In principle you do not need to do any preprocessing if you perform a wavelet transform. But you need to be careful when interpreting the results. The wavelet transform is a beautiful tool to reveal the structure of your time series, but it is also a sensitive tool.

So regarding 1) - in case of a time series with a strong trend, you will see the effect on the wavelet transform of the singularities at both the beginning and the end of the time series. These actually carry the information about the trend in the time series, and if you are not interested in the trend they may be considered as 'boundary effects'', but if the trend is important, you have it captured by the wavelet transform. So the answer depends on what you want to know about your time series.

Regarding 1), I can hardly think of any reason to low-pass filter prior to wavelet transforming, perhaps if you want to see how well your filter performs;-), you could do this and see the effect of the filter on your wavelet transform of the time series. But wavelet transform performs localised band pass filtering so all the information about the time series is there for you to pick what you need.

More important than any possible preprocessing is 'post-processing' - that is deriving useful information from the wavelet transform. This is in general a non-trivial task.

In wavelet transform removal of trend or low pass filtering are the steps followed by different algorithms for certain applications. It is not a thumb rule that, you have to preprocess your signal before applying WT. For what applications you would like to apply WT? If you make your query elaborately i may give you appropriate steps to be followed.

Dear Ramesh!

Thanks for your answer, and your kind offer of helping me!

My problem is Affective computing,

Actually, i measured a temperature signal during a stimulus of three different phases (p1,p2,p3) and these phases are randomly performed by the participant , each of them takes 10 sec!

i wonder whether the temperature would consider as a good indicator of the stimulus (could be statistically significant to classify p1, p2,and p3)

in order to do that we transform the problem into classification problem (pattern recognition) , we should:

1- preprocess the signal,

2- get some features.

3-apply suitable classifier.

for preprocessinbg the signal , i found in literature that temperature signal has five main frequency bands that are relative to stimulus!

also, i found that wavelet analysis is a powerful tool than using bandpass filters !

so, i decided to try to apply wavelet to study the known frequency components of the temperature signal , however i am a very new student in that area ,

actually , in order to apply it i must clarify that:

1) i have each phase takes only 10 sec with 25 hz(250 samples only) --short signal.

2) and if i am interested on the pure effect of the phase , i need to study the last 5 sec (125 samples only)

3) moreover , i also need to study the transition effect of the phases like p1-p2,p2-p3,p2-p1,...and all the 9 transitions!

there are in literature : time features and frequency features:

so, if we use the wavelet to

1) study the five frequency bands for each phase, we could compare the power changes (peak ,and frequency ) between the three phases. ( in that case we need to make the continous wavelet with scales between ( frequencies bands) ...then try to study the time average power spectrum regarding to frequency and compare it between the different phases!

2) to decompose the signal into the five component signals using wavelet , and reconstruct the corresponding time domain signal for it , then use the frequency representation to extract frequency features, and use the time domain signal to extract time features and then use the classifier to see which component of teh temperature signal is more relevant to the stimulus!!

dear sorry for long mail!! that is my idea at all!

enas

Dear Enas,

Good to hear that you going to use the wavelet analysis in your study. It is recommended to normalize your time series before applying wavelet transformation. In other word, to compare the power spectra of a time series it is recommended to normalize the time series by subtracting the mean and dividing by the standard deviation of the original time series. Now you would have a zero mean and a unit variance. I don't think you need to perform any low-pass filtering. Actually, continuous wavelet transformation (CWT) applies a wavelet as a band pass filter to the time series. While the Discrete wavelet transformation (DWT) applies two filters; a low-pass and a high-pass filters. for more details you could read in the following publication (page 157):

4th European Conference of the International Federation for Medical and Biological Engineering 23 - 27 November 2008, Antwerp, Belgium (Google eBook).

Good luck in your research,

Mohamed,

Dear Mohamed thanks for your answer!

Actually i do not know how the continuous wavelet uses the signal characteristics like ( sampling frequency , maximum frequency).....i do not know where we should assign these information!

actually , i have a doubt about that till now i did not get it? where should i consider the signal characteristic when implementing CWT:

Please, let me know whether if the following is true or false

when i assign the scale range for CWT : scale_min:scale_step:scale_max

signal characteristics:

sample points=125

sampling frequency=25hz

interested frequency range=0.005hz to 2hz

so, by using morlet wavelet , scale=1/frequency,

i used min scale range=1/(2hz)=0.5

maximum scale range=1/(0.005)=200

and i do not know the best scale step?

is that correct or false ?

Note: i found in your attached article that the author used:

the smallest resolvable scale was chosen to be 1.936...as for morlet wavelet is the corresponding Nyquest frequency!

thanks,

enas

Dear Enas,

The CWT perform the transformation on the time series continuously with different scales and transition over the whole sampling points (125). Therefore, if you start from min scale 0.5 you have to approximate it to 2 to the power 0 and then 2^1 ..... and so on. Keep in mind the zero padding (i.e. you time series after transformation will be shorter than 125. scale 1.936 is around 2^1

sorry, I do not understand, Mohamed!

What is the rule of 2 to the power!!! and the relation of that with the scale? ?

The scales can be represented as fractional powers of two. Sorry for the confusion. Please read the following paper it will help you:

A Practical Guide to Wavelet Analysis

what i found in matlab that : the scale and frequency have a relation :

s=fc/(fa x delta), where fc is the center frequency of mother wavelet, fa is the signal frequency (interested frequency you want to study wavelet at) and delta is the signal sampling time: so,

if i have my signal has 25 HZ as sampling frequency and iam interested in 0.5 HZ to 2 HZ : so the scale range can be calculated as following :

1) know the center frequency of your mother wavelet ('cmor1-1') =1

2) delta=1/25

smin=1/(2x0.04)=12.5

smax=1/(0.5x0.04)=50

so scale range= 12.5 to 50

is that correct?

if correct , how can i choose the best scale increment!

take care i am speaking a bout continuous wavelet not discrete!

Dear Enas,

I am assuming the equation you have provided is correct. Therefore, your scales are correct. However, you could adjust these scale to make it to the nearest fractional power or just check the mat-lab toolbox if it will accept your calculated scales. For me, usually I use another code to perform the wavelet transform so I am not familiar with that toolbox.

what kind of wavelet are you using? if morlet, then, dt is important, z is important..it defines how big your gaussian envelope is..