(Python) Verifying step size in time-series data

Question

Let's say I have a set of data that looks like the this. To my eye, there is a definite vertical "step size" to the signal, at least for the parts that ascend from 0 to max, and that descend from 0 to min. How best to determine that step size?

Of particular note is the fact that occasionally, the sampled value is between one well-defined step and the next, as happens in that first step up (values 474,000 between the step from 0 to 948,000).

Data in question:

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 474000, 474000, 948000, 948000, 948000, 948000, 948000, 948000, 948000, 948000, 948000, 948000, 1896000, 1896000, 1896000, 1896000, 1896000, 1896000, 1896000, 1896000, 1896000, 2844000, 2844000, 2844000, 2844000, 2844000, 2844000, 2844000, 2844000, 2844000, 2844000, 3796000, 3796000, 3796000, 3796000, 3796000, 3796000, 3796000, 3796000, 3796000, 4744000, 4744000, 4744000, 4744000, 4744000, 4744000, 4744000, 4744000, 4744000, 4744000, 4744000, 4744000, 5692000, 5692000, 5692000, 5692000, 5692000, 5692000, 5692000, 5692000, 5692000, 5692000, 6640000, 6640000, 6640000, 6640000, 6640000, 6640000, 6640000, 6640000, 6640000, 7592000, 7592000, 7592000, 7592000, 7592000, 7592000, 7592000, 7592000, 7592000, 7592000, 8540000, 8540000, 8540000, 8540000, 8540000, 8540000, 8540000, 8540000, 8540000, 9488000, 9488000, 9488000, 9488000, 9488000, 9488000, 9488000, 9488000, 9488000, 9488000, 9488000, 9488000, 8544000, 8544000, 7592000, 7592000, 6644000, 6644000, 5696000, 5696000, 4748000, 4748000, 4748000, 4748000, 3800000, 2848000, 2848000, 1900000, 1900000, 952000, 952000, 0, 0, 0, 0, -948000, -948000, -948000, -948000, -948000, -948000, -948000, -948000, -948000, -948000, -1896000, -1896000, -1896000, -1896000, -1896000, -1896000, -1896000, -1896000, -1896000, -2844000, -2844000, -2844000, -2844000, -2844000, -2844000, -2844000, -2844000, -2844000, -2844000, -3796000, -3796000, -3796000, -3796000, -3796000, -3796000, -3796000, -3796000, -3796000, -3796000, -4744000, -4744000, -4744000, -4744000, -4744000, -4744000, -4744000, -4744000, -4744000, -5692000, -5692000, -5692000, -5692000, -5692000, -5692000, -5692000, -5692000, -5692000, -5692000, -6640000, -6640000, -6640000, -6640000, -6640000, -6640000, -6640000, -6640000, -6640000, -6640000, -7592000, -7592000, -7592000, -7592000, -7592000, -7592000, -7592000, -7592000, -7592000, -8540000, -8540000, -8540000, -8540000, -8540000, -8540000, -8540000, -8540000, -8540000, -8540000, -9488000, -9488000, -9488000, -9488000, -9488000, -9488000, -9488000, -9488000, -9488000, -9488000, -9488000, -9488000, -8544000, -7592000, -7592000, -6644000, -6644000, -5696000, -5696000, -4748000, -4748000, -4748000, -4748000, -3800000, -3800000, -2848000, -2848000, -1900000, -1900000, -952000, -952000, 0, 0]

UPDATE I have some more problematic data now! As you can see, there are significant substeps for many of the steps now. I'm not sure this data lends itself well to analysis.

[0, 0, 0, 0, 0, 0, 0, 0, 3300000, 13860000, 13860000, 13860000, 13860000, 13860000, 13860000, 13860000, 13860000, 18150000, 27720000, 27720000, 27720000, 27720000, 27720000, 27720000, 35970000, 41580000, 41580000, 41580000, 41580000, 41580000, 41580000, 49830000, 49830000, 55440000, 55440000, 55440000, 55440000, 55440000, 65010000, 65010000, 69300000, 69300000, 69300000, 69300000, 69300000, 69300000, 69300000, 82170000, 83160000, 83160000, 83160000, 83160000, 83160000, 83160000, 97020000, 97020000, 97020000, 97020000, 97020000, 97020000, 98010000, 110880000, 110880000, 110880000, 110880000, 110880000, 110880000, 115500000, 124740000, 124740000, 124740000, 124740000, 124740000, 124740000, 124740000, 124740000, 132330000, 138600000, 138600000, 138600000, 138600000, 138600000, 138600000, 129030000, 118140000, 118140000, 105600000, 96030000, 96030000, 83160000, 69300000, 69300000, 58080000, 44880000, 32010000, 32010000, 22440000, 8580000, 8580000, -1980000, -13860000, -13860000, -13860000, -13860000, -13860000, -13860000, -13860000, -16830000, -27720000, -27720000, -27720000, -27720000, -27720000, -27720000, -34320000, -34320000, -41580000, -41580000, -41580000, -41580000, -41580000, -49170000, -49170000, -55440000, -55440000, -55440000, -55440000, -55440000, -55440000, -66660000, -66660000, -69300000, -69300000, -69300000, -69300000, -69300000, -69300000, -80190000, -80190000, -83160000, -83160000, -83160000, -83160000, -83160000, -97020000, -97020000, -97020000, -97020000, -97020000, -97020000, -98670000, -98670000, -110880000, -110880000, -110880000, -110880000, -110880000, -115500000, -115500000, -115500000, -124740000, -124740000, -124740000, -124740000, -124740000, -124740000, -130350000, -138600000, -138600000, -138600000, -138600000, -138600000, -138600000, -131010000, -131010000, -119460000, -108900000, -95370000, -95370000, -83160000, -69300000, -69300000, -57420000, -45870000, -45870000, -34320000, -21450000, -21450000, -21450000, -10890000, 0]

Answer 1

maybe that would help. Iterate over your data and extract each step. Then calculate all step sizes and the mean of them.

data = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 474000, 474000, 948000, 948000, 948000, 948000, 948000, 948000, 948000, 948000, 948000, 948000, 1896000, 1896000, 1896000, 1896000, 1896000, 1896000, 1896000, 1896000, 1896000, 2844000, 2844000, 2844000, 2844000, 2844000, 2844000, 2844000, 2844000, 2844000, 2844000, 3796000, 3796000, 3796000, 3796000, 3796000, 3796000, 3796000, 3796000, 3796000, 4744000, 4744000, 4744000, 4744000, 4744000, 4744000, 4744000, 4744000, 4744000, 4744000, 4744000, 4744000, 5692000, 5692000, 5692000, 5692000, 5692000, 5692000, 5692000, 5692000, 5692000, 5692000, 6640000, 6640000, 6640000, 6640000, 6640000, 6640000, 6640000, 6640000, 6640000, 7592000, 7592000, 7592000, 7592000, 7592000, 7592000, 7592000, 7592000, 7592000, 7592000, 8540000, 8540000, 8540000, 8540000, 8540000, 8540000, 8540000, 8540000, 8540000, 9488000, 9488000, 9488000, 9488000, 9488000, 9488000, 9488000, 9488000, 9488000, 9488000, 9488000, 9488000, 8544000, 8544000, 7592000, 7592000, 6644000, 6644000, 5696000, 5696000, 4748000, 4748000, 4748000, 4748000, 3800000, 2848000, 2848000, 1900000, 1900000, 952000, 952000, 0, 0, 0, 0, -948000, -948000, -948000, -948000, -948000, -948000, -948000, -948000, -948000, -948000, -1896000, -1896000, -1896000, -1896000, -1896000, -1896000, -1896000, -1896000, -1896000, -2844000, -2844000, -2844000, -2844000, -2844000, -2844000, -2844000, -2844000, -2844000, -2844000, -3796000, -3796000, -3796000, -3796000, -3796000, -3796000, -3796000, -3796000, -3796000, -3796000, -4744000, -4744000, -4744000, -4744000, -4744000, -4744000, -4744000, -4744000, -4744000, -5692000, -5692000, -5692000, -5692000, -5692000, -5692000, -5692000, -5692000, -5692000, -5692000, -6640000, -6640000, -6640000, -6640000, -6640000, -6640000, -6640000, -6640000, -6640000, -6640000, -7592000, -7592000, -7592000, -7592000, -7592000, -7592000, -7592000, -7592000, -7592000, -8540000, -8540000, -8540000, -8540000, -8540000, -8540000, -8540000, -8540000, -8540000, -8540000, -9488000, -9488000, -9488000, -9488000, -9488000, -9488000, -9488000, -9488000, -9488000, -9488000, -9488000, -9488000, -8544000, -7592000, -7592000, -6644000, -6644000, -5696000, -5696000, -4748000, -4748000, -4748000, -4748000, -3800000, -3800000, -2848000, -2848000, -1900000, -1900000, -952000, -952000, 0, 0]
sizes = []
pre_step = None
for x in data:
    if pre_step is None:
        pre_step = x
        continue
    else:
        if x == pre_step:
            continue
        else:
            sizes.append(abs(pre_step - x))
    pre_step = x
print("number of steps: " + str(len(sizes)))
vertical_step_size = sum(sizes) / len(sizes)
print("Mean vertical step size: " + str(vertical_step_size))

For the min/max-Phases you could use this idea.

sizes_zero_to_max = []
sizes_zero_to_min = []
pre_step = None
max = max(data)
min = min(data)
scan_max = True
scan_min = True

for x in data:
    if pre_step is None:
        pre_step = x
        continue
    else:
        if x == pre_step:
            continue
        else:
            if 0 < x <= max and scan_max:
                sizes_zero_to_max.append(abs(pre_step - x))
                if x == max:
                    scan_max = False
            if 0 > x >= min and scan_min:
                if x == min:
                    scan_min = False
                sizes_zero_to_min.append(abs(pre_step - x))
    pre_step = x
vertical_step_size_max_phase = sum(sizes_zero_to_max) / len(sizes_zero_to_max)
vertical_step_size_min_phase = sum(sizes_zero_to_min) / len(sizes_zero_to_min)

print("Mean vertical step size max phase: " + str(vertical_step_size_max_phase))
print("Mean vertical step size min phase: " + str(vertical_step_size_min_phase))