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FIDELITY POTENTIAL INDEX
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Calculation Method
Converting analog performance levels to a digital equivalent involves developing bit rate (sampling frequency) and bit depth (bits per sample) from the analog data.Since the sampling frequency for the CD format is 44.1 kHz - roughly double the highest frequency (20kHz) it can reproduce, the analog equivalent sampling frequency is calculated to be double the highest frequency that medium can deliver.
For the bit size figure, a 6dB difference in dynamic range is taken to be equal to 1 bit so an analog medium with a dynamic range of 60dB has an equivalent bit size to a 10 bit digital signal.
The bit depth times the sampling rate per second equals the number of bit per second the medium can deliver. This number divided by 100,000 for brevity is its Fidelity Potential Index.
How fully the fidelity potential of each medium is exploited by the format structure and electronics limitations could be covered only by an extremely drawn out discussion so here, briefly below is a very truncated list of caveats.
Formats and Specifications not included
Many formats both analog and digital were not included. Digital formats like Dolby ProLogic which are lossy (ie they drop bits and then try to re-construct the signal to make the signal more compact) are not included due to the a huge amount of guess work involved.We have not included frequency response and dynamic range figures for the digital formats - only their sampling frequencies and bit rates.
Column Descriptions
Bit Depth - a sample of the musical waveform at one point in time can be represented by one single byte of information. The resolution of this byte (the number of bits that it can have) dictates the dynamic range of the signal. The more bits, the greater the number of possible levels which means louder loud passages and quieter silences. The range of the dynamics in the music can be much better represented by a 24 bit system than an 8 bit system.Sampling Frequency - how often the bits are represented. The more often they are represented the higher the frequency they can represent. Sampling 2,000 times a second cannot represent a 5,000 Hz signal. A waveform must be represented by at least 2 data points per cycle so the minimum sampling frequency required to cover the highest level of human hearing (20,000Hz) would be 40 kHz.
Format Descriptions and Caveats
A sound signal starts out as an analog waveform - the original musical note - and finishes as an analog waveform - the sound that is reproduced for the listeners ears. The fidelity of a recording format is dependent not only on the raw ability of its core engine to capture high dynamic range and broad frequency response but on its ability to handle analog to digital conversions and processing of the recorded signal.The potential inherent in one medium does not guarantee sound quality superior over another medium of lower potential capability as music production standards vary immensely as does implementation of high standards of engineering in the recording and reproduction equipment.
Dynamic range is not signal to noise. Digital systems are inherently noise free. Any noise comes from their associated electronics, not their media. Analog systems, with their different types of mechanical noise (tape hiss, record ticks and pops) have a signal to noise level far smaller than their ultimate dynamic range.
Digital systems use various forms of filters in their recording and playback processes. These filters can introduce distortions in the audible frequency range. One of the most famous examples of this is the "brick wall" filters used above 20kHz on CDs. Early implementations of this introduced various phase anamolies down as far as 10kHz or even lower.
Commentary from the web
John:Of course, there are lots of ways to measure noise -- weighted, unweighted, and on phono recordings, whether you measure the pops of surface noise, or just the average.
I can give you ballpark estimates of dynamic range based on my experience. High quality vinyl LP: 60-65 db Average vinyl LP: 50-55 db cassette (excluding noise reduction) 45-50 db. Add 8-10 db with properly functioning noise reduction professional reel-to-reel quarter-inch 2-track 15ips: 60-70 db (depending on tape formulation) 78 rpm shellac: 30-40 cylinder (vertical modulation) perhaps 20-30 35 mm optical ("academy" cinema, pre-Dolby) 40-50 db
I have measured some of these -- reel-to-reel, vinyl test LPs. The others are what I would call educated estimates, based on what it sounds like to me over the years, in comparison to the other media.
I should give a heads-up for one of your caveats, in case you are not aware, that a numerical S/N figure, or a firm number on distortion, is not really possible on perceptually-based bit-compression schemes, such as mp3, ATRACS, Real Audio, Windows media, etc. These encoding systems will give near-perfect results on steady state tones, normally used to measure analog systems. They end up wrecking the signal depending on the complexity of the waveform. The idea behind these systems is an algorithm based on what in listening tests people could hear, and what would be "masked" by other sounds, based on spectral content from moment to moment. The encoder then throws away the data representing the parts that people supposedly will not miss. E.g. a 96 Khz mp3 file throws away more than 85% of the data of a CD quality 44.1 KHz stereo PCM datastream.
I am not aware of any reliable quantitative measurements of the quality of bit-compressed systems. They are all based on blind listening tests.
With strict uncompressed PCM, there is of course a direct mathematical correspondence to S/N radio and dynamic range.
Hope I have not belabored something you may already well know.
Best regards,
George
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