I am currently designing an alogirthm that is either based on Fourier Transform approach, or the Wavelet Transform Approach, or the combination of the two. Since Wavelet is new to me, I am having difficulty to decide which approach to take.
The system could be modelled as follows: between each time slot, we will be receving incoming data point, and we are supposed to analyze the frequency component from these incoming data point to see whether a problem has occur. There are two approach of this problem: Fourier Transform or Wavelet Transform.
The difference of two is explained by here :Difference between Fourier transform and Wavelets
It seems to me that, the only advantage Wavelet offers is that inaddition to having the frequency spectrum, it is also showing the time component such that it allows you to see at which time does this frequency peaks.
My question is: if we decide to aggregate the incoming data point for a certain time (say $[t_0, t_1]$), and then perform a FFT on those aggregated data. And because we already had the information that the frequency spectrum produced from FFt is for signal between $[t_0,t_1]$, given that we don't care at exactly what $t$ the problem occurs, does the Wavelet approach still offer any advantage over the Fourier?