Audio DSP kundur digital audio

Audio DSP Dr. Deepa Kundur University of Toronto Dr. Deepa Kundur (University of Toronto) Audio DSP 1 56 Intro to Audio Signals Amplitude and Loudness Sound I Sound: vibration transmitted through a medium (gas, liquid, solid and plasma) composed of frequencies capable of being detected by ears. I Note: sound cannot travel through a vacuum. I Human detectable sound is often characterized by air pressure variations detected by the human ear. I The amplitude, frequency and relative phase of the air pressure signal components determine (in part) the way the sound is perceived. Dr. Deepa Kundur (University of Toronto) Audio DSP 2 56 Intro to Audio Signals Amplitude and Loudness Sinusoids and Sound: Amplitude I A fundamental unit of sound is the sinusoidal signal. xa(t) = A cos(2πF0t + θ); t 2 R I A ≡ volume I F0 ≡ pitch (more on this . . . ) I θ ≡ phase (more on this . . . ) Dr. Deepa Kundur (University of Toronto) Audio DSP 3 56 Intro to Audio Signals Amplitude and Loudness Sound Volume I Volume = Amplitude of sound wavesaudio signals I quoted in dB, which is a logarithmic measure; 10 log(A2) I no soundnull is −1 dB I Loudness is a subjective measure of sound psychologically correlating to the strength of the sound signal. I the volume is an objective measure and does not have a onetoone correspondence with loudness I perceived loudness varies from persontoperson and depends on frequency and duration of the sound Dr. Deepa Kundur (University of Toronto) Audio DSP 4 56Intro to Audio Signals Amplitude and Loudness Music Volume Dynamic Range Tests conducted for the musical note: C6 (F0 = 1046:502 Hz). Dynamic Level Decibels Threshold of hearing 0 ppp (pianissimo) 40 p (piano) 60 f (forte) 80 fff (fortississimo) 100 Threshold of pain 120 Dr. Deepa Kundur (University of Toronto) Audio DSP 5 56 Intro to Audio Signals Frequency and Pitch Sinusoids and Sound: Frequency I A fundamental unit of sound is the sinusoidal signal. xa(t) = A cos(2πF0t + θ); t 2 R I A ≡ volume I F0 ≡ pitch I θ ≡ phase (more on this . . . ) Dr. Deepa Kundur (University of Toronto) Audio DSP 6 56 Intro to Audio Signals Frequency and Pitch Pure Frequency I Q: What type of sound does a pure frequency produce? I A: A pure tone with a single pitch. I Q: Can any instrument produce a pure tone by playing a single note? I A: No. Dr. Deepa Kundur (University of Toronto) Audio DSP 7 56 Intro to Audio Signals Frequency and Pitch Tuning Forks I A tuning fork is a twopronged instrument that is an acoustic resonator. It is usually made out of steel and resonates at a specific constant pitch which is a function of the length of the prongs. I Striking the tuning fork will produce the required sounds although initially there may be overtones that die out quickly. I A very common tuning fork used by musicians produces the A note (F0 = 440 Hz), which is international concert pitch used to tune orchestras. Dr. Deepa Kundur (University of Toronto) Audio DSP 8 56Intro to Audio Signals Frequency and Pitch Frequency and Pitch I Sinusoids can be represented either as: xa(t) = A cos(2πF0t + θ); t 2 R or for mathematical convenience when interpreting as Fourier signal components as: xa(t) = Aej(2πF0t+θ); t 2 R I Pitch is directly related to the frequency F0. I To be able to hear a frequency F0, it has to be in the human audible range. Dr. Deepa Kundur (University of Toronto) Audio DSP 9 56 Intro to Audio Signals Frequency and Pitch Harmonically Related Frequencies and Pitch Scientific Designation Frequency (Hz) k for F0 = 8:176 C1 32.703 4 C2 65.406 8 C3 130.813 16 C4 (middle C) 261.626 32 C5 523.251 64 C6 1046.502 128 C7 2093.005 256 C8 4186.009 512 C1 C2 C3 C4 C5 C6 C7 C8 Dr. Deepa Kundur (University of Toronto) Audio DSP 10 56 Intro to Audio Signals Frequency and Pitch Harmonically Related Frequencies I Recall harmonically related sinusoids have the following analytic form for k 2 Z: xa;k(t) = A cos(2πkF0t + θ) or xa;k(t) = Aej(2πkF0t+θ) I They are used in the context of the Fourier Series to build periodic signals: x(t) = 1 X k=−1 X(k)ej(2πkF0t) Dr. Deepa Kundur (University of Toronto) Audio DSP 11 56 Intro to Audio Signals Frequency and Pitch Signature Sounds I Q: If two different people sing the same note or two different instruments play the same note, why do they sound different? I The notes are not pure tones. There are natural overtones and undertones that provide distinguishing signatures that can be viewed in the associated spectra. Dr. Deepa Kundur (University of Toronto) Audio DSP 12 56Intro to Audio Signals Frequency and Pitch Fourier Transforms of the Same Note 0 f Instrument A 0 f Instrument B 0 f Tuning Fork Dr. Deepa Kundur (University of Toronto) Audio DSP 13 56 Intro to Audio Signals Frequency and Pitch Human Audible Range I Hearing is usually limited to frequencies between 20 Hz and 20 kHz. I The upper limit decreases with age. I The audible frequency range is different for animals Dr. Deepa Kundur (University of Toronto) Audio DSP 14 56 Intro to Audio Signals Frequency and Pitch Animal Audible Range Species Approx Range (Hz) human 20 20,000 dog 67 45,000 rabbit 360 42,000 bat 2,000 110,000 goldfish 20 3,000 Reference: R.R. Fay (1988), Hearing in Vertebrates: A Psychophysics Databook. Dr. Deepa Kundur (University of Toronto) Audio DSP 15 56 Intro to Audio Signals Phase and Sound Sinusoids and Sound: Phase I A fundamental unit of sound is the sinusoidal signal. xa (t) = A cos(2πF0t + θ); t 2 R I A ≡ volume I F0 ≡ pitch I θ ≡ phase Dr. Deepa Kundur (University of Toronto) Audio DSP 16 56Intro to Audio Signals Phase and Sound Phase and Sound Consider a general sound signal x(t) that is comprised of frequency components each with a specific phase shift. x(t) = Z−1 1 X(f )ej2πf tdf I jX(f )j: relative volume of a sinusoidal component I X(f ): relative phase of a sinusoidal component Dr. Deepa Kundur (University of Toronto) Audio DSP 17 56 Intro to Audio Signals Phase and Sound Phase and Sound I If x(t) is the general sound signal, then x(−t) is the sound signal in reverse. I Q: Do x(t) and x(−t) sound similar? I A: No. Dr. Deepa Kundur (University of Toronto) Audio DSP 18 56 Intro to Audio Signals Phase and Sound Phase and Sound I Recall, from the continuoustime Fourier transform (CTFT) that for a real signal x(t): x(t) F X(f ) x(−t) F X(−f ) and X(f ) = X ∗(−f ) Dr. Deepa Kundur (University of Toronto) Audio DSP 19 56 Intro to Audio Signals Phase and Sound Phase and Sound I Taking the magnitude and phase of both sides we have: X(f ) = X ∗(−f ) jX(f )j = jX ∗(−f )j = jX(−f )j X(f ) = X ∗(−f ) = −X(−f ) I Conjugate Symmetry (for real signals x(t)): I CTFT magnitude is even I CTFT phase is odd Dr. Deepa Kundur (University of Toronto) Audio DSP 20 56Intro to Audio Signals Phase and Sound Phase and Sound I Therefore, for x(t) F X (f ) x(−t) F X (−f ) I jX (f )j = jX (−f )j ) the CTFT magnitudes for forward and reverse sound signals are exactly the same. I X (f ) 6= X (−f ) ) the CTFT phases for forward and reverse sound signals are different. I Therefore, the relative phase of the sinusoidal components of sound contains very salient perceptual information much like for images. Dr. Deepa Kundur (University of Toronto) Audio DSP 21 56 Intro to Audio Signals Auditory Masking Auditory Masking I occurs when the perceived quality of one (primary) sound is affected by the presence of another (secondary) sound I Simultaneous masking: the secondary sound is heard at the same time as the primary sound I Can be exploited (as we see in an upcoming lab) to mask nonideal signal processing. Dr. Deepa Kundur (University of Toronto) Audio DSP 22 56 Audio Digital Signal Processing Analog and Digital Audio Why Digitize Audio? I Fidelity of digital audio is much higher than analog audio. I Manipulation tools for digital audio are much more sophisticated than those available for analog audio. I Compression of digital audio provides significantly reduced storage requirements. I Storage of digital audio (e.g., CDs) are much more convenient and compact. I Duplication of digital audio is exact in contrast to analog audio. Dr. Deepa Kundur (University of Toronto) Audio DSP 23 56 Audio Digital Signal Processing Analog and Digital Audio Benefits of Digital Audio I Convenient recording, enhancement, massproduction and distribution. I CDs, online stores such as iTunes, etc. I data files are distributed instead of physical media storing the information such as records and tapes. Dr. Deepa Kundur (University of Toronto) Audio DSP 24 56Audio Digital Signal Processing Analog and Digital Audio Concerns about Digital Audio I Convenient recording, enhancement, massproduction and distribution. I unlawful manipulation of recorded audio is difficult to detect I piracy: unlawful copying and redistribution of copyrighted content Dr. Deepa Kundur (University of Toronto) Audio DSP 25 56 Audio Digital Signal Processing Analog and Digital Audio Analog vs. Digital Audio: Analog Audio System Analog audio signal Transmission Storage Loudspeaker Transducer (e.g., microphone) I microphone: converts sound into an electrical signal; air pressure motion of conductorcoil magnetic field electrical signal I loudspeaker: converts electrical signal into acoustic waves; electrical signal magnetic field motion air pressure Dr. Deepa Kundur (University of Toronto) Audio DSP 26 56 Audio Digital Signal Processing Analog and Digital Audio Analog vs. Digital Audio: Analog Audio System Analog audio signal Transmission Storage Loudspeaker Transducer (e.g., microphone) I associated circuits suffer from inherent noise (noise floor) I capacitance and inductance of the circuits limit bandwidth, and resistance limits amplitude Dr. Deepa Kundur (University of Toronto) Audio DSP 27 56 Audio Digital Signal Processing Analog and Digital Audio Analog vs. Digital Audio: Digital Audio Chain Analog audio signal Digital audio signal Transmission Storage DA Converter AD Converter Error Correction Coding (ECC) ECC Decoding I fidelity limited by quantization noise I bandwidth limited by sampling rate I dynamic range limited by bit resolution Dr. Deepa Kundur (University of Toronto) Audio DSP 28 56Audio Digital Signal Processing Analog and Digital Audio Digitizing Audio AD Processing for Transmission Storage DA Analog audio input (from microphone transducer) Bandlimited analog audio signal Sampled data signal Analog audio output Ctstime dstamp “staricase” signal Digital signal {0100101} Digital signal {0110001} Audio DSP System Antialiasing Filter Sample and Hold Reconstruction Filter Dr. Deepa Kundur (University of Toronto) Audio DSP 29 56 Audio Digital Signal Processing Analog and Digital Audio Digitizing Audio AD Processing for Transmission Storage DA Analog audio input (from microphone transducer) Bandlimited analog audio signal Sampled data signal Analog audio output Ctstime dstamp “staricase” signal Digital signal {0100101} Digital signal {0110001} Audio DSP System Antialiasing Filter Sample and Hold Reconstruction Filter Antialiasing Filter: I ensures that analog audio input does not contain frequency components higher than half of the sampling frequency (to avoid aliasing) I Example: C6713 DSP, Fs = 8 kHz, therefore antialiasing filter must have a passband of 0 Hz to 4000 Hz. Dr. Deepa Kundur (University of Toronto) Audio DSP 30 56 Audio Digital Signal Processing Analog and Digital Audio Digitizing Audio t 2 3 2 1 1 2 3 4 2 4 Input Signal t 2 3 2 1 1 2 3 4 2 4 Antialiased Signal Dr. Deepa Kundur (University of Toronto) Audio DSP 31 56 Audio Digital Signal Processing Analog and Digital Audio Digitizing Audio AD Processing for Transmission Storage DA Analog audio input (from microphone transducer) Bandlimited analog audio signal Sampled data signal Analog audio output Ctstime dstamp “staricase” signal Digital signal {0100101} Digital signal {0110001} Audio DSP System Antialiasing Filter Sample and Hold Reconstruction Filter Sample and Hold: I holds a sampled analog audio value for a short time while the AD converts and interprets the value as a digital Dr. Deepa Kundur (University of Toronto) Audio DSP 32 56Audio Digital Signal Processing Analog and Digital Audio Digitizing Audio t 2 3 2 1 1 2 3 4 2 4 1 2 0 x(t) Antialiased Signal t 2 3 2 1 1 2 3 4 2 4 Sampled Data Signal antialiased signal Dr. Deepa Kundur (University of Toronto) Audio DSP 33 56 Audio Digital Signal Processing Analog and Digital Audio Digitizing Audio AD Processing for Transmission Storage DA Analog audio input (from microphone transducer) Bandlimited analog audio signal Sampled data signal Analog audio output Ctstime dstamp “staricase” signal Digital signal {0100101} Digital signal {0110001} Audio DSP System Antialiasing Filter Sample and Hold Reconstruction Filter AD: I converts a sampled data audio value into a digital number, in part, through quantization of the amplitude Dr. Deepa Kundur (University of Toronto) Audio DSP 34 56 Audio Digital Signal Processing Analog and Digital Audio Digitizing Audio t 2 3 2 1 1 2 3 4 2 4 Sampled Data Signal antialiased signal t 2 3 2 1 1 2 3 4 2 4 Digital Signal sampled data signal Dr. Deepa Kundur (University of Toronto) Audio DSP 35 56 Audio Digital Signal Processing Analog and Digital Audio Digitizing Audio AD Processing for Transmission Storage DA Analog audio input (from microphone transducer) Bandlimited analog audio signal Sampled data signal Analog audio output Ctstime dstamp “staricase” signal Digital signal {0100101} Digital signal {0110001} Audio DSP System Antialiasing Filter Sample and Hold Reconstruction Filter Processing for TransmissionStorage: I transmissionstorage contains inherent nonidealities that cause errors in the receivedretrieved data symbols I error correction coding (ECC) is employed to add redundancy to the digital signal so that errors can be compensated for during decoding Dr. Deepa Kundur (University of Toronto) Audio DSP 36 56Audio Digital Signal Processing Analog and Digital Audio Error Correction Coding Example: Nrepetition code Input Signal Bit Coded Sequence 0 0 0 0 · ·· 0 | {z } N zeros 1 1 1 1 · · · 1 | {z } N ones Therefore, for N = 3 the following input signal sequence: 0 0 1 would be coded as follows: 0 0 0 0 0 0 1 1 1: Dr. Deepa Kundur (University of Toronto) Audio DSP 37 56 Audio Digital Signal Processing Analog and Digital Audio Error Correction Coding Q: How would you interpret receiving the following coded sequence (with possible error): 1 1 1 0 1 0 0 0 0? 1 1 1 | {z } 1 0 1 0 | {z } 0 0 0 0 | {z } 0 A: Decoding can make use of majority vote logic. Dr. Deepa Kundur (University of Toronto) Audio DSP 38 56 Audio Digital Signal Processing Analog and Digital Audio Error Correction Coding Coder for N = 3: Input Signal Bit Coded Sequence 0 0 0 0 1 1 1 1 Majority vote logic decoder for N = 3: Received Coded Seq Decoded Signal Bit 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 Dr. Deepa Kundur (University of Toronto) Audio DSP 39 56 Audio Digital Signal Processing Analog and Digital Audio Digitizing Audio AD Processing for Transmission Storage DA Analog audio input (from microphone transducer) Bandlimited analog audio signal Sampled data signal Analog audio output Ctstime dstamp “staricase” signal Digital signal {0100101} Digital signal {0110001} Audio DSP System Antialiasing Filter Sample and Hold Reconstruction Filter DA: I converts a digital audio signal into a staircaselike signal for further reconstruction Dr. Deepa Kundur (University of Toronto) Audio DSP 40 56Audio Digital Signal Processing Analog and Digital Audio Digitizing Audio t 2 3 2 1 1 2 3 4 2 4 1 2 0 x(t) Digital Signal sampled data signal t 2 3 2 1 1 2 3 4 2 4 Staircase Signal digital signal sampled data signal Dr. Deepa Kundur (University of Toronto) Audio DSP 41 56 Audio Digital Signal Processing Analog and Digital Audio Digitizing Audio AD Processing for Transmission Storage DA Analog audio input (from microphone transducer) Bandlimited analog audio signal Sampled data signal Analog audio output Ctstime dstamp “staricase” signal Digital signal {0100101} Digital signal {0110001} Audio DSP System Antialiasing Filter Sample and Hold Reconstruction Filter Reconstruction Filter: I converts a staircaselike signal into an analog filter through lowpass filtering I depending on the application the filter can be similar to the antialiasing filter, or may be very cheap (e.g., compact disk receivers), or may using a different sampling rate for special effects Dr. Deepa Kundur (University of Toronto) Audio DSP 42 56 Audio Digital Signal Processing Analog and Digital Audio Digitizing Audio t 2 3 2 1 1 2 3 4 2 4 Staircase Signal digital signal sampled data signal t 2 3 2 1 1 2 3 4 2 4 Reconstructed Signal antialiased signal Dr. Deepa Kundur (University of Toronto) Audio DSP 43 56 Audio Digital Signal Processing Analog and Digital Audio Digitizing Audio The quality of digitizing audio is related to the following parameters: I sampling rate (Hz) I bit depth (bitssample) and dynamic range (related to number of quantization levels) I mono vs. stereo Dr. Deepa Kundur (University of Toronto) Audio DSP 44 56Audio Digital Signal Processing Analog and Digital Audio Digitizing Audio Note: For the same cost, digital audio provides higher signaltonoise ratio or lower meansquare error between the real sound and what is recordedplayed. I It is less expensive to increase sampling rate and quantization depth (i.e., reduce quantization noise) than to use less noisy analog circuitry (i.e., reduce noise floor) I When signals are represented digitally the natural noise in the circuits can be circumvented via error correction coding. Thus, it is possible to have near perfect storagetransmission. Dr. Deepa Kundur (University of Toronto) Audio DSP 45 56 Audio Digital Signal Processing Audio Quality Audio Quality and Sampling Rate Audio Quality as a Function of Sampling Rate: Sampling Rate (Hz) Quality Similar to 8,000 telephone 11,025 AM radio 22,050 FM radio 44,100 CD 48,000 DAT Dr. Deepa Kundur (University of Toronto) Audio DSP 46 56 Audio Digital Signal Processing Audio Quality Audio Quality, Sampling Rate, and Bit Depth Audio Quality as a Function of Sampling Rate, Bit Depth and StereoMonophony: Sampling Rate (Hz) Bit Depth StereoMono Quality 8,000 8 mono telephone 11,025 8 stereo low 22,050 8 stereo · 22,050 16 mono · 22,050 16 stereo · 44,100 16 mono good 44,100 16 stereo CD quality Dr. Deepa Kundur (University of Toronto) Audio DSP 47 56 Audio Digital Signal Processing Audio Quality Audio Quality Q: Why do some people insist that analog audio is superior to digital audio? A: What they think sounds good isn’t the exact original sound, but a nonlinearly distorted version generated from the analog components. Note: Some digital audio companies now make digital amplifiers that mimic the distortion from analog audio amplifiers. Quality of audio is a qualitative and psychological measure that is userspecific. Dr. Deepa Kundur (University of Toronto) Audio DSP 48 56Audio Digital Signal Processing Audio Equalizers Audio Equalization I Equalization ≡ Equalisation ≡ EQ I amplifying or attenuation different frequency components of an audio signal I Example: basstreble control in inexpensive car radios I Common goals of equalization: I provide fine granularity of frequency amplificationattenuation control without affecting adjacent frequencies. I correct for unwanted frequency attenuationamplification during recording processes I enhancing the presence of certain sounds I reducing the presence of unwanted signals such as noise Dr. Deepa Kundur (University of Toronto) Audio DSP 49 56 Audio Digital Signal Processing Audio Equalizers Equalizer Design Basics 1. Determine the processing band of your audio signal. I human audible range is: 20 Hz to 20 kHz I if sampling rate of a DSP is Fs then, the bandwidth of the audio signal to process is: 20 to F2s Hz I Example: Fs = 16; 000 Hz 1 8000 20 20 8000 Dr. Deepa Kundur (University of Toronto) Audio DSP 50 56 Audio Digital Signal Processing Audio Equalizers Equalizer Design Basics 2. Determine the granularity of your equalizer (i.e., number of frequency bands to independently control). I one approach might be to equally partition the audio signal bandwdith I more popular approaches suited to human auditory system models have bands that increase in width by two I Example: 3 frequency bands 8000 3000 1000 20 20 1000 3000 8000 Dr. Deepa Kundur (University of Toronto) Audio DSP 51 56 Audio Digital Signal Processing Audio Equalizers Equalizer Design Basics 3. Design your bandpass filters. I each bandpass filter is independently setcontrolled from the others I ideally, many people would like shelving EQ I Example: Ideal bandpass filters 1 8000 3000 1000 20 20 1000 3000 8000 Dr. Deepa Kundur (University of Toronto) Audio DSP 52 56Audio Digital Signal Processing Audio Equalizers Equalizer Design Basics 3. Design your bandpass filters. I each bandpass filter is independently setcontrolled from the others I ideally, many people would like shelving EQ I Example: Bell EQ 1 8000 3000 1000 20 20 1000 3000 8000 Dr. Deepa Kundur (University of Toronto) Audio DSP 53 56 Audio Digital Signal Processing Audio Equalizers Common Types of Equalizers I All bell filters and many other bandpass filters can be characterized by three parameters: I center frequency I width of the bell curve I gain (i.e. peak) of the bell curve 1 8000 3000 1000 20 20 1000 3000 8000 width peak amplitude center frequency Dr. Deepa Kundur (University of Toronto) Audio DSP 54 56 Audio Digital Signal Processing Audio Equalizers Common Types of Equalizers I Parametric Equalizers: the center frequency, passband width and peak amplitude can be independently selected for each filter I most powerful EQ, predominantly used for recording and mixing I Graphic Equalizers: the center frequency and passband width of each filter are preset; the gains of each filter can be independently controlled I used for live applications such as concerts Dr. Deepa Kundur (University of Toronto) Audio DSP 55 56 Audio Digital Signal Processing Audio Equalizers Common Types of Equalizers I Notch Filters: the passband width is small and fixed for each filter; center frequencies and gains are variable. I used in multimedia applicationsaudio mastering Dr. Deepa Kundur (University of Toronto) Audio DSP 56 56

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Audio DSP

Dr Deepa Kundur

University of Toronto

Sound

solid and plasma) composed of frequencies capable of being detected by ears

I Note: sound cannot travel through a vacuum

variations detected by the human ear

I Theamplitude, frequency and relative phase of the air pressure signal components determine (in part) the way the sound is perceived

Intro to Audio Signals Amplitude and Loudness

Sinusoids and Sound: Amplitude

I A ≡ volume

I F0 ≡ pitch (more on this )

I θ ≡ phase (more on this )

Intro to Audio Signals Amplitude and Loudness

Sound Volume

I the volume is an objective measure and does not have a one-to-one correspondence with loudness

I perceived loudness varies from person-to-person and depends on frequency and duration of the sound

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Music Volume Dynamic Range

Sinusoids and Sound: Frequency

I F0≡ pitch

I θ ≡ phase (more on this )

Intro to Audio Signals Frequency and Pitch

Pure Frequency

I A: A pure tonewith a singlepitch

note?

Tuning Forks

resonator It is usually made out of steel and resonates at a specific constant pitch which is a function of the length of the prongs

I Striking the tuning fork will produce the required sounds although initially there may be overtones that die out quickly

I A very common tuning fork used by musicians produces theA

note (F0= 440 Hz), which is international concert pitch used to tune orchestras

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Frequency and Pitch

signal components as:

xa(t) = Aej (2πF0 t+θ)

I Pitch is directly related to the frequency F0

audible range

Harmonically Related Frequencies and Pitch

Scientific Designation Frequency (Hz) k for F0 = 8.176

Harmonically Related Frequencies

xa,k(t) = A cos(2πkF0t + θ) or

xa, k(t) = Aej (2πkF0 t+θ)

periodic signals:

x (t) =

∞

X

X (k)ej (2πkF0 t)

Signature Sounds

I The notes arenot pure tones There are natural overtones and undertones that provide distinguishing signaturesthat can be viewed in the associated spectra

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Fourier Transforms of the Same Note

Instrument A

Instrument B

Tuning Fork

Human Audible Range

kHz

I Theupper limit decreases with age

I The audible frequency range is different for animals

Animal Audible Range

Species Approx Range (Hz)

Reference: R.R Fay (1988), Hearing in Vertebrates: A Psychophysics

Databook

Intro to Audio Signals Phase and Sound

Sinusoids and Sound: Phase

I F0≡ pitch

I θ ≡ phase

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Phase and Sound

x (t) =

−∞

X (f)ej 2πftdf

I |X (f )|: relative volume of a sinusoidal component

I ∠X (f ): relative phase of a sinusoidal component

Phase and Sound

signal in reverse

Phase and Sound

and

X (f ) = X∗(−f )

Phase and Sound

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Phase and Sound

I |X (f )| = |X (−f )| ⇒ the CTFT magnitudes for forward and

reverse sound signals are exactly thesame

I ∠X (f )6=∠X (−f ) ⇒ the CTFT phases for forward and reverse

sound signals aredifferent

sound contains very salient perceptual information much like for

images

Auditory Masking

affected by the presence of another (secondary) sound

I Simultaneous masking: thesecondarysound is heard at the same time as the primarysound

non-ideal signal processing

Audio Digital Signal Processing Analog and Digital Audio

Why Digitize Audio?

than those available for analog audio

storage requirements

and compact

Benefits of Digital Audio

distribution

I CDs, online stores such as iTunes, etc

I data files are distributed instead of physical media storing the information such as records and tapes

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Concerns about Digital Audio

distribution

I unlawful manipulation of recorded audio is difficult to detect

I piracy: unlawful copying and redistribution of copyrighted

content

Analog vs Digital Audio: Analog Audio System

Analog audio signal

Transmission/

Storage Loudspeaker

Transducer

(e.g., microphone)

I microphone: converts sound into an electrical signal;

air pressure → motion of conductor/coil → magnetic field → electrical signal

I loudspeaker: converts electrical signal into acoustic waves;

electrical signal → magnetic field → motion → air pressure

Analog vs Digital Audio: Analog Audio System

Analog audio signal

Transmission/

Storage Loudspeaker

Transducer

(e.g., microphone)

I associated circuits suffer from inherent noise (noise floor)

I capacitance and inductance of the circuits limit bandwidth, and resistance

limits amplitude

Analog vs Digital Audio: Digital Audio Chain

Analog audio signal

Digital audio signal

Transmission/

Storage D/A Converter

A/D Converter Error CorrectionCoding (ECC)

ECC Decoding

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Digitizing Audio

A/D Processing forTransmission/

Storage

D/A

Analog audio

input (from

microphone

transducer)

Bandlimited analog audio signal

Sampled data

output

Cts-time dst-amp

“staricase” signal

Digital signal {0100101}

Digital signal {01 1 0 01}

Audio DSP System

Antialiasing

Filter and HoldSample ReconstructionFilter

Digitizing Audio

Storage

D/A

Analog audio input (from microphone transducer)

Sampled data

output

Cts-time dst-amp

Audio DSP System Antialiasing

Anti-aliasing Filter:

components higher than half of the sampling frequency (to avoid

aliasing)

Digitizing Audio

t

2

-1 -2

-2 -4

t

1 2

-1 -2

0.5

-2 -4

x(t)

x[n]

-2

1

x[n]

-2

2

Input Signal

t

2

-1 -2

-2 -4

t

1 2

-1 -2

0.5

-2 -4

x(t)

n

x[n]

1

n

x[n]

2

Anti-aliased Signal

Digitizing Audio

Storage

D/A

Sampled data

output

Cts-time dst-amp

Audio DSP System

Antialiasing Filter and HoldSample ReconstructionFilter

Sample and Hold:

A/D converts and interprets the value as a digital

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Digitizing Audio

t

2

-1 -2

-2 -4

t

1 2

-1 -2

0.5

-2 -4

x(t)

x[n]

-2

1

x[n]

-2

2

Anti-aliased Signal

t

2

-1 -2

-2 -4

t

1 2

-1 -2

0.5

-2 -4

x(t)

x[n]

-2

1

x[n]

-2

2

Sampled Data Signal

anti-aliased signal

Digitizing Audio

Storage

D/A

Sampled data

output

Cts-time dst-amp

Digital signal

{0100101}

Audio DSP System

A/D:

part, through quantization of the amplitude

Digitizing Audio

t

2

-1 -2

-2 -4

t

1 2

-1 -2

0.5

-2 -4

x(t)

x[n]

-2

1

x[n]

-2

2

Sampled Data Signal

anti-aliased signal

t

2

-1 -2

-2 -4

t

1 2

-1 -2

0.5

-2 -4

x(t)

n

x[n]

1

n

x[n]

2

Digital Signal

sampled data signal

Digitizing Audio

Storage

D/A

Sampled data

output

Cts-time dst-amp

Digital signal

{0100101}

Digital signal

{01 1 0 01}

Audio DSP System

Processing for Transmission/Storage:

errors in the received/retrieved data symbols

the digital signal so that errors can be compensated for during decoding

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Error Correction Coding

N zeros

N ones

Q: How would you interpret receiving the following coded sequence (with possible error):

1 1 1 0 1 0 0 0 0?

1 1 1

| {z } 1

0 1 0

| {z } 0

0 0 0

| {z }

0

A: Decoding can make use of majority vote logic

Input Signal Bit Coded Sequence

Received Coded Seq Decoded Signal Bit

Digitizing Audio

Storage

D/A

Sampled data

output

Cts-time dst-amp

Digital signal

{01 1 0 01}

Audio DSP System

D/A:

further reconstruction

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Digitizing Audio

t

2

-1 -2

-2 -4

t

1 2

-1 -2

0.5

-2 -4

x(t)

x[n]

-2

1

x[n]

-2

2

Digital Signal

sampled data signal

t

2

-1 -2

-2 -4

t

1 2

-1 -2

0.5

-2 -4

x(t)

x[n]

-2

1

x[n]

-2

2

Staircase Signal

digital signal

sampled data signal

Digitizing Audio

Storage

D/A

Sampled data

output

Cts-time dst-amp

Audio DSP System

Reconstruction Filter:

lowpass filtering

anti-aliasing filter, or may be very cheap (e.g., compact disk receivers), or may using a different sampling rate for special effects

Digitizing Audio

t

2

-1 -2

-2 -4

t

1 2

-1 -2

0.5

-2 -4

x(t)

x[n]

-2

1

x[n]

-2

2

Staircase Signal

digital signal

sampled data signal

t

2

-1 -2

-2 -4

t

1 2

-1 -2

0.5

-2 -4

x(t)

n

x[n]

1

n

x[n]

2

Reconstructed Signal

anti-aliased signal

Digitizing Audio

The“quality” of digitizing audio is related to the following parameters:

of quantization levels)

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Digitizing Audio

Note: For the same cost, digital audio provides higher signal-to-noise

ratio or lower mean-square errorbetween the real sound and what is

recorded/played

circuits can be circumvented via error correction coding Thus,

Audio Quality and Sampling Rate

Audio Quality as a Function of Sampling Rate:

Sampling Rate (Hz) Quality Similar to

Audio Digital Signal Processing Audio Quality

Audio Quality, Sampling Rate, and Bit Depth

Audio Quality as a Function of Sampling Rate, Bit Depth and

Stereo/Monophony:

Sampling Rate (Hz) Bit Depth Stereo/Mono Quality

Audio Digital Signal Processing Audio Quality

Audio Quality

Q: Why do some people insist that analog audio is superior to digital audio?

nonlinearly distorted version generated from the analog components Note: Some digital audio companies now make digital amplifiers that mimic the distortion from analog audio amplifiers

Quality of audio is a qualitative and psychological measure that is user-specific

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Audio Equalization

I amplifying or attenuation different frequency components of an

audio signal

I Example: bass/treble control in inexpensive car radios

I provide fine granularity of frequency amplification/attenuation

control without affecting adjacent frequencies

I correct for unwanted frequency attenuation/amplification during

recording processes

I enhancing the presence of certain sounds

I reducing the presence of unwanted signals such as noise

Equalizer Design Basics

I human audible range is: 20 Hz to 20 kHz

I if sampling rate of a DSP is Fs then, the bandwidth of the audio signal to process is: 20 to Fs

I Example: Fs = 16, 000 Hz

1

8000

Audio Digital Signal Processing Audio Equalizers

frequency bands to independently control)

I one approach might be to equally partition the audio signal

bandwdith

I more popular approaches suited to human auditory system

models have bands that increase in width by two

8000 3000

1000

I each bandpass filter isindependently set/controlled from the others

I ideally, many people would likeshelving EQ

I Example: Ideal bandpass filters

1

8000 3000

1000

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I each bandpass filter is independently set/controlled from the

others

I ideally, many people would like shelving EQ

1

8000 3000

1000

Common Types of Equalizers

characterized by three parameters:

I center frequency

I width of the bell curve

I gain (i.e peak) of the bell curve

1

8000 3000

1000

width amplitudepeak

center frequency

I Parametric Equalizers: the center frequency, passband width and

peak amplitude can be independently selected for each filter

I most powerful EQ, predominantly used for recording and mixing

I Graphic Equalizers: the center frequency and passband width of

each filter are pre-set; the gains of each filter can be

independently controlled

I used for live applications such as concerts

I Notch Filters: the passband width is small and fixed for each filter; center frequencies and gains are variable

I used in multimedia applications/audio mastering

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