Difference between revisions of "Wavelet"
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Intuitive explanation of wavelet transform | Intuitive explanation of wavelet transform | ||
| − | Before trying to understand wavelets, | + | Before trying to understand wavelets, consider what a Fourier transform does. It decomposes a signal into its frequency components. A big downside is that the temporal information of the time-domain signal is encoded indirectly in the phase of the frequency-domain signal. It is well known that phase information in this form is difficult to interpret. |
| − | signal into | + | Imagine that I have with me an audio signal of a song, and I want to find out what note is being played at what instant. If I use a Fourier transform, I get frequency characteristics for the entire signal. There's nothing I can directly say about any time instant. How to get out of this |
| − | information of the time-domain signal is encoded indirectly in the phase of the frequency- | ||
| − | domain signal. It is well known that phase information in this form is difficult to interpret. | ||
| − | Imagine that I have with me an audio signal of a song, and I want to find out what note is being | ||
| − | played at what instant. If I use a Fourier transform, I get frequency characteristics for the entire | ||
| − | signal. There's nothing I can directly say about any time instant. How | ||
problem? | problem? | ||
| − | One solution is to break my signal into windows of fixed-sized duration, and then apply my | + | |
| − | Fourier transform there. This is called Short-time Fourier transform (STFT). | + | One solution is to break my signal into windows of fixed-sized duration, and then apply my Fourier transform there. This is called Short-time Fourier transform (STFT). With this you essentially get frequency characteristics for time intervals (rather than instants). |
| − | get frequency characteristics for time intervals (rather than instants). | ||
==References== | ==References== | ||
[[Category: Physics]] | [[Category: Physics]] | ||
Latest revision as of 21:11, 30 March 2023
Full Title or Meme
Context
Intuitive explanation of wavelet transform
Before trying to understand wavelets, consider what a Fourier transform does. It decomposes a signal into its frequency components. A big downside is that the temporal information of the time-domain signal is encoded indirectly in the phase of the frequency-domain signal. It is well known that phase information in this form is difficult to interpret. Imagine that I have with me an audio signal of a song, and I want to find out what note is being played at what instant. If I use a Fourier transform, I get frequency characteristics for the entire signal. There's nothing I can directly say about any time instant. How to get out of this problem?
One solution is to break my signal into windows of fixed-sized duration, and then apply my Fourier transform there. This is called Short-time Fourier transform (STFT). With this you essentially get frequency characteristics for time intervals (rather than instants).
