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Thread: Cross Correlation analysis with two series of wavelets
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    Default Cross Correlation analysis with two series of wavelets

    Hey all,

    This one will be a tough one to explain...

    I essentially have 3 columns of data and 40000+ rows of it. Column A measures seconds from time 0 to say 10. Column B is a series of values creating on a graph wavelets from a source detected by receiver one and Column C is the same series of wavelets detected by receiver two. The two receivers are relatively closely spaced apart and therefore the profiles of these waves will be very similar although NOT identical. The spacing between the wavelets also changes due to the density of the soil/rock they travel throughThe aim is for excel to detect the peaks of each correlating wave and detect the lag time between the two series at each source. An example of a lag between two wavelets is shown

    https://www.google.co.uk/search?q=wa...tm%3B365%3B152

    This lag time calculation (column 4!?) allows me to do all the statistical analysis for my job. The traditional way is to manually pick the peaks using ancient software but this simply isn't feasible with the amount of data I have.

    My VB ability is marginally better than just recording but only slightly.

    Please help!
    Sean

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    Default Re: Cross Correlation analysis with two series of wavelets

    show us the raw data that produces a wave - my first thought, if there is enough data, is to detect the max value and take the average of it and say 10 data values either side

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    Default Re: Cross Correlation analysis with two series of wavelets

    Seconds x1 x2
    0 -5.87E-05 -1.00E-04
    0.000417 -1.05E-05 -2.16E-05
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    0.0025 2.38E-06 -9.34E-06
    0.002917 2.43E-05 2.88E-05
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    0.00375 2.64E-05 4.24E-05
    0.004167 3.66E-05 5.96E-05
    0.004583 3.98E-05 7.17E-05
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    0.005417 5.28E-05 8.52E-05
    0.005833 5.39E-05 8.75E-05
    0.00625 5.18E-05 8.56E-05
    0.006667 5.28E-05 8.54E-05
    0.007083 5.40E-05 9.17E-05
    0.0075 5.90E-05 9.97E-05
    0.007917 1.08E-04 1.60E-04
    0.008333 1.45E-04 1.99E-04
    0.00875 1.39E-04 1.99E-04
    0.009167 1.36E-04 1.80E-04
    0.009583 1.30E-04 1.80E-04
    0.01 1.16E-04 1.54E-04
    0.010417 6.84E-05 7.92E-05
    0.010833 6.07E-05 6.89E-05
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    Default Re: Cross Correlation analysis with two series of wavelets

    I plotted the data and the peak from the last column is higher, but both peak widths are the same. What info would you like. I do not think it is possible to detect any lag between the peaks hitting a maximum because there are very few data points maybe 5 that define the peak

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    Default Re: Cross Correlation analysis with two series of wavelets

    Sorry my apologies, I pasted the top of the data then went home after work. The top of the data doesn't show anything really. This shows a bit more. Peak or trough is required. So in this data set the troughs would be appropriate

    3.495 0.003115 0.001985
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    3.557917 0.000319 -0.00176
    3.558334 0.000493 -0.00143
    3.55875 0.000688 -0.00102
    3.559167 0.000791 -0.00064
    3.559584 0.000846 -0.00024
    3.56 0.000862 0.000145
    3.560417 0.000833 0.000543
    3.560834 0.000738 0.000879
    3.56125 0.00056 0.001115
    3.561667 0.000355 0.001324
    3.562084 0.000147 0.001476
    3.5625 -7.3E-05 0.001586
    3.562917 -0.00027 0.001671
    3.563334 -0.00046 0.001679
    3.56375 -0.00065 0.0016
    3.564167 -0.00079 0.001485
    3.564584 -0.00087 0.00136
    3.565 -0.00092 0.001206
    3.565417 -0.00092 0.001057
    3.565834 -0.00089 0.000903
    3.56625 -0.00085 0.000769
    3.566667 -0.00079 0.000657
    3.567084 -0.00072 0.000595
    3.5675 -0.00064 0.000576
    3.567917 -0.00049 0.000638
    3.568334 -0.00021 0.000808
    3.56875 4.79E-05 0.000932
    3.569167 0.000385 0.001122
    3.569584 0.00077 0.001288
    3.57 0.001197 0.001422
    3.570417 0.001565 0.001463
    3.570834 0.001884 0.001503
    3.57125 0.002141 0.001604
    3.571667 0.002322 0.001716
    3.572084 0.002467 0.001869
    3.5725 0.002583 0.002053
    3.572917 0.00265 0.002205
    3.573334 0.002726 0.002355
    3.57375 0.002815 0.002467


    Is the kind of thing I'm looking for possible? Cheers for your reply

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    Default Re: Cross Correlation analysis with two series of wavelets

    I used conditional formatting to find all the minima in cols B and C using =and(b2
    are you interested in the time difference between each pair of minima or the minimum value itself

    PM me if you want to continue off line as I think there is nothing fundamental of interest to the general forum readers

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    MrExcel MVP shg's Avatar
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    Default Re: Cross Correlation analysis with two series of wavelets

    Uisng formulas, you can see that the correlation of the first 150 samples of W1 peaks with a 5-sample delay to W2:

    Row\Col
    A
    B
    C
    D
    E
    F
    G
    1
    T
    W1
    W2
    Offset
    2
    3.4950
    0.0031
    0.0020
    0
    0.825
    F2: =CORREL($B$2:$B$151, INDEX($C$2:$C$191, E2 + 1):INDEX($C$2:$C$191, E2 + 150))
    3
    3.4954
    0.0033
    0.0019
    1
    0.856
    4
    3.4958
    0.0034
    0.0019
    2
    0.882
    5
    3.4963
    0.0035
    0.0018
    3
    0.902
    6
    3.4967
    0.0036
    0.0017
    4
    0.916
    7
    3.4971
    0.0037
    0.0017
    5
    0.923
    8
    3.4975
    0.0037
    0.0017
    6
    0.921
    9
    3.4979
    0.0037
    0.0017
    7
    0.910
    10
    3.4983
    0.0036
    0.0017
    8
    0.890
    11
    3.4988
    0.0034
    0.0018
    9
    0.859
    12
    3.4992
    0.0032
    0.0019
    10
    0.819
    13
    3.4996
    0.0030
    0.0020
    11
    0.769
    14
    3.5000
    0.0027
    0.0020
    12
    0.710
    15
    3.5004
    0.0025
    0.0021
    13
    0.644
    16
    3.5008
    0.0024
    0.0021
    14
    0.570
    17
    3.5013
    0.0022
    0.0020
    15
    0.490
    18
    3.5017
    0.0021
    0.0019
    16
    0.405
    19
    3.5021
    0.0020
    0.0018
    17
    0.317
    20
    3.5025
    0.0019
    0.0016
    18
    0.226
    21
    3.5029
    0.0017
    0.0014
    19
    0.135
    22
    3.5033
    0.0015
    0.0011
    20
    0.044
    23
    3.5038
    0.0012
    0.0008
    21
    -0.045
    24
    3.5042
    0.0009
    0.0005
    22
    -0.130
    25
    3.5046
    0.0006
    0.0004
    26
    3.5050
    0.0002
    0.0002
    27
    3.5054
    -0.0003
    0.0000
    28
    3.5058
    -0.0008
    -0.0002
    29
    3.5063
    -0.0015
    -0.0004
    30
    3.5067
    -0.0021
    -0.0007
    31
    3.5071
    -0.0027
    -0.0009
    32
    3.5075
    -0.0033
    -0.0012
    33
    3.5079
    -0.0038
    -0.0014

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    MrExcel MVP shg's Avatar
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    Default Re: Cross Correlation analysis with two series of wavelets

    EDIT: For the first set of data, which has smaller time values, the correlation peak is at 0 offset. Maybe a better test is to see what time dilation of W1 is a best fit for W2. Does that make sense?

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    Default Re: Cross Correlation analysis with two series of wavelets

    shg, I've not tried this yet but this is EXACTLY what I'm looking for!! Makes perfect sense I'll get back to you

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    Default Re: Cross Correlation analysis with two series of wavelets

    Works perfectly! Thank you, you've no idea how much time I've spent trying to figure this out.

    What do you mean by time dilation? Do you mean the amount of time change between the two waves as if one was stretched? If so how would I go about this?

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