound x() ha is comprised of frequency componens each wih a specific phase shif. x() = X (f )e jπf df X (f ) : relaive volume of a sinusoidal componen X (f ): relaive phase of a sinusoidal componen If x() is he general sound, hen x( ) is he sound in reverse. Q: Do x() and x( ) sound similar? A: No. Dr. Deepa Kundur (Universiy of Torono) Audio DSP 17 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 18 / 56 Recall, from he coninuous-ime Fourier ransform (CTFT) ha for a real x(): x() x( ) F X (f ) F X ( f ) Taking he magniude and phase of boh sides we have: X (f ) = X ( f ) X (f ) = X ( f ) = X ( f ) X (f ) = X ( f ) = X ( f ) and X (f ) = X ( f ) Conjugae Symmery (for real s x()): CTFT magniude is even CTFT phase is odd Dr. Deepa Kundur (Universiy of Torono) Audio DSP 19 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 0 / 56
Audiory Masking Audiory Masking Therefore, for x() x( ) F X (f ) F X ( f ) X (f ) = X ( f ) he CTFT magniudes for forward and reverse sound s are exacly he same. X (f ) X ( f ) he CTFT phases for forward and reverse sound s are differen. Therefore, he relaive phase of he sinusoidal componens of sound conains very salien percepual informaion much like for images. occurs when he perceived qualiy of one (primary) sound is affeced by he presence of anoher (secondary) sound Simulaneous masking: he secondary sound is heard a he same ime as he primary sound Can be exploied (as we see in an upcoming lab) o mask non-ideal processing. Dr. Deepa Kundur (Universiy of Torono) Audio DSP 1 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP / 56 Why Digiize Audio? Benefis of Audio Fideliy of digial is much higher han analog. Manipulaion ools for digial are much more sophisicaed han hose available for analog. Compression of digial provides significanly reduced sorage requiremens. of digial (e.g., CDs) are much more convenien and compac. Duplicaion of digial is exac in conras o analog. Convenien recording, enhancemen, mass-producion and disribuion. CDs, online sores such as itunes, ec. daa files are disribued insead of physical media soring he informaion such as records and apes. Dr. Deepa Kundur (Universiy of Torono) Audio DSP 3 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 4 / 56
Concerns abou Audio vs. Audio: Audio Sysem Transducer (e.g., microphone) Convenien recording, enhancemen, mass-producion and disribuion. unlawful manipulaion of recorded is difficul o deec piracy: unlawful copying and redisribuion of copyrighed conen Loudspeaker microphone: convers sound ino an elecrical ; air pressure moion of conducor/coil magneic field elecrical loudspeaker: convers elecrical ino acousic waves; elecrical magneic field moion air pressure Dr. Deepa Kundur (Universiy of Torono) Audio DSP 5 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 6 / 56 vs. Audio: Audio Sysem vs. Audio: Audio Chain Transducer (e.g., microphone) A/D Converer Error Correcion Coding (ECC) Loudspeaker D/A Converer ECC Decoding associaed circuis suffer from inheren noise (noise floor) capaciance and inducance of he circuis limi bandwidh, and resisance limis ampliude fideliy limied by quanizaion noise bandwidh limied by sampling rae dynamic range limied by bi resoluion Dr. Deepa Kundur (Universiy of Torono) Audio DSP 7 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 8 / 56
Audio DSP Sysem Audio DSP Sysem Anialiasing Sample and Hold A/D Processing for D/A Reconsrucion Anialiasing Sample and Hold A/D Processing for D/A Reconsrucion inpu (from microphone ransducer) Bandlimied analog Sampled daa {0100101} {0110001} Cs-ime ds-amp saricase oupu inpu (from microphone ransducer) Bandlimied analog Sampled daa {0100101} {0110001} Cs-ime ds-amp saricase oupu Ani-aliasing : ensures ha analog inpu does no conain frequency componens higher han half of he sampling frequency (o avoid aliasing) Example: C6713 DSP, F s = 8 khz, herefore ani-aliasing filer mus have a passband of 0 Hz o 4000 Hz. Dr. Deepa Kundur (Universiy of Torono) Audio DSP 9 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 30 / 56 Inpu Signal Audio DSP Sysem Anialiasing Sample and Hold A/D Processing for D/A Reconsrucion -3 - -1 1 3 4 - inpu (from microphone ransducer) Bandlimied analog Sampled daa {0100101} {0110001} Cs-ime ds-amp saricase oupu Ani-aliased Signal Sample and Hold: holds a sampled analog value for a shor ime while he A/D convers and inerpres he value as a digial -3 - -1 1 3 4 - Dr. Deepa Kundur (Universiy of Torono) Audio DSP 31 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 3 / 56
Ani-aliased Signal Audio DSP Sysem Anialiasing Sample and Hold A/D Processing for D/A Reconsrucion -3 - -1 1 3 4 - inpu (from microphone ransducer) Bandlimied analog Sampled daa {0100101} {0110001} Cs-ime ds-amp saricase oupu Sampled Daa Signal ani-aliased A/D: convers a sampled daa value ino a digial number, in par, hrough quanizaion of he ampliude -3 - -1 1 3 4 - Dr. Deepa Kundur (Universiy of Torono) Audio DSP 33 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 34 / 56 Sampled Daa Signal Audio DSP Sysem ani-aliased Anialiasing Sample and Hold A/D Processing for D/A Reconsrucion -3 - -1 1 3 4 - inpu (from microphone ransducer) Bandlimied analog Sampled daa {0100101} {0110001} Cs-ime ds-amp saricase oupu Signal sampled daa Processing for : ransmission/sorage conains inheren non-idealiies ha cause errors in he received/rerieved daa symbols -3 - -1 1 3 4 - x() error correcion coding (ECC) is employed o add redundancy o he digial so ha errors can be compensaed for during decoding Dr. Deepa Kundur (Universiy of Torono) Audio DSP 35 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 36 / 56 1
Error Correcion Coding Example: N-repeiion code Inpu Signal Bi Coded Sequence 0 } 0 0 0 {{ 0} N zeros 1 } 1 1 1 {{ 1} N ones Therefore, for N = 3 he following inpu sequence: 0 0 1 would be coded as follows: 0 0 0 0 0 0 1 1 1. Error Correcion Coding Q: How would you inerpre receiving he following coded sequence (wih possible error): 1 1 1 0 1 0 0 0 0? 1 1 1 }{{} 1 0 1 0 }{{} 0 0 0 0 }{{} 0 A: Decoding can make use of majoriy voe logic. Dr. Deepa Kundur (Universiy of Torono) Audio DSP 37 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 38 / 56 Error Correcion Coding Coder for N = 3: Inpu Signal Bi Coded Sequence 0 0 0 0 1 1 1 1 Majoriy voe logic decoder for N = 3: Received Coded Seq Decoded Signal Bi 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 Audio DSP Sysem inpu (from microphone ransducer) Anialiasing Sample and Hold Bandlimied analog Sampled daa A/D {0100101} Processing for {0110001} D/A Cs-ime ds-amp saricase Reconsrucion D/A: convers a digial ino a saircase -like for furher reconsrucion oupu Dr. Deepa Kundur (Universiy of Torono) Audio DSP 39 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 40 / 56
Signal Audio DSP Sysem sampled daa Anialiasing Sample and Hold A/D Processing for D/A Reconsrucion -3 - -1 1 3 4 - inpu (from microphone ransducer) Bandlimied analog Sampled daa {0100101} {0110001} Cs-ime ds-amp saricase oupu digial Saircase Signal -3 - -1 1 3 4 - sampled daa Reconsrucion : convers a saircase -like ino an analog filer hrough lowpass filering depending on he applicaion he filer can be similar o he ani-aliasing filer, or may be very cheap (e.g., compac disk receivers), or may using a differen sampling rae for special effecs Dr. Deepa Kundur (Universiy of Torono) Audio DSP 41 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 4 / 56 digial Saircase Signal -3 - -1 1 3 4 - sampled daa Reconsruced Signal ani-aliased The qualiy of digiizing is relaed o he following parameers: sampling rae (Hz) bi deph (bis/sample) and dynamic range (relaed o number of quanizaion levels) mono vs. sereo -3 - -1 1 3 4 - x() Dr. Deepa Kundur (Universiy of Torono) Audio DSP 43 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 44 / 56 1
Audio Qualiy Audio Qualiy and Sampling Rae Noe: For he same cos, digial provides higher -o-noise raio or lower mean-square error beween he real sound and wha is recorded/played. I is less expensive o increase sampling rae and quanizaion deph (i.e., reduce quanizaion noise) han o use less noisy analog circuiry (i.e., reduce noise floor) When s are represened digially he naural noise in he circuis can be circumvened via error correcion coding. Thus, i is possible o have near perfec sorage/ransmission. Audio Qualiy as a Funcion of Sampling Rae: Sampling Rae (Hz) Qualiy Similar o 8,000 elephone 11,05 AM radio,050 FM radio 44,100 CD 48,000 DAT Dr. Deepa Kundur (Universiy of Torono) Audio DSP 45 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 46 / 56 Audio Qualiy Audio Qualiy, Sampling Rae, and Bi Deph Audio Qualiy as a Funcion of Sampling Rae, Bi Deph and Sereo/Monophony: Sampling Rae (Hz) Bi Deph Sereo/Mono Qualiy 8,000 8 mono elephone 11,05 8 sereo low,050 8 sereo,050 16 mono,050 16 sereo 44,100 16 mono good 44,100 16 sereo CD qualiy Audio Qualiy Audio Qualiy Q: Why do some people insis ha analog is superior o digial? A: Wha hey hink sounds good isn he exac original sound, bu a nonlinearly disored version generaed from he analog componens. Noe: Some digial companies now make digial amplifiers ha mimic he disorion from analog amplifiers. Qualiy of is a qualiaive and psychological measure ha is user-specific. Dr. Deepa Kundur (Universiy of Torono) Audio DSP 47 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 48 / 56
Audio Equalizaion Equalizer Design Basics Equalizaion Equalisaion EQ amplifying or aenuaion differen frequency componens of an Example: bass/reble conrol in inexpensive car radios Common goals of equalizaion: provide fine granulariy of frequency amplificaion/aenuaion conrol wihou affecing adjacen frequencies. correc for unwaned frequency aenuaion/amplificaion during recording processes enhancing he presence of cerain sounds reducing he presence of unwaned s such as noise 1. Deermine he processing band of your. human audible range is: 0 Hz o 0 khz if sampling rae of a DSP is Fs hen, he bandwidh of he o process is: 0 o Fs Hz Example: Fs = 16, 000 Hz -8000-0 0 8000 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 49 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 50 / 56 Equalizer Design Basics Equalizer Design Basics 1. Deermine he granulariy of your equalizer (i.e., number of frequency bands o independenly conrol). one approach migh be o equally pariion he bandwdih more popular approaches suied o human audiory sysem models have bands ha increase in widh by wo Example: 3 frequency bands 3. Design your bandpass filers. each bandpass filer is independenly se/conrolled from he ohers ideally, many people would like shelving EQ Example: Ideal bandpass filers -8000-3000 -1000-0 0 1000 1 3000 8000-8000 -3000-1000 -0 0 1000 3000 8000 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 51 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 5 / 56
Equalizer Design Basics Common Types of Equalizers 3. Design your bandpass filers. each bandpass filer is independenly se/conrolled from he ohers ideally, many people would like shelving EQ Example: Bell EQ All bell filers and many oher bandpass filers can be characerized by hree parameers: cener frequency widh of he bell curve gain (i.e. peak) of he bell curve cener frequency -8000-3000 -1000-0 0 1000 1 3000 8000-8000 -3000-1000 -0 0 1000 1 3000 widh 8000 peak ampliude Dr. Deepa Kundur (Universiy of Torono) Audio DSP 53 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 54 / 56 Common Types of Equalizers Common Types of Equalizers Parameric Equalizers: he cener frequency, passband widh and peak ampliude can be independenly seleced for each filer mos powerful EQ, predominanly used for recording and mixing Graphic Equalizers: he cener frequency and passband widh of each filer are pre-se; he gains of each filer can be independenly conrolled used for live applicaions such as concers Noch s: he passband widh is small and fixed for each filer; cener frequencies and gains are variable. used in mulimedia applicaions/ masering Dr. Deepa Kundur (Universiy of Torono) Audio DSP 55 / 56 Dr. Deepa Kundur (Universiy of Torono) Audio DSP 56 / 56