There should be a law against entities wasting the time and resources of the courts, such as this persistent RIAA filing suits against people before they even bother to gather the facts. This is a waste of the taxpayers' public institutions and personnel.
Doing a bit more reading, it seems what I was describing was a combination of aliasing and band-limitation.
The filtration used to solve aliasing itself indicates the signal is not being accurately represented.
Theory: Even if a speaker accurately displaced its position, reproducing the 16-bit digital amplitudes with their discrete, digital precision, the motion of the air molecules affected by this discrete movement would not be identical, and they would tend to 'round the edges' off these square digital amplitudes as they dissipated the energy imparted from inter-molecular collisions.
The Nyquist rate, or twice the highest frequency, is adequate for a signal that doesn't change. However, audio consists of a set of frequencies that are constantly changing, and this reduces the highest frequency that is accurately represented at a given sampling rate.
While I don't have any reference to give you, I find it a matter of common sense. If you sample a 1hz signal @ 2hz, you'll see consistent peaks & valleys, and the signal can be assumed almost immediately, after 3 samples (ignoring issues of quantized amplitude sensitivity over time). If you sample a 0.9hz signal @ 2hz, you'll see peaks & valleys alternating as before, but their amplitudes are both approaching zero, then cross zero, approach peak, and repeat. After analyzing this signal for a duration, you could assume it was a 0.9hz signal because of the relationship between the rate of amplitude change and the rate at which those amplitudes cross zero.. although this also assumes that you'd never see a 1hz signal simply increasing and decreasing amplitude at that same rate - considering this condition places stipulations on both frequency AND amplitude over time, whereas a 0.9hz signal only stipulates the frequency over time, we can only make a definitive assumption if we know the frequency doesn't change over time.
Hence, considering the frequencies are changing over time, we can't possibly accurately reconstruct an audio signal using a sample rate at twice the highest frequency, unless you get very lucky. As we consider a lower and lower highest frequency, our chosen sampling rate becomes more and more accurate, though I don't believe you ever reach perfect 100% reconstruction because of the irrational nature of true time-varying frequencies. One could, theoretically, calculate the accuracy of a given sampling rate for a given maximum frequency - I'm sure someone has at some point.
In fact you could analyze the typical audio signals that are digitized today, and develop some rough statistical analysis of how often a given frequency changes at a rate that could be interpreted as another frequency. This would likely vary depending on the individual frequency, the relative location within a song, and the musical genre. You could use these numbers to select an appropriate sampling rate to achieve N% accuracy of frequencies up to a X-hz maximum.
According to NIST http://www.epic.org/privacy/biometrics98.6% accuracy can be achieved with one fingerprint, 99.6% with two, and 99.9% with four or more fingers. Wonder how many fingers they're working with.
'For it to be sustainable, we should break even and make a little bit of money.' Yes, it'd be tragic if Citigroup provided a service that benefited millions of poor people and they'd have to pay for it.
I don't think any higher up (in organized government) would be dumb enough to order a hit this sloppy. Radioactive poisoning is a sloppy death for a nuclear plant operator. If someone simply wanted him dead, he would've been shot. That being said, seems either Putin or one of his cronies wanted to send a message, or an enemy of Putin wanted to make it appear as such.
I highly doubt someone found radiological contamination to be the most convenient method of murder.
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There should be a law against entities wasting the time and resources of the courts, such as this persistent RIAA filing suits against people before they even bother to gather the facts. This is a waste of the taxpayers' public institutions and personnel.
It could be useful to see a picture of all the turns when getting directions.
Doing a bit more reading, it seems what I was describing was a combination of aliasing and band-limitation. The filtration used to solve aliasing itself indicates the signal is not being accurately represented.
Theory: Even if a speaker accurately displaced its position, reproducing the 16-bit digital amplitudes with their discrete, digital precision, the motion of the air molecules affected by this discrete movement would not be identical, and they would tend to 'round the edges' off these square digital amplitudes as they dissipated the energy imparted from inter-molecular collisions.
The Nyquist rate, or twice the highest frequency, is adequate for a signal that doesn't change. However, audio consists of a set of frequencies that are constantly changing, and this reduces the highest frequency that is accurately represented at a given sampling rate.
While I don't have any reference to give you, I find it a matter of common sense. If you sample a 1hz signal @ 2hz, you'll see consistent peaks & valleys, and the signal can be assumed almost immediately, after 3 samples (ignoring issues of quantized amplitude sensitivity over time). If you sample a 0.9hz signal @ 2hz, you'll see peaks & valleys alternating as before, but their amplitudes are both approaching zero, then cross zero, approach peak, and repeat. After analyzing this signal for a duration, you could assume it was a 0.9hz signal because of the relationship between the rate of amplitude change and the rate at which those amplitudes cross zero.. although this also assumes that you'd never see a 1hz signal simply increasing and decreasing amplitude at that same rate - considering this condition places stipulations on both frequency AND amplitude over time, whereas a 0.9hz signal only stipulates the frequency over time, we can only make a definitive assumption if we know the frequency doesn't change over time.
Hence, considering the frequencies are changing over time, we can't possibly accurately reconstruct an audio signal using a sample rate at twice the highest frequency, unless you get very lucky. As we consider a lower and lower highest frequency, our chosen sampling rate becomes more and more accurate, though I don't believe you ever reach perfect 100% reconstruction because of the irrational nature of true time-varying frequencies. One could, theoretically, calculate the accuracy of a given sampling rate for a given maximum frequency - I'm sure someone has at some point.
In fact you could analyze the typical audio signals that are digitized today, and develop some rough statistical analysis of how often a given frequency changes at a rate that could be interpreted as another frequency. This would likely vary depending on the individual frequency, the relative location within a song, and the musical genre. You could use these numbers to select an appropriate sampling rate to achieve N% accuracy of frequencies up to a X-hz maximum.
No, apparently we're here.
Considering Windows 2000 will continue to receive security updates through July 2010, I can't think of anything.
According to NIST http://www.epic.org/privacy/biometrics 98.6% accuracy can be achieved with one fingerprint, 99.6% with two, and 99.9% with four or more fingers. Wonder how many fingers they're working with.