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amylase

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**SHORT VERSION**

According to Nyquist's theory, if I want to digitally record a live opera and be able to reconstruct back to exactly the original sound quality, I have to sample at at least twice the frequency of the original signal.

(1) Am I right on this?

(2) But an opera has lots of different instruments and voices all at different frequencies. At twice of which frequency do we sample?

**LONG VERSION**

Nyquist's theory says if you want to sample something, and be able to reconstruct to get the original, then you have to sample at at least twice the frequency of the original signal.

For example assume there is a rather complex wave, which can be plotted on Y vs X axis, and its frequency is f.

Looking at the graph of this curve, it is made of a huge number of points on the X-Y plane. For example each X has a corresponding Y value.

Suppose I want to note down only some values of the curve, and hope I can reconstruct back to get the exact original complex wave from only the values I jotted down.

Imagine I walk along the x-axis and periodically I look at the Y value and I note it down.

How often do I have to record a Y value, in order for me to be able to later reconstruct the original complex wave exactly the way it is?

Ie. what should my minimum sampling rate be, in order to be able to reconstruct the original signal exactly, using my sampled values.

According to Nyquist's theory, if the original wave is of frequency f, then I have to sample at a frequency of at least 2f in order to be able to reconstruct back to original exact wave.

Am I right so far?

My second question is this: suppose that original complex wave is recording of an opera. It's going to have all sorts of instruments plus the singer. What do you call the frequency of this complex wave? It's going to be a wave complex as hell, what do you call its frequency? Do we break it down by Fourier Transformation and then deal with each component wave separately?

Thanks very much. Hope my two questions are clear. Firstly am I right about Nyguist's theory, and secondly what's the frequency of opera recording.

(Please note this is not home work. I know my questions might sound like home work but I assure you they are not. I don't get home work).