Created
October 12, 2016 21:59
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Simple and stupid signal and bandstop butterworth filter
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import numpy as np | |
import scipy | |
from scipy import signal | |
import matplotlib.pyplot as plt | |
freq1 = 60 # Hz | |
freq2 = 90 # Hz | |
sampling_rate = 1000 # samples per second | |
time = 1 # segundos | |
t = np.linspace(0, time, time * sampling_rate) | |
# sinal com as duas frequencias | |
y = np.sin(2*np.pi*freq1*t) + np.sin(2*np.pi*freq2*t) | |
# y + ruido | |
yn = y * 0.3 * np.random.rand(len(t)) | |
dt = 250 # faixa de observacao | |
# plot | |
plt.figure(tight_layout=True) | |
plt.subplot(811) | |
plt.plot(t[:dt], y[:dt]) | |
plt.title('y(t)') | |
plt.subplot(812) | |
plt.plot(t[:dt], yn[:dt]) | |
plt.title('yn(t)') | |
plt.grid() | |
plt.xlabel('t(s)') | |
# fft | |
Y = np.abs(np.fft.fft(y)) | |
Yn = np.abs(np.fft.fft(yn)) | |
f = np.arange(0, len(Y)) * sampling_rate/len(Y) | |
df = int(200 * len(y) / sampling_rate) | |
#fft plots | |
plt.subplot(813) | |
plt.plot(f[:df], Y[:df]) | |
plt.title('|Y(f)|') | |
plt.subplot(814) | |
plt.plot(f[:df], Yn[:df]) | |
plt.title('|Yn(f)|') | |
plt.grid() | |
plt.xlabel('f(Hz)') | |
# filter bandstop - reject 60 Hztop) | |
lowcut = 59 | |
highcut = 61 | |
order = 4 | |
nyq = 0.5 * sampling_rate | |
low = lowcut / nyq | |
high = highcut / nyq | |
b, a = signal.butter(order, [low, high], btype='bandstop') | |
y_filt = signal.filtfilt(b, a, y) | |
yn_filt = signal.filtfilt(b, a, yn) | |
plt.subplot(815) | |
plt.plot(t[:dt], y_filt[:dt]) | |
plt.title('y_filt(t)') | |
plt.subplot(816) | |
plt.plot(t[:dt], yn_filt[:dt]) | |
plt.title('yn_filt(t)') | |
plt.grid() | |
plt.xlabel('t(s)') | |
# fft | |
Y = np.abs(np.fft.fft(y_filt)) | |
Yn = np.abs(np.fft.fft(yn_filt)) | |
f = np.arange(0, len(Y)) * sampling_rate/len(Y) | |
df = int(200 * len(y_filt) / sampling_rate) | |
#fft plots | |
plt.subplot(817) | |
plt.plot(f[:df], Y[:df]) | |
plt.title('|Y(f) filered|') | |
plt.subplot(818) | |
plt.plot(f[:df], Yn[:df]) | |
plt.title('|Yn(f)| filered') | |
plt.grid() | |
plt.xlabel('f(Hz)') | |
plt.show() |
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