# [discuss] How to detect a feeble singal with wavelet?

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#### dragon_boat

##### Junior Member level 1
with my minds in a haze .

model in matlab：

fs = 1000;
A = 3;
B =1;
f1 = 200;
fd = 30;
noise = 30;
t = 0:1/fs:5;
data_len = length(t);
u = A*cos(2*pi*f1*t) +B*cos(2*pi*(f1+fd)*t)+noise*rand(1,data_len);

#### dragon_boat

##### Junior Member level 1
now i want to find out the singal , fd , except fft,what about wavelet analysis?

#### dora

##### Full Member level 3
Hi dragon_boat

It seems to me that Fourier analysis are the best tool for solving your problem (as your signals of interest are sine waves)
The wavelets are best applicable for other kind of signals.
For are simple introduction of the wavelets you can search the google for ROBI POLIKAR + wavelet

Best Regards
dora

#### dragon_boat

##### Junior Member level 1
thanks for dora,but which kind of signals can be better solved using wavelet?

#### dora

##### Full Member level 3

This is the copy from an article 'WAVELETS AND THEIR USE'

Wavelets became a necessary mathematical tool in many investigations. They are used in those
cases when the result of the analysis of a particular signal1 should contain not only the list of its
typical frequencies (scales) but also the knowledge of the defnite local coordinates where these
properties are important. Thus, analysis and processing of diferent classes of nonstationary (in
time) or inhomogeneous (in space) signals is the main feld of applications of wavelet analysis . The
most general principle of the wavelet construction is to use dilations and translations. Commonly
used wavelets form a complete orthonormal system of functions with a finite support constructed
in such a way. That is why by changing a scale (dilations) they can distinct the local characteristics
of a signal at various scales, and by translations they cover the whole region in which it is studied.
Due to the completeness of the system, they also allow for the inverse transformation to be done.
In the analysis of nonstationary signals, the locality property of wavelets leads to their substantial
advantage over Fourier transform which provides us only with the knowledge of global frequencies
(scales) of the object under investigation because the system of the basic functions used (sine,
cosine or imaginary exponential functions) is defined on the infinite interval2. However, as we
shall see, the more general definitions and, correspondingly, a variety of forms of wavelets are
used which admit a wider class of functions to be considered. According to Y. Meyer [1], "the
wavelet bases are universally applicable: "everything that comes to hand", whether function or
distribution, is the sum of a wavelet series and, contrary to what happens with Fourier series, the
coeficients of the wavelet series translate the properties of the function or distribution simply,
precisely and faithfully."

But I am sure that you can find plenty of good information in this forum about wavelets ... just search

Best regards
dora

#### dragon_boat

##### Junior Member level 1
thanks very much!!

u are so a good-hearted man,thanks again.

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