The following copy of email messages from one of the user:
Dear Sirs,

Congratulations for the excellent page

I have 3 questions

1.Any periodically repeating wave - however complex its shape is - can be resolved into sine and cosine waves. okay. It is possible to resolve any complex shaped signal similarly into sines and cosines, even if it is not periodically repeating - considering wave length as infinity and approximating..
Now consider a recorded wave form of a song (amplitude vs time) lasting say 5 minutes. This wave when resolved into component sines and cosines shall contain a lot of harmonics. Each with its specific frequency. If all the important components are selected and replayed the sound produced will be an approximate reproduction of the original sound. This is done posteriori.
Now consider a small intervel of time. say one second. after say 2 minutes from the start. The portion of the signal in this small duration if seperately considered and resolved (done in the current running time) the condition of the constituent harmonics will be same as that of the original signal of 5 minute duration considered for this particular one second.

But while we do this, we donot know what is going to happen after say the 3rd minute. But the happenings after the 3rd minute (or all the instants after the 2nd minute and one secondth instant) decide what should be shape of this particular one second - being part of the larger 5 minute duration. There is an apparent anomaly of having the future already getting fixed or a future event determining the present condition. What is the wrong in this argument?
Please check out the following URL :[url=]Fourier Analysis of Time Series[/url]

It is just a superposition of linear signal. For different time interval, the sume of the contribution is not the same. It is a relation between two different representations.  It is not one of them determined another one.

2. High level languages like Basic etc. have words for sound. But can, at a time, produce only one sound of only one frequency. A complex wave after resolving into its components can be heard faithfully only if the multiple frequencies weighted with its respective amplitudes are heard simultaneously. In your programme how it is achieved?
The program was written many years ago with JDK1.0.2.  At the time, it was an undocumented java library (I found out how to generate single frequency sound with java code from the web. However, I can not remember where I found it).

3. The amplitude Vs time wave form of a song (vocal) if resolved into components, will contain what range of harmonics?
Thanking you,
Mathematically, there are infiniite number of possible frequency. However, we can not hear it if it's requency is not within 20Hz-20000Hz.