Filtering¶

Filtering is employed to remove unwanted frequency components from a given signal;

• lowpass filtering suppresses frequencies that are higher than a user-defined cut-off frequency (Freq1),
• highpass filtering allows frequencies that are higher than the cut-off frequency (Freq1) to pass through,
• bandpass filtering allows signals within a given frequency range (Freq1 to Freq2) bandwidth to pass through and
• bandstop filtering suppresses signals within the given frequency range (Freq1 to Freq2)-Note that Freq2 cannot be higher than 1/2 of the record's time-step frequency.

To create any of the above four filtering configurations, three classical infinite-impulse-response (IIR) filter types are available in gmspy: Butterworth, Chebyshev and Bessel filters.

In [1]:

import numpy as np
import matplotlib.pyplot as plt

import gmspy as gm

# %%
# load "ChiChi" records
ts, acc = gm.load_gm_examples("ChiChi")
dt = ts[1] - ts[0]


# %%
# ['lowpass', 'highpass', 'bandpass', 'bandstop']
# ['Butterworth', 'Chebyshev', 'Bessel']

colors = ["#037ef3", "#f85a40", "#00c16e", "#7552cc"]

fig, axs = plt.subplots(4, 1, figsize=(9, 12), sharex=True)
for i, b in enumerate(["lowpass", "highpass", "bandpass", "bandstop"]):
    ax = axs[i]
    ax.plot(ts, acc, c="gray", lw=1, label="origin", alpha=0.6)
    ax.hlines(0, np.min(ts), np.max(ts), lw=0.5, colors="k")
    ax.set_xlim(np.min(ts), np.max(ts))
    ax.grid(False)
    ax.set_ylabel("acceleration", fontsize=15)
    ax.tick_params(labelsize=12)
    ax.set_title(b, fontsize=15)
    for j, f in enumerate(["Butterworth", "Chebyshev", "Bessel"]):
        acc2 = gm.freq_filt(
            dt,
            acc,
            ftype=f,  # 'Butterworth', 'Chebyshev', 'Bessel'
            btype=b,  # 'lowpass', 'highpass', 'bandpass', 'bandstop'
            order=4,
            freq1=9,
            freq2=20,
            rp=3,
            plot=False,
        )
        ax.plot(ts, acc2, c=colors[j], lw=1, alpha=0.9, label=f"{f}")
axs[0].legend(fontsize=12, ncol=4, loc="center", bbox_to_anchor=(0.5, 1.35))
axs[-1].set_xlabel("Time (s)", fontsize=15)
plt.subplots_adjust(hspace=0.25)
plt.show()

import numpy as np import matplotlib.pyplot as plt import gmspy as gm # %% # load "ChiChi" records ts, acc = gm.load_gm_examples("ChiChi") dt = ts[1] - ts[0] # %% # ['lowpass', 'highpass', 'bandpass', 'bandstop'] # ['Butterworth', 'Chebyshev', 'Bessel'] colors = ["#037ef3", "#f85a40", "#00c16e", "#7552cc"] fig, axs = plt.subplots(4, 1, figsize=(9, 12), sharex=True) for i, b in enumerate(["lowpass", "highpass", "bandpass", "bandstop"]): ax = axs[i] ax.plot(ts, acc, c="gray", lw=1, label="origin", alpha=0.6) ax.hlines(0, np.min(ts), np.max(ts), lw=0.5, colors="k") ax.set_xlim(np.min(ts), np.max(ts)) ax.grid(False) ax.set_ylabel("acceleration", fontsize=15) ax.tick_params(labelsize=12) ax.set_title(b, fontsize=15) for j, f in enumerate(["Butterworth", "Chebyshev", "Bessel"]): acc2 = gm.freq_filt( dt, acc, ftype=f, # 'Butterworth', 'Chebyshev', 'Bessel' btype=b, # 'lowpass', 'highpass', 'bandpass', 'bandstop' order=4, freq1=9, freq2=20, rp=3, plot=False, ) ax.plot(ts, acc2, c=colors[j], lw=1, alpha=0.9, label=f"{f}") axs[0].legend(fontsize=12, ncol=4, loc="center", bbox_to_anchor=(0.5, 1.35)) axs[-1].set_xlabel("Time (s)", fontsize=15) plt.subplots_adjust(hspace=0.25) plt.show()