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The Analog to Digital Conversion Process

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Artur D'Assumpção

on 19 March 2013

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Transcript of The Analog to Digital Conversion Process

The Analog to Digital Conversion Process Artur D'Assumpção mail: adassumpcao@gmail.com Introduction to
Music Production Week 2 Assignment Nowadays computers are used almost in every task, music is no exception.

Computers provided tools that allowed us to improve the process of music recording, production and distribution. Among many other advantages computers provided us: Better audio fidelity
Reliable storage
Sophisticated editing tools
Sophisticated processing tools
Better project management
Advanced collaboration tools
Seamless duplication
Easy distribution But how can we get sounds in the computer in the first place?

How can we get audio signals out of the real world into the "computer world"? Real world signals are referred to as Analog Signals.

The analog signal is a continuous signal that varies over time. Computer signals are referred to as Digital Signals.

The digital signal is a discrete signal that varies over time. Continuous signals have:
Infinite resolution, either in amplitude (y) and in time (x) Digital signals have:
Finite resolution, either in amplitude (y) and in time (x) Analog signals are continuous and have infinite resolution because all events in nature behave like this. Voltage
Current
Temperature
Velocity
SPL
etc. Digital signals are discrete and have finite resolution because computers have finite resources: Limited clock
Limited precision
Limited storage Examples: Real world signals are converted to computer signals through a process called Analog-to-Digital Conversion. The inverse process is called Digital-to-Analog Conversion. The Analog to Digital process is accomplished by a piece of hardware called the Analog-to-Digital Converter also known as the AD Converter! In audio applications this piece of hardware usually is included in the audio interface, but they can also come as separated units! But how exactly is this Analog-to-Digital conversion process accomplished by the AD Converter? Although it is similar we won't be covering the inverse process in this presentation! The AD Converter converts an Analog Signal to a Digital Signal through a process called Sampling. In lame terms, sampling is like taking several pictures of a signal, and storing these for later signal processing and recreation. The sampling process measures an audio signal several times a second and records each time the measured amplitude level. The amount of times a signal is measured each second is called Sampling Frequency or Sampling Rate. The precision that's used to measure and store a signal's amplitude is called Bit Depth. The Sampling Rate has a direct relationship with the maximum frequency you can can faithfully sample. The bigger the Sampling Rate is, the bigger is the range of frequencies you can sample faithfully. The Nyquist theorem says that you must sample a signal at least double the maximum frequency. So, what is the correct rate to sample an audio signal? So, if you want to sample a signal that has 10kHz as its maximum frequency, you must sample it at least 20 thousand times a second, or 20 kHz times a second, to be able to sample it faithfully. Example: Since the human hearing frequency range is about 22.05 kHz, to be able to sample an audio signal accurately we must use a sampling rate of 44.1 kHz. This is the reason why the Digital Audio CD standard adopted a sampling rate of 44.1 kHz/s There are other commercial and professional audio standards that use higher sampling rates, such as:
44.1 kHz - 88.2 kHz - 176.4 kHz
48 kHz - 96 kHz - 192 kHz This graduation/codification process is called Quantization. Because the digital precision is limited by the Bit Depth, each sample has to be properly graded. The Bit Depth has a direct relationship with the dynamic range of the audio being sampled. The bigger the Bit Depth is, the bigger is the Dynamic Range you can sample faithfully. The Bit Depth defines the amount of bits that are used to digitally codify and store a sample. The Digital Audio CD uses a 16 bit depth. Example: The picture on the left exemplifies how bit depth can influence the dynamic range of an image. Quantization Process Each sample is quantized by a binary word which size is defined by the Bit Depth size. If a Bit Depth of 16 bits is being used, then each sample is measured and quantized in a 16 bit size word. Example: Because precision is limited, the quantification process always introduces some errors! The bigger the Bit Depth used, the more negligible are quantification errors. The following table shows the relationship between the amount of bits used by each sample, the precision/resolution of the quantification process and the obtained dynamic range. So what's the best bit depth to use? Choosing Bit Depth will be always a tradeoff between audio quality (dynamic range), audio size and audio processing capacity! 16 bits - Standard Digital Audio CD distribution
16 bits - Professional Audio (low dynamic range)
24 bits - Professional Audio (good dynamic range)
32 bits - Professional Audio (best dynamic range) Common Bit Depth sizes and uses: What's the size of audio? Now that we know the Sample Rate and the Bit Depth it's fairly easy to calculate what's the size of audio! Here are a few examples of how much space a 1 second audio recording will take on your hardrive Sample Rate = 44.1 kHz and Bit Depth = 16 bits 44.100 samples * 1 second * 16 bits <=>
44.100 samples * 2 bytes <=> 88.200 bytes <=>
88.200/1024 = 86.13 Kbytes Here are a few examples of how much space a 1 second audio recording will take on your hardrive Sample Rate = 48 kHz and Bit Depth = 24 bits 48.000 samples * 1 second * 24 bits <=>
48.000 samples * 3 bytes <=> 144.000 bytes <=> 144.000 / 1024 = 140,6 Kbytes Here are a few examples of how much space a 1 second audio recording will take on your hardrive Sample Rate = 192 kHz and Bit Depth = 32 bits 192.000 samples * 1 second * 32 bits <=>
192.000 samples * 4 bytes <=> 768.000 bytes <=> 768.000 / 1024 = 750 Kbytes
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