octaveFilter_octave fir 滤波

octaveFilter：

 倍频带和分数倍频带滤波器(倍频带和分数倍频带滤波器)
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倍频带是指最高频率是最低频率的两倍的频带。倍频带和分数倍频带滤波器通常用于模拟人类感知响度的方式。当在对数尺度上观察时，倍频程滤波器最好被理解，对数尺度模拟了人耳如何加权频谱。

Example: octFilt = octaveFilter(1000,‘1/3 octave’,‘SampleRate’,96000)
创建一个中心频率为1000 Hz、1/3倍频程滤波器带宽和采样率为96000 Hz的系统对象octFilt。
一般而言，倍频程滤波器有如下属性值：
阶数：指定为偶数整数。
中心频率（Hz）：指定为正标量，使用parameterTuner时，中心频率必须在[0.2，SampleRate/2]Hz范围内。
以八度音阶(octave)为单位的滤波器带宽：指定为“1个八度音阶”、“2/3个八度音”、“1/2个八度音调”、“1/3个八度音符”、“1/6个八度音节”、“1/12个八度和弦”、“1/24个八度音高”或“1/48个八度音色”。
过采样切换:指定为false或true。false–倍频程滤波器以输入采样率运行。true––倍频程滤波器以输入采样率的两倍运行。过采样使双线性变换引入的频率扭曲效应最小化。FIR半带内插器在倍频程滤波之前实现过采样。半带抽取器在倍频程滤波之后将采样率降低回输入采样率。

实例：

注意虚线，采用如下程序的，如果虚线是绿色，符合合规，红色不符合合规(在规范里定义了滤波器的标准中心频率和衰减)；
-对于高通：
使倍频程滤波器设计符合要求的一个选项是将“过采样”属性设置为true。这将以指定SampleRate的两倍设计和运行滤波器，以减少设计阶段双线性变换的影响
或者增大滤波器order，使边沿更陡峭
centerFrequencies = getANSICenterFrequencies(octFilt)
octFilt.CenterFrequency = centerFrequencies(38);
visualize(octFilt,‘class 0’)


对于低通:
比如：octFilt = octaveFilter(‘FilterOrder’,6, …
‘Bandwidth’,‘2/3 octave’, …
‘SampleRate’,96e3);
%设计一个采样率为96 kHz的六阶2/3倍频程滤波器。
centerFrequencies = getANSICenterFrequencies(octFilt)
%获取ANSI S1.11-2004标准定义的中心频率。标准定义的中心频率取决于“带宽”和“采样率”属性
倍频程滤波器组中的低频滤波器具有非常低的归一化中心频率，并且为其设计的滤波器具有几乎在单位圆上的极点。为了使该过滤器符合ANSI标准，必须以较低的采样率进行设计和操作。要使倍频程滤波器设计符合要求，请将采样率设置为48 kHz。<只是针对matlab设计来说>

数字滤波器设计

matlab中的设计参考的Orfanidis, Sophocles J. Introduction to Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 2010.
在这种设计方法中，所需的数字带通滤波器映射到巴特沃斯低通模拟原型，然后将其映射回数字带通过滤器：

1.模拟巴特沃斯滤波器表示为二阶部分的级联：

N是由FilterOrder属性指定的筛选顺序。
2.使用双线性变换的带通版本将模拟巴特沃斯滤波器映射到数字滤波器：

其中c为：

此映射导致如下替换：

3.模拟原型：

因为s在z中是二阶的，所以双线性变换的带通版本在z中为四阶的。

附：滤波器分析常用

fvtool       -  Filter visualization tool
info         -  Filter information
freqz        -  Frequency response
phasez       -  Phase response
zerophase    -  Zero-phase response
grpdelay     -  Group delay response
phasedelay   -  Phase delay response
impz         -  Impulse response
impzlength   -  Length of impulse response
stepz        -  Step response
zplane       -  Pole/zero plot
cost         -  Cost estimate for implementation of the filter System object
measure      -  Measure characteristics of the frequency response 
order        -  Filter order
coeffs       -  Filter coefficients in a structure
firtype      -  Determine the type (1-4) of a linear phase FIR filter System object
tf           -  Convert to transfer function
zpk          -  Convert to zero-pole-gain
ss           -  Convert to state space representation

isallpass    -  Verify if filter System object is allpass
isfir        -  Verify if filter System object is FIR
islinphase   -  Verify if filter System object is linear phase
ismaxphase   -  Verify if filter System object is maximum phase
isminphase   -  Verify if filter System object is minimum phase
isreal       -  Verify if filter System object is minimum real
issos        -  Verify if filter System object is in second-order sections form
isstable     -  Verify if filter System object is stable

realizemdl   -  Filter realization (Simulink diagram)   

specifyall   -  Fully specify fixed-point filter System object settings  

cascade      -  Create a FilterCascade System object  

Second-order sections:

scale        -  Scale second-order sections of BiquadFilter System object
scalecheck   -  Check scaling of BiquadFilter System object
reorder      -  Reorder second-order sections of BiquadFilter System object
cumsec       -  Cumulative second-order section of BiquadFilter System object
scaleopts    -  Create an options object for second-order section scaling
sos          -  Convert to second-order-sections (for IIRFilter System objects only)

Fixed-Point (Fixed-Point Designer Required):

freqrespest  -  Frequency response estimate via filtering
freqrespopts -  Create an options object for frequency response estimate
noisepsd     -  Power spectral density of filter output due to roundoff noise
noisepsdopts -  Create an options object for output noise PSD computation

Multirate Analysis:

polyphase                - Polyphase decomposition of multirate filter System object
gain (CIC decimator)     - Gain of CIC decimator filter System object
gain (CIC interpolator)  - Gain of CIC interpolator filter System object

For decimator, interpolator, or rate change filter System objects
the analysis tools perform computations relative to the rate at
which the filter is running. If a sampling frequency is specified,
it is assumed that the filter is running at that rate.
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参考：matlab ——octaveFilter