how to obtain a filtered signal by using scipy.signal.butter & lfilter?

Question

I have a program whose purpose is to filter a noisy signal using butterworth filter. the code is listed below. The program cannot be complied because I did something wrong at the last step "y = butter_bandpass_filter(v_numbers, lowcut, highcut, fs, order=6)". What i want to get are three plots: 1.input signal in time domain, 2. butterworth filter in frquency domain. 3. output filtered signal in time domain.

Can you help me solve the problem? Thank you.

from scipy.signal import butter, lfilter
def butter_bandpass(lowcut, highcut, fs, order=5):
nyq = 0.5 * fs
low = lowcut / nyq
high = highcut / nyq
b, a = butter(order, [low, high], btype='band')
return b, a


def butter_bandpass_filter(data, lowcut, highcut, fs, order=5):
b, a = butter_bandpass(lowcut, highcut, fs, order=order)
y = lfilter(b, a, data)
return y


if __name__ == "__main__":
import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import freqz

# Sample rate and desired cutoff frequencies (in Hz).

fs = 5000.0
lowcut = 0.0
highcut = 2000.0

# Plot the frequency response for a few different orders.
plt.figure(1)
plt.clf()
for order in [3, 6, 9]:
b, a = butter_bandpass(lowcut, highcut, fs, order=order)
w, h = freqz(b, a, worN=2000)
plt.plot((fs * 0.5 / np.pi) * w, abs(h), label="order = %d" % order)

plt.plot([0, 0.5 * fs], [np.sqrt(0.5), np.sqrt(0.5)],
         '--', label='sqrt(0.5)')
plt.xlabel('Frequency (Hz)')
plt.ylabel('Gain')
plt.grid(True)
plt.legend(loc='best')

# Filter a noisy signal.
T = 0.9004
nsamples = T * fs
t = np.linspace(0, T, nsamples, endpoint=False)
a = 0.02
f0 =600.0
# Plot the frequency response for a few different orders.
f = open('NIRS_data.txt','r')
number_string = f.readline()
v_numbers = []
while number_string != '':
numbers = number_string.split()
for number in numbers:

    v_numbers.append( number )
number_string = f.readline()

plt.figure()
plt.clf()
plt.plot(t,v_numbers, label = 'Noisy signal') 

y = butter_bandpass_filter(v_numbers, lowcut, highcut, fs, order=6)
plt.plot(t, y, label='Filtered signal (%g Hz)')
plt.xlabel('time (seconds)')

plt.show()

A part of txt file is shown below. The amount of datas is 4502.

8.2178200e-02 8.2173600e-02 8.2129400e-02 8.2209000e-02 8.2183000e-02 8.2098900e-02 8.2162500e-02 8.2157700e-02 8.2177900e-02 8.2177600e-02 8.2088400e-02 8.2142900e-02 8.2179600e-02 8.2159200e-02 8.2144800e-02 8.2139000e-02 8.2121200e-02 8.2157900e-02 8.2142600e-02 8.2190600e-02 8.2129500e-02 8.2125800e-02 8.2097500e-02 8.2087300e-02 8.2206800e-02 8.2175400e-02 8.2183300e-02 8.2197400e-02 8.2129500e-02 8.2101600e-02 8.2117800e-02 8.2125900e-02 8.2131300e-02 8.2107600e-02 8.2146900e-02 8.2122400e-02 8.2111800e-02 8.2156100e-02 8.2088500e-02 8.2135300e-02 8.2119700e-02 8.2100800e-02 8.2135700e-02 8.2126900e-02 8.2134000e-02 8.2111000e-02 8.2101600e-02 8.2108600e-02 8.2142900e-02 8.2091000e-02 8.2117700e-02 8.2061400e-02 8.2085200e-02 8.2080400e-02 8.2075400e-02 8.2064400e-02 8.2059700e-02 8.2098200e-02 8.2077200e-02 8.2138200e-02 8.2116300e-02 8.2092000e-02 8.2071900e-02 8.2092500e-02 8.2056900e-02 8.2108900e-02 8.2061300e-02 8.2064300e-02 8.2063900e-02 8.2120600e-02 8.2049500e-02 8.2087 300e-02 8.2066800e-02 8.2074900e-02 8.2052400e-02 8.2093200e-02 8.2061800e-02 8.2043700e-02 8.2070500e-02 8.2056900e-02 8.2084000e-02 8.2075900e-02 8.2065900e-02 8.2054200e-02 8.2037400e-02 8.2040600e-02 8.2085500e-02 8.2029000e-02 8.2057000e-02 8.2045700e-02 8.2112600e-02 8.2068000e-02 8.2034900e-02 8.2045200e-02 8.2046400e-02 8.2067300e-02 8.2080500e-02 8.2021400e-02 8.2047300e-02 8.2060200e-02 8.2042900e-02 8.2065200e-02 8.2056100e-02 8.1990900e-02 8.2055700e-02 8.2030300e-02 8.2103400e-02 8.2092600e-02 8.1995200e-02 8.2075300e-02 8.2001500e-02 8.2064000e-02 8.2033500e-02 8.2042800e-02 8.2037400e-02 8.2002000e-02 8.2057900e-02 8.2025100e-02 8.2038900e-02 8.2035200e-02 8.2005700e-02 8.2016700e-02 8.2012800e-02 8.1984900e-02 8.2066200e-02 8.2029600e-02 8.2027400e-02 8.2012200e-02 8.2009400e-02 8.2024900e-02 8.2038700e-02 8.2034700e-02 8.2016200e-02 8.1964500e-02 8.2019400e-02 8.2010500e-02 8.2004100e-02 8.2057500e-02 8.2052300e-02 8.2004500e-02 8.1998400e-02 8.2011600e-02 8.2038400e-0 2 8.2002500e-02 8.2005700e-02 8.2065900e-02 8.1991200e-02 8.2039900e-02 8.2028200e-02 8.2027000e-02 8.2021300e-02 8.2019600e-02 8.2032900e-02 8.2011700e-02 8.2017400e-02 8.2069400e-02 8.1998400e-02 8.2059400e-02 8.1958300e-02 8.1995800e-02 8.2018500e-02 8.1973400e-02 8.2008800e-02 8.1995900e-02 8.1989400e-02 8.1991800e-02 8.2000600e-02 8.2040400e-02 8.2035700e-02 8.1987800e-02 8.2027400e-02 8.2010800e-02 8.1991300e-02 8.1999400e-02 8.1926800e-02 8.2021100e-02 8.1967800e-02 8.1992600e-02 8.2022200e-02 8.1933100e-02 8.1998900e-02 8.2004300e-02 8.1991300e-02 8.2039500e-02 8.1998900e-02 8.2005400e-02 8.1997600e-02 8.1954500e-02 8.2000000e-02 8.1978000e-02 8.1990800e-02 8.1966200e-02 8.1997400e-02 8.2028700e-02 8.1957700e-02 8.2013700e-02 8.2052000e-02 8.1961400e-02 8.2007200e-02 8.1984800e-02 8.1999600e-02 8.2041800e-02 8.1990100e-02 8.2014500e-02 8.2008300e-02 8.1980400e-02 8.2000800e-02 8.1988200e-02 8.1979900e-02 8.2003400e-02 8.1921000e-02 8.1985600e-02 8.1995500e-02 8.1951000e-02 8.20 06500e-02 8.1977500e-02 8.2005200e-02 8.2000100e-02 8.1938300e-02 8.1993000e-02 8.1983800e-02 8.1995600e-02 8.1992500e-02 8.1976700e-02 8.2020400e-02 8.1986800e-02 8.1990200e-02 8.2007100e-02 8.1957500e-02 8.2021900e-02 8.1954900e-02 8.1995800e-02 8.1993800e-02 8.1992400e-02 8.1970100e-02 8.1989200e-02 8.1998800e-02 8.1991700e-02 8.1970500e-02 8.2000800e-02 8.1938300e-02 8.1965400e-02 8.1985000e-02 8.1930300e-02 8.1970600e-02

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the error is stated below.

Traceback (most recent call last): File "C:\\WinPython-32bit-2.7.5.3\\python learning files\\python 2.7 DSP\\read_the_input_signal_with_certain_frequency.py", line 65, in y = butter_bandpass_filter(v_numbers, lowcut, highcut, fs, order=6) File "C:\\WinPython-32bit-2.7.5.3\\python learning files\\python 2.7 DSP\\read_the_input_signal_with_certain_frequency.py", line 14, in butter_bandpass_filter y = lfilter(b, a, data) File "C:\\WinPython-32bit-2.7.5.3\\python-2.7.5\\lib\\site-packages\\scipy\\signal\\signaltools.py", line 565, in lfilter return sigtools._linear_filter(b, a, x, axis)

ValueError: data type must provide an itemsize

Thanks

Answer 1

In this part of the code:

f = open('NIRS_data.txt','r')
number_string = f.readline()
v_numbers = []
while number_string != '':
    numbers = number_string.split()
    for number in numbers:
        v_numbers.append( number )
    number_string = f.readline()

you haven't converted the fields to floating point values, so v_numbers is a list of strings. The error occurs when you call lfilter with this list.

You could change the call to append to

        v_numbers.append(float(number))

If each row in the file has the same number of fields, a better solution is to completely replace the code that reads the file with a call to np.loadtxt . That is,

v_numbers = np.loadtxt('NIRS_data.txt').ravel()