PHY-2464 Physical Basis of Music Presentation 26 Sound Reproduction and Synthesis: Digital Reproduction Adapted in substantial part from Sam Matteson s Unit 4 Session 40 & 41 Sam Trickey April 18, 2005 Lay of the land - Digital recording uses the states of electronic switches to encode the amplitude of the waveform in a binary representation. This approach spectral sampling In digital recording a waveform is digitized by an analog- to-digital converter (ADC) a digital transducer. The digital data are stored on magnetic tape (DAT) or compact optical disk (CD) in coded form. Playback occurs via a digital-to to analog converter (DAC) Notice transducer reciprocity.
Write the number five. five. Did you write 5? You could have written V. What about? If you were Babylonian or Sumerian you might have written: A number is a quantity; the How many? of something. A numeral is a graphic representation of the number. V is the Roman Numeral for five. The Babylonians used clay and a stylus to record words and symbols in wedge writing, cuneiform.
There are ten Arabic numerals in our system of representing numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. How do we count higher than 9? Place value! 12034 = 1 x 10 4 + 2 x 10 3 + 0 x 10 2 + 3 x 10 1 + 4 x 10 0 The Babylonians had a sexagesimal (base 60) system Binary representation: There are 10 kinds of people: Those who understand binary representation, And those who don t.
Binary representation: In binary (base two) representation there are only two numerals: 0 and 1. The place value is a power of two: [101101] 2 = 1 x 2 5 +0 x 2 4 +1 x 2 3 + 1 x 2 2 + 0 x 2 1 + 1 x 2 0 = 32 + 0 + 8 + 4 + 0 + 1 = 45 The number Forty-five. What number is represented by [1110] 2? Fourteen Write the binary representation for thirteen. [1101] 2 The secret of digital electronics: Very clever arrangements of very dumb switches. A simple switch has two states only: On represented by 1 Off represented by 0 +3 Volts 0101
A binary numeral can be represented by an arrangement of switches - on =1, (high); off = 0 (low). 8: 10: 2: [1000] [1010] [0010] 2 10 0 Most Significant Bit (MSB) Voltage 0 1 0 Least Significant Bit (LSB) Digitization: the process of converting a waveform into a series of binary numerals that represent the amplitude of the signal at equal intervals of time. Analog Waveform Digitized Waveform Pressure Binary Coded Data [1000] 2 [0100] 2 [0010] 2 [0001] 2
Digitization fidelity depends upon Precision the binary word length. Sampling rate the number of encoding measurements per second. Word Length +3-4+5-5+6-5+4-4+3+1-3-2+2-1-2-2 1-0 -0-1 Sign bit 2 3 2 2 2 1 2 0 [11010] 2 =+(8+0+2+0)=+10 10011 00100 10011 00101 10101 00101 10100 00100 10011 10001 00011 00010 10010 00001 00100 00100 00001 00000 00000 00001 Digitization fidelity depends upon Precision the binary word length. Sampling rate the number of encoding measurements per second. Word Length +1 2+3-2+3-2+2-2+1-0-2-0+1-0-1-1 0-0 -0-0 Sign bit 2 2 2 1 2 0 [1010] 2 =+(0+2+0)=+2 1001 0010 1011 0010 1011 0011 1010 0011 1001 0000 1011 0000 1001 0000 0001 0001 0000 0000 0000 0000 0000
Digitization fidelity depends upon Precision the binary word length. Sampling rate the number of encoding measurements per second. Sampling Rate +3-4+5-5+6-5+4-4+3+1-3-2+2-1-2-2 1-0 -0-1 10011 00100 10011 00101 10101 00101 10100 00100 10011 10001 00011 00010 10010 00001 00100 00100 00001 00000 00000 00001 Digitization fidelity depends upon Precision the binary word length. Sampling rate the number of encoding measurements per second. Sampling Rate +3 +5 +6 +4 +3-3 +2 3 +2-2 1-0 Nyquist Criterion: The maximum frequency that can be represented is ½ the sampling rate. max = ½ R f max 10011 10101 10110 10100 10011 00011 10010 00010 00001 00000
Nyquist Criterion: The maximum frequency that can be represented is ½ the sampling rate. f max = ½ R The Standard Sampling Rate for CDs is 44.1 khz. What is the maximum audio frequency that can be recorded according to the Nyquist Criterion? f max = ½ R = ½ (44.1 khz) = 22.05 khz Fast, inexpensive, reliable Analog to Digital Converters are now available. ADC Integrated Circuit
The digitized signal is stored as states of a solid state memory: Flip-Flop Flop 01 01 The digitized signal is stored as states of an array of Flip-Flops. Flops. C 1 C 0 C 0 C 1 Parallel c = clock 1 0 0 1 C C C C 101 Serial 01 10 01 10
Much of the real estate on a microprocessor chip is used for solid state memory. Much of the real estate on a microprocessor chip is used for solid state memory.
Compact Disks store binary data in a non-volatile form pits pits that that are optically readable using a laser. In CDs the digitized waveform is stored along with a label that includes timing information in phase coding: a 1 is recorded whenever there is a change in the binary data stream. Compare LtoR: [1001100111101110] 2 [1001010100011001] phase [1 0 1 0 1 0 1 0]
A laser reads the pits: a pit scatters the light and the signal from a photodiode drops. Pit scatters light Lands reflect light into photodiode In Digital Theater Sound (DTS TM ) a digital code (SMPTE time stamp) synchronizes the film with an audio CD. (SMPTE: Society of Motion Picture and Television Engineers) SMPTE time stamp Synchronization Audio CD
Compact Disk: The CD is read multiple times (over-sampled) and read errors are corrected. The data are read in quickly and stored in a buffer, then clocked out at the audio standard sampling rate of 44.1 khz into a DAC for playback. Digital Input Input Buffer Phase Converter Digital-to to-analog Converter (DAC) Analog output Digital to Analog Conversion (DAC) 1 2 4 8 0001 0010 0100 1000 DAC (Concept) 1010 1101 0011
Electronic Digital-to to-analog Conversion 1 0 1 0 1 0 10 Input Number Output Voltage Electronic Digital-to to-analog Conversion 1 0 1 0 1 0 10 Input Number Output Voltage
Electronic Digital-to to-analog Conversion 1 0 1 0 1 0 10 Input Number Output Voltage MDI Acronym for Musical Instrument Digital Interface. nterface. MIDI is a control protocol that uses binary codes to remotely control electronic musical instruments. MIDI uses a current loop to communicate in which current flowing means 0 and no current means 1. 1. The Electronic wind instrument (EWI), Electronic Valve Instrument (EVI) and Electronic String Instrument (ESI) use MIDI for control.
MIDI (1982) sends, not a digitized wave form, but rather a binary coded performance message to control electronic instruments (synthesizers) & conventional ones (organs). Primary MIDI Out MIDI In Secondary MIDI Physical: A five pin connector labeled MIDI Out, MIDI In, or MIDI Thru. Communication is via current. MIDI Out MIDI In Communication via current: current = 0, no current = 1
MIDI Physical: A five pin connector labeled MIDI Out, MIDI In, or MIDI Thru. Communication is via current. MIDI Physical: A MIDI chain can be assembled with up to 64 channels: [0000] 2 to [1111] 2. MIDI Out MIDI Thru Channel 00 01 02 03 04
MIDI Coding: A MIDI command is a word of three 8-bit 8 bytes status byte and 2 data bytes. Example: Status Data Data [10010100] [00111100] [011111111]: {09, 04} Note on, Channel 04 {060} {255} C 4 Speed 255, (hardest) 100101 00001111 001111 0001111 01111 1111 MIDI command - a binary code that follows a prescribed syntax and grammar. Example: Status Data Data [10000100] [00111100] [011111111]: {08, 04} Note off, Channel 04 {060} {xxx} C 4 Irrelevant 100001 00001111 001111 0001111 01111 1111
MIDI Instruments: Electronic Wind Instrument (EWI; Nyle Steiner) originally analog. Sax fingering MIDI signals: Note, pressure, lip, touch http://www.patchmanmusic patchmanmusic.com/.com/nylesteinerhomepage.html MIDI Instruments: Electronic Valve Instrument (EVI); also Steiner
MIDI Instruments: Electronic String Instrument (ESI) Janos Warren Bond Electric Strad http://www.electronicstrad electronicstrad.co..co.uk MIDI Instruments: Gesture Instruments (GI)h The Glove Prof. Butch Rovan (U. N. Texas)
Summary: Digital recording uses the states of electronic switches to encode the amplitude of the waveform in a binary representation. In digital recording a waveform is digitized by an analog-to to-digital converter (ADC). The digital data are stored on magnetic tape (DAT) or compact optical disk (CD) in a coded form. Playback occurs via a digital-to to-analog conversion (DAC). Summary (continued): The two most important parameters for precision of digital encoding are word length and sampling rate. The maximum frequency that can be digitized is equal to ½ the sampling rate. Digital data can be processed serially, i.e. one bit after the other, or parallel, a word at a time.
Summary (concluded): MIDI is the acronym for Musical Instrument Digital Interface. nterface. MIDI is a control protocol that uses binary codes to control musical instruments remotely A current loop is used to communicate The Electronic wind instrument (EWI), Electronic Valve Instrument (EVI) and Electronic String Instrument (ESI) use MIDI for control. Conventional instruments can be controlled as well.