Wavelets vs disadvantages of Fourier Analysis and Synthesis?

[ramdas]

I am a beginner. The Fourier
series, Fourier Transform and it's
inverse play very important role in
Fourier Analysis and Fourier
Synthesis. I have read that Fourier
transform is localised in only
frequency domain.Also,it contains
information about the signal in
phase and frequency spectrum.
Every approach has advantages
and disadvantages.

My question is what are
disadvantages of

1.Fourier Analysis
and

2.Fourier Synthesis compared to wavelets?

 

[jvicens]

1. Disadvantages of Fourier Analysis:
- Requires the signal to be periodic, which may not always be the case in real-world signals.
- Does not provide time-localized information, meaning it cannot pinpoint when a particular frequency component occurs in a signal.
- The frequency resolution is limited by the length of the signal, which can lead to inaccuracies in the frequency spectrum.
- Can be computationally expensive for large or complex signals.

2. Disadvantages of Fourier Synthesis:
- Limited to reconstructing signals that can be represented by a finite number of sinusoidal components.
- Cannot handle non-periodic or non-stationary signals.
- Can introduce artifacts or distortions in the reconstructed signal if the number of components used is not carefully chosen.
- Requires knowledge of the exact frequencies present in the signal, which may not always be known.

Compared to Fourier analysis and synthesis, wavelet analysis and synthesis have the following advantages:
- Can handle non-periodic and non-stationary signals.
- Provides better time and frequency localization, allowing for more precise analysis and reconstruction of signals.
- Can adapt to the signal's characteristics, providing more accurate representation of the signal.
- Can be more computationally efficient for certain types of signals.

However, wavelet analysis and synthesis also have some disadvantages, such as:
- Can be more complex to understand and implement compared to Fourier analysis and synthesis.
- May require specific knowledge and expertise in choosing the appropriate wavelet and parameters for a given signal.
- The interpretation of the results may not be as intuitive as in Fourier analysis and synthesis.