Digitizing an analog signal

Question

I have a array of CSV values representing a digital output. It has been gathered using an analog oscilloscope so it is not a perfect digital signal. I'm trying to filter out the data to have a perfect digital signal for calculating the periods (which may vary). I would also like to define the maximum error i get from this filtration.

Something like this:

Idea

Apply a treshold od the data. Here is a pseudocode:

for data_point_raw in data_array:
    if data_point_raw < 0.8: data_point_perfect = LOW
    if data_point_raw > 2  : data_point_perfect = HIGH

else:
    #area between thresholds
    if previous_data_point_perfect == Low : data_point_perfect = LOW
    if previous_data_point_perfect == HIGH: data_point_perfect = HIGH

There are two problems bothering me.

1. This seems like a common problem in digital signal processing, however i haven't found a predefined standard function for it. Is this an ok way to perform the filtering?
2. How would I get the maximum error?

Answer 1

Here's a bit of code that might help.

from __future__ import division

import numpy as np


def find_transition_times(t, y, threshold):
    """
    Given the input signal `y` with samples at times `t`,
    find the times where `y` increases through the value `threshold`.

    `t` and `y` must be 1-D numpy arrays.

    Linear interpolation is used to estimate the time `t` between
    samples at which the transitions occur.
    """
    # Find where y crosses the threshold (increasing).
    lower = y < threshold
    higher = y >= threshold
    transition_indices = np.where(lower[:-1] & higher[1:])[0]

    # Linearly interpolate the time values where the transition occurs.
    t0 = t[transition_indices]
    t1 = t[transition_indices + 1]
    y0 = y[transition_indices]
    y1 = y[transition_indices + 1]
    slope = (y1 - y0) / (t1 - t0)
    transition_times = t0 + (threshold - y0) / slope

    return transition_times


def periods(t, y, threshold):
    """
    Given the input signal `y` with samples at times `t`,
    find the time periods between the times at which the
    signal `y` increases through the value `threshold`.

    `t` and `y` must be 1-D numpy arrays.
    """
    transition_times = find_transition_times(t, y, threshold)
    deltas = np.diff(transition_times)
    return deltas


if __name__ == "__main__":
    import matplotlib.pyplot as plt

    # Time samples
    t = np.linspace(0, 50, 501)
    # Use a noisy time to generate a noisy y.
    tn = t + 0.05 * np.random.rand(t.size)
    y = 0.6 * ( 1 + np.sin(tn) + (1./3) * np.sin(3*tn) + (1./5) * np.sin(5*tn) +
               (1./7) * np.sin(7*tn) + (1./9) * np.sin(9*tn))

    threshold = 0.5
    deltas = periods(t, y, threshold)
    print("Measured periods at threshold %g:" % threshold)
    print(deltas)
    print("Min:  %.5g" % deltas.min())
    print("Max:  %.5g" % deltas.max())
    print("Mean: %.5g" % deltas.mean())
    print("Std dev: %.5g" % deltas.std())

    trans_times = find_transition_times(t, y, threshold)

    plt.plot(t, y)
    plt.plot(trans_times, threshold * np.ones_like(trans_times), 'ro-')
    plt.show()

The output:

Measured periods at threshold 0.5:
[ 6.29283207  6.29118893  6.27425846  6.29580066  6.28310224  6.30335003]
Min:  6.2743
Max:  6.3034
Mean: 6.2901
Std dev: 0.0092793

You could use numpy.histogram and/or matplotlib.pyplot.hist to further analyze the array returned by periods(t, y, threshold).

Answer 2

This is not an answer for your question, just and suggestion that may help. Im writing it here because i cant put image in comment.

I think you should normalize data somehow, before any processing.

After normalization to range of 0...1 you should apply your filter.