# What is the scaling function and wavelet function at wavelet analysis?

I'm trying to looking the meaning and functionality about scaling function and wavelet function at wavelet analysis. I have googling already. But I can't find and understand the meaning.

What does those affect to analysis? Does anyone help me to understand roughly?

• Why the down vote - the question was researched but not understood so an example could not be provided. – Barnaby May 6 '15 at 0:45

## 1 Answer

Wavelets are functions which are form by two resulting coefficients. The detail coefficient and the scale coefficient. From wikipedia Wavelets are defined by the wavelet function ψ(t) (i.e. the mother wavelet) and scaling function φ(t) (also called father wavelet) in the time domain.

The wavelet function is in effect a band-pass filter and scaling it for each level halves its bandwidth.

The scaling and detail basically divide the signal into two applying a high-pass filter resulting into the detail coefficients - (which is the highest level of the transform) and a low-pass filter which results in the scaling coefficients - (which is the lowest level of the transform). This coefficients are calculated for each frequency of the discrete wavelet.

used to for example to extract the deterministic part of a signal and the stockastic part of the signal. They are also used through different procedures to denoise via thresholding the coefficients.

• Thanks, did you mean that a way like this HH HL LH LL? Do you want talk to me the LL is called scaling function? how to corver the all spectrum when it was halved? – gmotree May 6 '15 at 1:43
• If you add the coefficients from the high and low filters (scaling and detail coefficients) you obtain the signal. The wavelet function divides the signal into two portions representing each a range from zero to 1/2 the frequency and from that to a Nyquish frequency level. – Barnaby May 23 '15 at 8:52
• wavelet function is a band-pass filter? How come? – quantum231 Mar 11 '17 at 23:54
• You can use a wavelet to extract the frequencies by which the wavelet segments the frequencies or you could threshole a signal by using wavelets as the wavelet will filter the signal into a clean signal. – Barnaby Mar 24 '17 at 21:01