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## digital audio

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**In digital audio, the purpose of binary numbers is to**express the values of samples that represent analog sound. (contrasted to MIDI binary use)**characteristics of sound**ANALOG DIGITAL frequency (time based) sample rate (time based) = measured in hertz - samples per second measured in hertz - cycles per second**characteristics of sound**ANALOG DIGITAL sample rate (time) frequency (time) = quantization(level) amplitude (level) = measured in bits measured in decibel**characteristics of sound**analog-to-digital conversion : two steps (1) sampling (2) quantization**sampling theorem**• “A continuous audio signal can be replaced by a discrete sequence of samples without loss of any information and the original continuous audio signal can be reconstructed from the samples.”**When a digital recorder takes a sample, it takes a snapshot**of the audio waveform and turns it into bits that can be stored and manipulated. 010001111101100000110010011000001010010010100011111011000001100100110000010100100101000111110110000011001001100000101001001010001111101100000110010011000001010010010100011111011000001100100110000010100100101000111110110000011001001100000101001001010001111101100000110010011000001010010010100011111011000001100100110000010100100101000111110110000011001001100000101001001010001111101100000110010011000001010010010100011111011000001100100110000010100100101000111110110000011001001100000101001001 0100011111011000001100100110000010100100101000111110110000011001001100000101001001**sample rate**The frequency of the 'snapshots' of the audio stream in a single second Just as in measuring frequency, hertz is used to define the number of samples taken per second**flip cards**http://www.youtube.com/watch?v=xSrDnIVgVv0**flip cards**http://www.youtube.com/watch?v=Ql4Kkb-89D0**sample rate:**the number of samples (measurements) taken of an analog signal in 1 second**sample rate:**The sample rate determines the frequency range (bandwidth) of a system.**sample rate:**the number of samples (measurements) taken of an analog signal signal in 1 second The sample rate determines the frequency range (bandwidth) of a system. The faster the sample rate, the better the accuracy of getting a true picture of higher frequencies.**Some common sample rates are:**22,050 aka 22.05 kHz - 22,050 samples per second. A sample every 1/22,050 of a sec. 24,000 aka 24 kHz - 24,000 samples per second. A sample every 1/24,000 of a sec. 30,000 aka 30 kHz - 30,000 samples per second. A sample every 1/30,000 of a sec. 44,100 aka 44.1 kHz - 44,100 samples per second. A sample every 1/44,000 of a sec. 48,000 aka 48 kHz - 48,000 samples per second. A sample every 1/48,000 of a sec.**The higher the sample rate, the better the quality of the**sample. A sample taken at 44.1 kHz will contain twice the information as a sample taken at 22,050 kHz.**High sample rates are better at capturing high frequency**waveforms, but if you are sampling lower frequency sounds, such as kick drum, bass, etc.,...not as critical. you might consider sampling at the lower rate to save hard drive space.**NYQUIST THEORY**Named after a Bell engineer who worked on the speed of telegraphs in the 1920s**There must be two samples per period. In other words, the**sampling frequency must be at least twice the highest signal frequency recorded in order to be effective.**Sample rates with Nyquist yield**22,050 kHz = 11,025 kHz (Nyquist) 24,000 kHz = 12,000 kHz 30,000 kHz = 15,000 kHz 44,100 kHz = 22,050 kHz**It is therefore important to take into consideration the**highest frequency of the audio material to be recorded.**If a frequency of A-14,080 Hz is to be recorded, a sample**rate of 44.1 kHz would be the logical choice to use. 14,080 Hz falls within the range of the Nyquist of 44.1 kHz which is 22.05 kHz.**CD is 44.1 kHz**The choice of sample rate determines the audio bandwidth of the recorder used. Considering that the human hearing range at best ranges from 20 Hz to 20 kHz, a 44.1 kHz sample rate theoretically should satisfy most audio needs.**If a 25 kHz waveform is sampled at 44.1 kHz (which has a**Nyquist value of 22.05 kHz), the Nyquist rule is broken. 44 kHz - 25 kHz , results in a 19 kHz waveform which is heard as distortion. This is also known as aliasing or foldover.**- 2k**- 4k In audio: Alias is mirrored the same distance below the Nyquist frequency as the original was above it, at the original amplitude (foldover)**Once aliasing is introduced into the digital stream, it**can’t be removed. It must be stopped before entering the digital stream.**QUANTIZATION**The technique of measuring an audio event to form a numerical value. In digital audio, the values = voltages voltages represent amplitude the more bits, the more voltages that can be represented.**sample rate = frequency**quantization = amplitude gain staging (p. 133)**quantization error**The difference between the actual analog value at the sample time and the selected quantization interval value**The amplitude of the audio signal is broken down into a**series of discrete steps. Each step is then given a binary word that digitally encodes the level of the signal. The length of the digital word determines the quality of the representation.**etc**0111 1100 0110 0011 1000 0100 0010 0001 0000 4 bits 16 voltages**The larger the word, the better the quality (16 bit word**compared to an 8 bit word). The larger the bit word, the greater the headroom of the audio system (6 dB for every bit).**The more steps with which to describe the signal, the**smoother the result will be.**SAMPLE BITS**The more bits used to describe something, the better the clarity and fidelity An 8 bit sample contains 256 steps of information while a 16 bit sample contains up to 65,536 steps.**The bit resolution of a system defines the dynamic range of**the system. 6dB is gained for every bit signal to noise ratio (analog) signal to error ratio (digital)**8 bits equals 256 states = 48 dB**16 bits equals 65,536 states = 96 dB To find the dynamic range of a system, multiply the bit rate X 6.**In a 16 bit system, there are 65,536 different numbers, each**number representing a different analog signal voltage