Please could anyone explain what is meant by the following, and how I can find this using MATLAB? Any help would be appreciated.
Statistical features of wavelet transform
Statistical features can be any statistical value like mean, entropy, power, power over frequency band. This statement means using a wavelet transform calculate statistical feature of signal.
An example of it would be like generating a wavelet transform for transient detection. Now transient is a jump in signal it can be from custom statistical feature like change_in_amplitude/change_in_frequency.
Related
I have been trying to implement these two filters in MATLAB:
Daubechies 4 undecimated wavelet 3.75 Hz e wavelet 7.5Hz
Daubechies 4 undecimated filter bank 7.5 Hz
I have massively researched the wavelet toolbox and I still can't figure out what is the correct implementation of the algorithm, as well as the definition of the cut-off frequencies.
Does someone have experience with this?
What I tried was:
movementOut = movementIn;
% Set Daubechies wavelet name.
wname = strcat('db',num2str(order));
% Compute the corresponding scaling filter.
daubechies=dbwavf(wname);
movementOut = filter(daubechies,1,coordinates_values);
%movementOut = filtfilt(daubechies,1,coordinates_values);
I tried both filter and filtfilt but the output result seems pretty much similar. I am processing Kinect Z data (varying from 4.5m to 1.0m and then again to 4.5m) but I don't seem to see any difference using wavelets. In state-of-art approaches, the db4 wavelets are being often used.
Doubts:
is this implementation correct?
how can I set the cut-off frequency?
how to implement the filter bank?
Thanks in advance.
It's not super clear to me what you want to do but you need to use wavelet filters in wavelet algorithms. Do you have the wavelet toolbox? It has good documentation!
Wavelet transforms do band-pass filtering, so you may want to use another algorithm for your purpose. To see what would be 3.75 Hz or 7.50 Hz in your signal, you can compute the upper and lower bounds, if you know the sampling rate of your input.
Have a look at this post, which provides some links to matlab scripts for fast wavelet transforms (a sequence of filtering and up-/downsampling combinations) you can use if you don't have the wavelet toolbox.
Mind you, the fast wavelet transform does use downsampling so it is not 'undecimated'. There are a number of ways to do that, in the wavelet toolbox, in WaveLab and other places (see this paper for an overview). Some more reading may be a good idea, the references in that paper should do the trick.
One final warning: the name db4 is sometimes used for the filters with 4 coefficients (2 vanishing moments), and sometimes for the filters with 4 vanishing moments (8 coefficients)! Google "Daubechies 4" and you'll find both.
I am currently looking into some image processing project and just wondering how to obtain the low, middle and high frequency components of an image? For example, as this picture showed (I got it from googling without detailed description how to obtained this picture, but presumably using some filtering).
Also, I came across this post of using discrete cosine transform (DCT), and it can help us to get the low and high frequency components of an image. Just wondering how to use DCT to get the middle frequency component?
Link of DCT
I also have very basic knowledge about filtering. I think there are also Gaussian high/low pass filters available to use. And also wavelet based filtering. Just wondering what are the differences between Gaussian, Wavelet and DCT based filtering? Which one should I use?
Typical steps would be:
use a Fourier Transform to bring the image into frequency domain
apply filtering by zero-ing out areas of the fft image
reverse the fourier transform to bring image back to spatial domain
This is a really good example of high/low/mid pass filters in frequency domain: http://paulbourke.net/miscellaneous/imagefilter/
You will want to use MatLab's built in fft our fast fourier transform function. Fourier transforms are an extremely powerful method to filter frequencies. http://www.mathworks.com/help/matlab/ref/fft.html has some great examples on how to use the fft. Once you find the frequencies that make up the image you can take out the undesired frequencies to fit and then reverse fourier transform to obtain the new image.
Am quite new to wavelet analysis as well as stackoverflow and would wold like some help. I am performing a spatio-temporal analysis of rainfall data.
With PCA, I can reduce the dimension of the rainfall data into a few leading modes, yielding EOFs (which explain spatial variability)
and principal components (explaining temporal variability).
I would like to perform a similar analysis with wavelets using Matlab Wavelet Toolbox. As of now, I am able to decompose a 2D data (spatial decomposition)
but unable to take into account the temporal variability in the data.
My first course of action has been to first compress the data with PCA and then perform wavelet decomposition of the leading modes in both the
spatial (EOFs) and temporal (PCs) domain.
I am wondering if this is the right way to perform such an analysis and would like suggestions as to how to proceed.
Thanks alot.
I was reading a report today which looked at measuring heat storage of a lake from temperature measurements where to reduce the the impacts of temperature fluctuations that can confound estimates of short-term changes in heat storage, a wavelet de-noising routine was used (daubechies 4 wavelet, single rescaling, min/max thresholds used on the wden function in the wavelet toolbox) where 2 levels of wavelet filtering was applied. This technique results in smoother temporal variations in water temperature, while preserving patterns of diurnal heat gain and loss.
From this description, consider that my temperature measurements are similar to
load sumsin;
s = sumsin;
plot(s);
How would I apply the techniques described using the wden functions in matlab.
Apologies for the vagueness of this post, but seeing as I am clueless on how to complete this task I would be very greatfull for some advice.
I assume you're talking about de-noising by thresholding the detail coefficients of the wavelet transform. wden does do this. You've not specified however whether it is hard or soft thresholding.
For not wanting to reproduce matlab's help here,
help wden
Will give you what you need on how to use the function. Given the information you've provided, and the assumption that soft thresholding is appropriate; (as it is with most methods except Donoho's Visushrink, referred to by wden as 'sqtwolog')
[s_denoised, ~, ~] = wden(s, 'minimaxi', 's', 'sln', 2, 'db4');
Should give you what you want. This does also assume you're not interested in the decomposed wavelet tree
I have some dynamic light scattering data. The machine pumps out the autocorrelation function, and a count-rate.
I can do a simple fit to the ACF
ACF = exp(-D*q^2*t)
and obtain the diffusion coefficient.
I want to obtain the same D from the power spectrum. I have been able to create a power spectrum in two ways -- from the Fourier transform of the ACF, and from the count rate. Both agree, but the power spectrum does not look like in the one in the books, so I'm not sure how to use it to work out the line width.
Attached is an image from a PDF that shows what you should get, and what I get from MATLAB. Can anyone make sense of whats going on?
I have used the code of answer #3 on this question. The resulting autocorrelation comes out exactly the same as
the machine gives me and
using MATLAB's autocorr command on the photoncount data.
Thank you for your time.
When you compute the Fourier transform from short sequences of data it often looks very noisy. There are a number of reasons for this. One reason is that the statistics of individual Fourier components are not Gaussian, and so averaging the spectra across multiple samples of data will only slowly improve the quality of the estimate.
Another causes of "noisiness" in empirical spectra behavior is that you are applying (to a finite data sample) a transform which involves a pathological sinc function and which assumes an infinite length signal. To diminish this problem, it helps to apply a "windowing-function" to your data before computing the Fourier transform. One of the more complicated but also more powerful windowing approaches is the use of so-called 'Slepian tapers'.
MATLAB conveniently implements well-known windows in functions such as hamming and hann.