5 ms·
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 o
by 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.