What is a wavelet?
Q: What is a wavelet?
A: A wavelet is a mathematical function used to write down a function or signal in terms of other functions that are simpler to study. It can be seen under the lens with a magnification given by the scale of the wavelet, allowing us to see only the information determined by its shape.
Q: Who introduced the term "wavelet"?
A: The English term "wavelet" was introduced in the early 1980s by French physicists Jean Morlet and Alex Grossman, who used the French word "ondelette" (which means "small wave"). Later, this word was brought into English by translating "onde" into "wave", giving us "wavelet".
Q: What must a wavelet satisfy for practical applications?
A: For practical applications, a wavelet must have finite energy and satisfy an admissibility condition. This admissibility condition states that it must have zero mean and also satisfy an integral over frequency which is less than infinity.
Q: What is meant by translation and dilatation when referring to wavelets?
A: Translation refers to shifting or moving of the mother wavelet along time axis while dilatation refers to scaling or stretching/shrinking of mother wavelets along time axis. These two parameters (translation & dilatation) are described by b & a respectively.
Q: What does it mean for a wavelet to have zero mean?
A: Zero mean implies that when integrating over all values of t from negative infinity to positive infinity, then sum should be equal to 0 i.e., ∫−∞∞ψ(t)dt=0 . This requirement follows from admissibility condition itself as mentioned above.
Q: How is mother wavelets defined?
A: Mother Wavelets are defined as normalized versions of translated (shifted) and dilated (scaled) version of original mother Wavelets which has parameters 'a' = 1 & 'b' = 0 .
