Please see all my comments to the question. Read thoroughly.
Here is my advice: give up. You will save a lot of time and avoid great frustration. All tasks of audio comparison are extremely difficult. There are very few products which gets relatively close to such tasks, but only in a very narrow field of application. And you have no background just to understand what do you really want, set aside explaining it. Really, do something more realistic.
If you are interested to get basic understanding of the field, read the basic information on spectral analysis, Fourier transform:
http://en.wikipedia.org/wiki/Audio_spectrum#Sound[
^],
http://en.wikipedia.org/wiki/Spectrum[
^],
http://en.wikipedia.org/wiki/Fourier_analysis[
^],
http://en.wikipedia.org/wiki/Harmonic_analysis[
^],
http://en.wikipedia.org/wiki/Fourier_transform[
^],
http://en.wikipedia.org/wiki/Fft[
^].
Every fragment of sound has a spectrum which can be considered as a discreet spectrum consisting of a series with, in general case, infinite number of periodic members (like sine functions), but even this is only an approximation, which is strictly the case only for the sound of infinite duration. If the sound sample is limited in time, it can only be represented as an
continuous spectrum. In functional analysis, the set of the components which gives a general-case continuous function is not just infinite, it is considered as a point in a space of infinite number of dimensions (!). Of course, in "technical" spectral analysis, some reasonable approximations are used (which does not make the theory simple then with the ideal analysis; it makes it only more difficult). For example, there is no a practical need to consider frequencies not perceived but the human organs of hearing. Besides, it should be taken into account that the digital record has limited finite number of samples, but this is again, a complication of the theory, not simplification.
No sound record is one frequency. There is no a "frequency level". All measurable characteristics of a record should be carefully defined to make some sense. And the comparison of different but similar records is even more complex. Try to define it strictly (otherwise you cannot even talk in term of programming, a formal system), and you probably will be able to see how hard is that.
—SA
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