4 ms·

I don't know enough about DSP to get into a debate about this, but I'm going to trust that Monty, who is one of the foremost experts on digital audio, is correc

I don't know enough about DSP to get into a debate about this, but I'm going to trust that Monty, who is one of the foremost experts on digital audio, is correct with what he's talking about. Plus the wikipedia article on the nyquist-shannon sampling theorem [0] suggests the same. 0: https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampli...

msandford 11y ago
http://parlos.tamu.edu/MEEN651/E4.pdf http://parlos.tamu.edu/MEEN651/E4.pdf Read page 3. It completely validates what I'm saying. Monty might be a really smart guy, and he might be worthy of lots of praise for a great many things. But in this particular very limited instance, he is not as correct as he could be. If all you can do is link me to the Wikipedia page about this, you're way out of your depth. I took multiple classes on this in college and I raised exactly this issue with my professors. They said that technically I was right, but in practice nobody samples at exactly the Nyquist rate (or even that close to it!) and it's really more of a guideline for the slowest sample rate you could possibly get away with, not the sample rate you should pick once you know your frequency content. Both Shannon and Nyquist were very smart and they've made a gigantic contribution to DSP. But knowing the phrases "Nyquist rate" and "2x the highest frequency" doesn't a signal processing expert make. You can read plenty more here too if you'd like to get more educated. http://www.wescottdesign.com/articles/Sampling/sampling.pdf http://www.wescottdesign.com/articles/Sampling/sampling.pdf Here's a snippet: "The theme of this paper can be summed up to this: the Nyquist rate isn’t a line in the sand that you can toe up to with complete safety. It is more like an electric fence or a hot poker; something that won’t hurt you if you keep your distance, but never something you want to saunter up to and lean against." I totally understand if you just want to argue on the internet and given that I don't have the same credentials or reputation that Monty does, feel free to disregard what I'm saying. But that doesn't make me wrong one iota. The truth isn't dictated with the folks with the proper credentials, the truth is and you have to try and figure out what it is.
- msandford 11y ago
  From the Wikipedia page that you linked to: The symbol T = 1/fs is customarily used to represent the interval between samples and is called the sample period or sampling interval. And the samples of function x(t) are commonly denoted by x[n] = x(nT) (alternatively "xn" in older signal processing literature), for all integer values of n. The mathematically ideal way to interpolate the sequence involves the use of sinc functions, like those shown in Fig 2. Each sample in the sequence is replaced by a sinc function, centered on the time axis at the original location of the sample, nT, with the amplitude of the sinc function scaled to the sample value, x[n]. Subsequently, the sinc functions are summed into a continuous function. A mathematically equivalent method is to convolve one sinc function with a series of Dirac delta pulses, weighted by the sample values. Neither method is numerically practical. Instead, some type of approximation of the sinc functions, finite in length, is used. The imperfections attributable to the approximation are known as interpolation error. You'll notice that it says "imperfections" and "interpolation error" both of which should lead you to recognize that this is an approximation, not perfection. Why? Because truly perfect reconstruction requires a sinc function, which is infinite in time. Want to play a CD back? OK, but first just wait forever for the sound to be reconstructed. Or instead you could build a non-causal system (causality means that it honors the arrow of time, non-causal systems do not) which has infinite, perfect knowledge of the future. With this handy device, you can then perfectly reconstruct the sampled signal. Oh, you don't have one? Bummer. Another snippet: Practical digital-to-analog converters produce neither scaled and delayed sinc functions, nor ideal Dirac pulses. Instead they produce a piecewise-constant sequence of scaled and delayed rectangular pulses (the zero-order hold), usually followed by an "anti-imaging filter" to clean up spurious high-frequency content. And there you go! Real life is approximations of theoretical perfection, not the equivalent. This is why people who do real work on real signals like to oversample.

msandford 11y ago

http://parlos.tamu.edu/MEEN651/E4.pdf http://parlos.tamu.edu/MEEN651/E4.pdf Read page 3. It completely validates what I'm saying. Monty might be a really smart guy, and he might be worthy of lots of praise for a great many things. But in this particular very limited instance, he is not as correct as he could be. If all you can do is link me to the Wikipedia page about this, you're way out of your depth. I took multiple classes on this in college and I raised exactly this issue with my professors. They said that technically I was right, but in practice nobody samples at exactly the Nyquist rate (or even that close to it!) and it's really more of a guideline for the slowest sample rate you could possibly get away with, not the sample rate you should pick once you know your frequency content. Both Shannon and Nyquist were very smart and they've made a gigantic contribution to DSP. But knowing the phrases "Nyquist rate" and "2x the highest frequency" doesn't a signal processing expert make. You can read plenty more here too if you'd like to get more educated. http://www.wescottdesign.com/articles/Sampling/sampling.pdf http://www.wescottdesign.com/articles/Sampling/sampling.pdf Here's a snippet: "The theme of this paper can be summed up to this: the Nyquist rate isn’t a line in the sand that you can toe up to with complete safety. It is more like an electric fence or a hot poker; something that won’t hurt you if you keep your distance, but never something you want to saunter up to and lean against." I totally understand if you just want to argue on the internet and given that I don't have the same credentials or reputation that Monty does, feel free to disregard what I'm saying. But that doesn't make me wrong one iota. The truth isn't dictated with the folks with the proper credentials, the truth is and you have to try and figure out what it is.

msandford 11y ago
From the Wikipedia page that you linked to: The symbol T = 1/fs is customarily used to represent the interval between samples and is called the sample period or sampling interval. And the samples of function x(t) are commonly denoted by x[n] = x(nT) (alternatively "xn" in older signal processing literature), for all integer values of n. The mathematically ideal way to interpolate the sequence involves the use of sinc functions, like those shown in Fig 2. Each sample in the sequence is replaced by a sinc function, centered on the time axis at the original location of the sample, nT, with the amplitude of the sinc function scaled to the sample value, x[n]. Subsequently, the sinc functions are summed into a continuous function. A mathematically equivalent method is to convolve one sinc function with a series of Dirac delta pulses, weighted by the sample values. Neither method is numerically practical. Instead, some type of approximation of the sinc functions, finite in length, is used. The imperfections attributable to the approximation are known as interpolation error. You'll notice that it says "imperfections" and "interpolation error" both of which should lead you to recognize that this is an approximation, not perfection. Why? Because truly perfect reconstruction requires a sinc function, which is infinite in time. Want to play a CD back? OK, but first just wait forever for the sound to be reconstructed. Or instead you could build a non-causal system (causality means that it honors the arrow of time, non-causal systems do not) which has infinite, perfect knowledge of the future. With this handy device, you can then perfectly reconstruct the sampled signal. Oh, you don't have one? Bummer. Another snippet: Practical digital-to-analog converters produce neither scaled and delayed sinc functions, nor ideal Dirac pulses. Instead they produce a piecewise-constant sequence of scaled and delayed rectangular pulses (the zero-order hold), usually followed by an "anti-imaging filter" to clean up spurious high-frequency content. And there you go! Real life is approximations of theoretical perfection, not the equivalent. This is why people who do real work on real signals like to oversample.