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The problem with Fourier analysis arise with non-stationary signals. The frequency components in signals can be found with fourier techniques. But these techniques does not tell us at what times these frequency components occur? This is not a problem in stationary signals (signals whose frequency content do not change in time are called stationary signals). Because the answer is simply at all times. In non stationary signals we can use short time fourier transform but it has a time-frequency resolution problem. At this point wavelet transform solve our problem. A good intuitive reference for wavelet is hxxp://users.rowan.edu/~polikar/WAVELETS/WTpart1.html
Here you can find the answer of your question.
consider,u have 2 signals---- sin (2*pi*100*t) + sin (2*pi*200*t) ...the other isa time varying one with sin (2*pi*100*t) for 10 secs and then changes to sin (2*pi*200*t) from 10th second onwards..when we take fourier transform,
for the first signal and second signal,then we find that both have the same transform(i.e. impulse at the same frequencies.)so,even though they are different in time domain,they have same freq domain graph which is obsurd.so,to bring the time domain into picture,we go for wavelets,were we plot time,freq and amplitude simultaneously..
The Fourier series is meant for periodic signals..
i will explain using an example as robi Poliker does in his site:
First consider a stationary signal containing 100 and 200 hz ..
Then take its fourier .. u will get a spike at both these freq.. fine the story has a happy ending till now..
Now consider a non stationary signal with same two freq.. take its Fourier.. U will be perplexed to see that the transform is same except a minor diff that the width of the freq component is slightly more because implulse is ideal and not practical..
So for two diff signals we end up with same freq represenation.. here we need the time info also to distinguish the two.. there comes wavelet.
a signal containing a transitory frequency in other words for example the knocking sound of a valve in a running engine .when this signal is converted to the frequency domain the knocking sound dispaears.Because it's components will be averaged with all the rest of the NON TRANSITORY signals. So this INFORMATION DISAPEARS of sight ,or is no longuer localized!
Fourier transforms are great to analize standing signals .It means non transitory!
For Transitory analisis .Wavelet or even Join Time- Frequency analysis is required