time frequency analysis

[ashayk]

Hi,

Apologies, I sent the email below already, but just thought I'd repost here for others. I'm hoping you might be able to provide an example of time-frequency analysis using wavelib. Thanks.

I've come across your wavelib project and it looks really cool. I'm not terribly familiar with wavelets outside of what I've used with Matlab for time-frequency analysis. I typically do this with STFT in C, but would like to see if I can use wavelib for that as well. I've looked through the demos, but didn't see anything immediately obvious with which I could do a spectral decomposition. Would you be able to provide me with some guidance on doing time-frequency analysis with wavelib? I'd very much appreciate the help.

Thanks,

--Alex

[rafat]

Hi Alex,

You'll have to use Continuous Wavelet Transform to perform time frequency analysis. Here is the wavelib example code using El Nino data.

https://github.com/rafat/wavelib/wiki/CWT-Example-Code

You can run the code in your browser here.

https://rafat.github.io/wavelib/index.html

Choose CWT -> Test Signals (El Nino Data) and then use the values from CWT example code to plot the time-scale , time-period and time-frequency plots.

Matlab also has a very good tutorial comparing STFT and CWT time-frequency analysis.

https://in.mathworks.com/help/wavelet/examples/time-frequency-analysis-with-the-continuous-wavelet-transform.html

Hope this helps. Let me know if there are any issues with running the code.

Rafat

On 6/18/18, ashayk notifications@github.com wrote:

Hi,

Apologies, I sent the email below already, but just thought I'd repost here for others. I'm hoping you might be able to provide an example of time-frequency analysis using wavelib. Thanks.

I've come across your wavelib project and it looks really cool. I'm not terribly familiar with wavelets outside of what I've used with Matlab for time-frequency analysis. I typically do this with STFT in C, but would like to see if I can use wavelib for that as well. I've looked through the demos, but didn't see anything immediately obvious with which I could do a spectral decomposition. Would you be able to provide me with some guidance on doing time-frequency analysis with wavelib? I'd very much appreciate the help.

Thanks,

--Alex

-- You are receiving this because you are subscribed to this thread. Reply to this email directly or view it on GitHub: https://github.com/rafat/wavelib/issues/10

-- https://rafat.github.io/#/

[journeytosilius]

Hi @rafat , thank you for this library ! I am also interested on doing some experiments with real time data, and trying to use the library. My problem is that I am not sure of the total of the outputs that the CWT gives.

when I run the demo I get this :

j              Scale          Period         ABS(w)^2        
0              0.250000       0.258261       0.044181        
1              0.297302       0.307126       1.140611        
2              0.353553       0.365236       22.612155       
3              0.420448       0.434341       236.000960      
4              0.500000       0.516522       750.555613      
5              0.594604       0.614251       272.558792      
6              0.707107       0.730472       65.406557       
7              0.840896       0.868683       661.907029      
8              1.000000       1.033044       1590.717326     
9              1.189207       1.228503       623.593524      
10             1.414214       1.460944       156.254372      
11             1.681793       1.737365       317.761119      
12             2.000000       2.066087       401.100893      
13             2.378414       2.457006       318.397824      
14             2.828427       2.921889       269.638035      
15             3.363586       3.474731       2.999744        
16             4.000000       4.132175       1579.680775     
17             4.756828       4.914011       4318.945007     
18             5.656854       5.843777       2501.997548     
19             6.727171       6.949462       566.284186      
20             8.000000       8.264349       636.197879      
21             9.513657       9.828023       603.262260      
22             11.313708      11.687555      201.174291      
23             13.454343      13.898923      257.993096      
24             16.000000      16.528698      301.898877      
25             19.027314      19.656046      349.147914      
26             22.627417      23.375109      321.394832      
27             26.908685      27.797846      514.251514      
28             32.000000      33.057397      638.538828      
29             38.054628      39.312091      322.292455      
30             45.254834      46.750219      157.413156      
31             53.817371      55.595693      311.426801      
32             64.000000      66.114793      392.982432      
33             76.109255      78.624183      148.883971      
34             90.509668      93.500438      203.412015      
35             107.634741     111.191386     435.336832      
36             128.000000     132.229587     469.408336      
37             152.218511     157.248366     343.498364      
38             181.019336     187.000875     180.679727      
39             215.269482     222.382771     65.307551       
40             256.000000     264.459174     69.525971       
41             304.437021     314.496731     78.369819       
42             362.038672     374.001750     92.867511       
43             430.538965     444.765542     124.686172      

Another edit, I see now that frequency is not included in the calculations.

[rafat]

cwt output w is a complex number . abs(w)^2 is the square of the absolute value.

On Wed, Oct 13, 2021 at 11:32 PM chromafunk @.***> wrote:

Hi @rafat https://github.com/rafat , thank you for this library ! I am also interested on doing some experiments with real time data, and trying to use the library. My problem is that I am not sure of the total of the outputs that the CWT gives.

when I run the demo I get this :

j Scale Period ABS(w)^2 0 0.250000 0.258261 0.044181 1 0.297302 0.307126 1.140611 2 0.353553 0.365236 22.612155 3 0.420448 0.434341 236.000960 4 0.500000 0.516522 750.555613 5 0.594604 0.614251 272.558792 6 0.707107 0.730472 65.406557 7 0.840896 0.868683 661.907029 8 1.000000 1.033044 1590.717326 9 1.189207 1.228503 623.593524 10 1.414214 1.460944 156.254372 11 1.681793 1.737365 317.761119 12 2.000000 2.066087 401.100893 13 2.378414 2.457006 318.397824 14 2.828427 2.921889 269.638035 15 3.363586 3.474731 2.999744 16 4.000000 4.132175 1579.680775 17 4.756828 4.914011 4318.945007 18 5.656854 5.843777 2501.997548 19 6.727171 6.949462 566.284186 20 8.000000 8.264349 636.197879 21 9.513657 9.828023 603.262260 22 11.313708 11.687555 201.174291 23 13.454343 13.898923 257.993096 24 16.000000 16.528698 301.898877 25 19.027314 19.656046 349.147914 26 22.627417 23.375109 321.394832 27 26.908685 27.797846 514.251514 28 32.000000 33.057397 638.538828 29 38.054628 39.312091 322.292455 30 45.254834 46.750219 157.413156 31 53.817371 55.595693 311.426801 32 64.000000 66.114793 392.982432 33 76.109255 78.624183 148.883971 34 90.509668 93.500438 203.412015 35 107.634741 111.191386 435.336832 36 128.000000 132.229587 469.408336 37 152.218511 157.248366 343.498364 38 181.019336 187.000875 180.679727 39 215.269482 222.382771 65.307551 40 256.000000 264.459174 69.525971 41 304.437021 314.496731 78.369819 42 362.038672 374.001750 92.867511 43 430.538965 444.765542 124.686172

j are the sample bins, scale is the scale result, period is the sampled period ... but what is ABS(w)^2 ?

Also, in the online test app we can get scale, frequency and period, but how do you get these separated outputs ? I have read the documentation pdf but I can't find how, any guidance would help ! Thank you very much

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[journeytosilius]

Thanks ! Just another couple of questions : can you confirm that to get frequency as in your online app, we do it like this :

        double Fb;
        double Fc = 0.8125;
        vector<double> frequency;

        for (int v = 0; v < N; ++v)
        {
            Fb = dt * Fc / wt->scale[v];
            frequency.push_back(Fb);
        }

Also, do you think I can thread the computation on C++ without much problems ? Thank you again !

[rafat]

This seems correct but it is better if you check the code to see if the numerators and denominators are accurate.

https://github.com/rafat/wavelib/blob/master/src/cwt.c

wave-function calculates period.

On Thu, Oct 14, 2021 at 5:42 AM chromafunk @.***> wrote:

Thanks ! Just another couple of questions : can you confirm that to get frequency as in your online app, we do it like this :

    double Fb;
    double Fc = 0.8125;
    vector<double> frequency;

    for (int v = 0; v < N; ++v)
    {
        Fb = dt * Fc / wt->scale[v];
        frequency.push_back(Fb);
    }

Also, do you think I can thread the computation on C++ without much problems ? Thank you again !

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[journeytosilius]

Hi @rafat, as far as I understand, following and comparing the test against the online app with "el nino" dataset, the results at wt->scale and wt->period are the Y / scale or period values. But how do you access the Z binned values present on your online app ? Sorry but I don't understand how are you getting the output, can't see it anywhere in the docs either. Then probably the frequency result is not correctly calculated either, since I am iterating over the entire N / X range ? Thank you very much