What is the wavelet transform?
Q: What is the wavelet transform?
A: The wavelet transform is a time-frequency representation of a signal used for noise reduction, feature extraction or signal compression.
Q: How is the wavelet transform of continuous signals defined?
A: The wavelet transform of continuous signals is defined as an integral over all values of a function multiplied by a mother wavelet, where the parameters 'a' and 'b' denote the dilation and time shift respectively.
Q: What are dyadic discrete wavelet transforms?
A: Dyadic discrete wavelet transforms are discrete versions of the regular discrete wavelet transforms with frequency scale 'm', time scale 'k' and constant 'T'. They can be rewritten as an integral over all values of a function multiplied by an impulse characteristic filter which is identical to the mother wavelet for given m.
Q: What does "mother wavelet" refer to in this context?
A: In this context, "mother wavelets" refers to functions that are used in conjunction with other functions to form the basis for calculating a particular type of transformation (in this case, the Wavelet Transform).
Q: How does one calculate dyadic discrete Wavelets?
A: Dyadic Discrete Wavelets are calculated using an integral over all values of a function multiplied by an impulse characteristic filter which is identical to the mother wavelet for given m. Additionally, they require frequency scale m, time scale k and constant T as parameters.
Q: What do ‘a’ and ‘b’ represent when defining continuous Wavelets?
A: When defining continuous Wavelets, ‘a’ represents dilation while ‘b’ represents time shift.
