[Python3] Octave-Band and Fractional Octave-Band filter. For signal in time domain.
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José Manuel Requena Plens 3b5bcbe146

# PyOctaveBand

Octave-Band and Fractional Octave-Band filter. For signal in time domain.

### Public Methods

##### octavefilter

The function that filters the input signal according to the selected parameters.

``````x # signal
fs # sample rate
fraction # Bandwidth 'b'. Examples: 1/3-octave b=3, 1-octave b=1, 2/3-octave b = 3/2. [Optional] Default: 1
order # Order of Butterworth filter. [Optional] Default: 6.
limits # Minimum and maximum limit frequencies. [Optional] Default [12,20000]
show # Boolean for plot o not the filter response.
sigbands # Boolean to also return the signal in the time domain divided into bands. A list with as many arrays as there are frequency bands

# Only octave spectra
spl, freq = octavefilter(x, fs, fraction=1, order=6, limits=None, show=0, sigbands=0)

# Octave spectra and bands in time domain
spl, freq, xb = octavefilter(x, fs, fraction=1, order=6, limits=None, show=0, sigbands=1)
``````
##### getansifrequencies

Returns the frequency vector according to ANSI s1.11-2004 and IEC 61260-1-2014 standards.

``````fraction # Bandwidth 'b'. Examples: 1/3-octave b=3, 1-octave b=1, 2/3-octave b = 3/2.
limits # Minimum and maximum limit frequencies. [Optional] Default [12,20000]
freq = getansifrequencies(fraction, limits=None)
``````
##### normalizedfreq

Returns the normalized frequency vector according to ANSI s1.11-2004 and IEC 61260-1-2014. Only for octave and third octave bands.

``````fraction # Bandwidth 'b'. For 1/3-octave b=3 and b=1 for one-octave.
freq = normalizedfreq(fraction)
``````

### The filter

The filter used to design the octave filter bank is a Butterworth with SOS coefficients. You can find more information about the filter here: scipy.signal.butter.

### Frequency values

The values of the center frequencies and the upper and lower edges are obtained with the calculation defined in the ANSI s1.11-2004 and IEC 61260-1-2014 standards.

### Automatic downsampling

To obtain the best filter coefficients, especially at low frequency, it is necessary to downsampling, this is done automatically by calculating the necessary downsampling factor for each frequency band.

``````fs # sample rate
freq # frequency
factor = ((fs / 2) / freq)
``````

The resampling is done with the resample function of the SciPy library (Thanks to @ashley-b - ISSUE) :

``````x # signal
xdown = signal.resample(x, round(len(x) / factor))
``````

### Anti-aliasing

The frequency bands of the filters that are above the Nyquist's frequency (`sample_rate/2`) are automatically removed because the values will not be correct.

### Examples of filter responses

Fraction Butterworth order: 6 Butterworth order: 16
1-octave
1/3-octave
2/3-octave

### Usage example

This example is included in the file test.py.

``````import PyOctaveBand
import numpy as np
import scipy.io.wavfile

# Sample rate and duration
fs = 48000
duration = 5  # In seconds

# Time array
x = np.arange(np.round(fs * duration)) / fs

# Signal with 6 frequencies
f1, f2, f3, f4, f5, f6 = 20, 100, 500, 2000, 4000, 15000
# Multi Sine wave signal
y = 100 \
* (np.sin(2 * np.pi * f1 * x)
+ np.sin(2 * np.pi * f2 * x)
+ np.sin(2 * np.pi * f3 * x)
+ np.sin(2 * np.pi * f4 * x)
+ np.sin(2 * np.pi * f5 * x)
+ np.sin(2 * np.pi * f6 * x))

# Filter (only octave spectra)
spl, freq = PyOctaveBand.octavefilter(y, fs=fs, fraction=3, order=6, limits=[12, 20000], show=1)

# Filter (get spectra and signal in bands)
splb, freqb, xb = PyOctaveBand.octavefilter(y, fs=fs, fraction=3, order=6, limits=[12, 20000], show=0, sigbands=1)

# Store signal in bands in separated wav files
for idx in range(len(freq)):
scipy.io.wavfile.write(
"test_"+str(round(freq[idx]))+"_Hz.wav",
fs,
xb[idx]/np.max(xb[idx]))
``````

The result is as follows:

One Octave filter One-Third Octave filter
1/12 Octave filter 1/24 Octave filter