Implementing basic high pass filter using difference equation

Question

For the following signal, I am trying to remove the gradual positive drift but retain the spikes using a high pass filter.

I am aware that I can use implement a high pass filter using difference equation. I am familiar with convolution, and I have implemented simple low pass filter using moving average and first order recursive filter in the past. But I am not sure how to use difference equation to implement a high order filter that fits this particular problem. I am looking for a simple starting point using difference equation that I can tweak around, and then maybe move toward something a bit more complicated.

Any starting point would be appreciated.

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I've tried difference equation $y[n] = \alpha y[n-1] + x[n] - x[n-1]$ posted on How to remove or filter the drift problem in measured Strain signal?, but I do not get the expected result. The signal can be found here as a Python list, and I chose $\alpha$ value to be 0.8.

Expected result,

Answer 1

I get the same thing you do. Another possibility is to just do a detrend on the data.

The top plot is your data, and the DC blocker approach.

The bottom plot is your data, and removing the straight line fit through your data.

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Python code

import matplotlib.pyplot as plt
import numpy as np
from scipy import signal
alpha = 0.9
b = [1,-1]
a = [1,-alpha]
dc_blocked_data = signal.lfilter(b,a,data)
plt.subplot(211)
plt.plot(data)
plt.plot(dc_blocked_data)
gradient,bias = np.polyfit(np.arange(0,len(data)),data,1)
estimate = gradient*np.arange(0,len(data))+bias
linear_subtraction = np.subtract(data,estimate)
plt.subplot(212)
plt.plot(data)
plt.plot(linear_subtraction)