python实现1/n倍频程计算

倍频程定义

在音频分析领域，经常要分析音频信号的频谱，这时最常用的是倍频程功率谱和1/3倍频程功率谱。
所谓倍频程功率谱，是将音频分为一个个的频段，然后分别计算每个频段内的功率谱。相邻频段的宽度为二比一的关系。
1/3倍频程是将倍频程再细分为三段。 1/n倍频程是将倍频程再细分为n段。

倍频程介绍参考链接

代码实现

所需模块

import numpy as np
import matplotlib.pyplot as plt
from scipy import signal as sg

实现代码

首先实现1/96倍频程中心频率

order_96 = np.array([2.92644400e+00, 2.94806600e+00, 2.96984800e+00, 2.99179100e+00,
           3.01389700e+00, 3.03616500e+00, 3.05859800e+00, 3.08119700e+00,
           3.10396300e+00, 3.12689700e+00, 3.15000000e+00, 3.17362400e+00,
           3.19742400e+00, 3.22140400e+00, 3.24556300e+00, 3.26990300e+00,
           3.29442600e+00, 3.31913300e+00, 3.34402500e+00, 3.36910300e+00,
           3.39437000e+00, 3.41982600e+00, 3.44547300e+00, 3.47131300e+00,
           3.49734600e+00, 3.52357500e+00, 3.55000000e+00, 3.57657900e+00,
           3.60335700e+00, 3.63033600e+00, 3.65751600e+00, 3.68490000e+00,
           3.71248900e+00, 3.74028500e+00, 3.76828900e+00, 3.79650200e+00,
           3.82492700e+00, 3.85356400e+00, 3.88241600e+00, 3.91148400e+00,
           3.94076900e+00, 3.97027400e+00, 4.00000000e+00, 4.02955400e+00,
           4.05932700e+00, 4.08932000e+00, 4.11953400e+00, 4.14997200e+00,
           4.18063400e+00, 4.21152400e+00, 4.24264000e+00, 4.27398800e+00,
           4.30556700e+00, 4.33737900e+00, 4.36942600e+00, 4.40171000e+00,
           4.43423200e+00, 4.46699500e+00, 4.50000000e+00, 4.52973000e+00,
           4.55965700e+00, 4.58978200e+00, 4.62010500e+00, 4.65063000e+00,
           4.68135500e+00, 4.71228400e+00, 4.74341600e+00, 4.77475500e+00,
           4.80630100e+00, 4.83805500e+00, 4.87001900e+00, 4.90219400e+00,
           4.93458100e+00, 4.96718300e+00, 5.00000000e+00, 5.03554100e+00,
           5.07133400e+00, 5.10738200e+00, 5.14368700e+00, 5.18024900e+00,
           5.21707100e+00, 5.25415500e+00, 5.29150200e+00, 5.32911500e+00,
           5.36699600e+00, 5.40514600e+00, 5.44356600e+00, 5.48226000e+00,
           5.52122900e+00, 5.56047500e+00, 5.60000000e+00, 5.64137600e+00,
           5.68305800e+00, 5.72504800e+00, 5.76734800e+00, 5.80996100e+00,
           5.85288800e+00, 5.89613300e+00, 5.93969700e+00, 5.98358300e+00,
           6.02779300e+00, 6.07233000e+00, 6.11719700e+00, 6.16239400e+00,
           6.20792500e+00, 6.25379300e+00, 6.30000000e+00, 6.34724800e+00,
           6.39484900e+00, 6.44280700e+00, 6.49112600e+00, 6.53980600e+00,
           6.58885100e+00, 6.63826500e+00, 6.68804900e+00, 6.73820600e+00,
           6.78874000e+00, 6.83965300e+00, 6.89094700e+00, 6.94262600e+00,
           6.99469200e+00, 7.04715000e+00, 7.10000000e+00, 7.15315800e+00,
           7.20671400e+00, 7.26067100e+00, 7.31503200e+00, 7.36980100e+00,
           7.42497900e+00, 7.48057000e+00, 7.53657700e+00, 7.59300400e+00,
           7.64985400e+00, 7.70712900e+00, 7.76483200e+00, 7.82296800e+00,
           7.88153900e+00, 7.94054800e+00, 8.00000000e+00, 8.05910900e+00,
           8.11865400e+00, 8.17863900e+00, 8.23906900e+00, 8.29994400e+00,
           8.36126900e+00, 8.42304700e+00, 8.48528100e+00, 8.54797600e+00,
           8.61113400e+00, 8.67475800e+00, 8.73885200e+00, 8.80342000e+00,
           8.86846400e+00, 8.93399000e+00, 9.00000000e+00, 9.05946100e+00,
           9.11931400e+00, 9.17956400e+00, 9.24021100e+00, 9.30125900e+00,
           9.36271000e+00, 9.42456700e+00, 9.48683300e+00, 9.54951000e+00,
           9.61260100e+00, 9.67610900e+00, 9.74003800e+00, 9.80438700e+00,
           9.86916300e+00, 9.93436600e+00, 1.00000000e+01, 1.00710820e+01,
           1.01426690e+01, 1.02147650e+01, 1.02873740e+01, 1.03604980e+01,
           1.04341420e+01, 1.05083100e+01, 1.05830050e+01, 1.06582310e+01,
           1.07339920e+01, 1.08102910e+01, 1.08871330e+01, 1.09645200e+01,
           1.10424590e+01, 1.11209500e+01, 1.12000000e+01, 1.12771350e+01,
           1.13548000e+01, 1.14330020e+01, 1.15117410e+01, 1.15910220e+01,
           1.16708510e+01, 1.17512280e+01, 1.18321590e+01, 1.19136480e+01,
           1.19956980e+01, 1.20783130e+01, 1.21614960e+01, 1.22452530e+01,
           1.23295870e+01, 1.24145010e+01, 1.25000000e+01, 1.25944540e+01,
           1.26896210e+01, 1.27855070e+01, 1.28821180e+01, 1.29794600e+01,
           1.30775370e+01, 1.31763530e+01, 1.32759180e+01, 1.33762350e+01,
           1.34773090e+01, 1.35791480e+01, 1.36817560e+01, 1.37851390e+01,
           1.38893040e+01, 1.39942560e+01, 1.41000000e+01, 1.42118430e+01,
           1.43245740e+01, 1.44381990e+01, 1.45527260e+01, 1.46681600e+01,
           1.47845110e+01, 1.49017840e+01, 1.50199870e+01, 1.51391280e+01,
           1.52592130e+01, 1.53802530e+01, 1.55022510e+01, 1.56252170e+01,
           1.57491590e+01, 1.58740840e+01, 1.60000000e+01, 1.61126060e+01,
           1.62260060e+01, 1.63402020e+01, 1.64552020e+01, 1.65710120e+01,
           1.66876370e+01, 1.68050840e+01, 1.69233570e+01, 1.70424610e+01,
           1.71624050e+01, 1.72831920e+01, 1.74048290e+01, 1.75273230e+01,
           1.76506790e+01, 1.77749020e+01, 1.79000000e+01, 1.80245360e+01