Package: dsp
Tunable secondorder parametric equalizer filter
Note:
The 
The ParametricEQFilter
object is a tunable,
secondorder parametric equalizer filter.
To apply the filter to each channel of the input:
Define and set up your equalizer filter. See Construction.
Call step
to filter each channel
according to the properties of dsp.ParametricEQFilter
.
The behavior of step
is specific to each object in
the toolbox.
Note:
Starting in R2016b, instead of using the 
H = dsp.ParametricEQFilter
returns a secondorder
parametric equalizer filter that independently filters each channel
of the input over time, using the default values for Bandwidth
, CenterFrequency
,
and PeakGaindB
. The center frequency
and bandwidth
are
specified in Hz and are tunable. The peak gain
(dip)
is specified in dB and is also tunable. The bandwidth
is
measured at the arithmetic mean between the peak gain
in
absolute power units and one.
H = dsp.ParametricEQFilter('Specification', 'Quality
factor and center frequency')
specifies the quality factor
(Q factor) of the filter. The Q factor
is defined
as the center frequency/bandwidth. A higher Q factor
corresponds
to a narrower peak/dip. The Q factor should be a scalar value greater
than 0. The Q factor is tunable.
H = dsp.ParametricEQFilter('Specification', 'Coefficients')
specifies the gain values for the bandwidth and center frequency.
This removes the trigonometry calculations involved when the properties
are tuned. The CenterFrequencyCoefficient
should
be a scalar between 1 and 1, with 1 corresponding to 0 Hz, and 1
corresponding to the Nyquist frequency. The BandwidthCoefficient
should
be a scalar between 1 and 1, with 1 corresponding to the largest
bandwidth, and 1 corresponding to the smallest bandwidth. In this
mode, the peak gain is specified in linear units rather than dB.
H = dsp.ParametricEQFilter('Name', Value, ...)
returns
a parametric equalizer filter with each specified property name set
to the specified value. You can specify several namevalue pair arguments
in any order as ('Name1',Value1,...,'NameN',ValueN)
.

Design parameters or coefficients that specify the filter Choose one of the following
The default value is Using 

bandwidth of filter Specify the bandwidth of the filter as a finite positive numeric
scalar that is less than half the sample rate of the input signal,
in Hz. This property is applicable if 

Coefficient for bandwidth of filter Specify the value that determines the filter's bandwidth as
a finite numeric scalar in the range
This property is only applicable if 

Center frequency of the filter Specify the filter's center frequency as a finite positive numeric
scalar that is less than half the sample rate of the input signal,
in Hz. This property is only applicable if 

Coefficient for center frequency of filter Specify the value that determines the filter's center frequency as a finite numeric scalar between 1 and 1:
This property is only applicable if This property is tunable. 

Peak or dip gain of the filter in linear units Specify the filter's peak or dip gain in linear units. A value greater than one boosts the signal. A value less than one attenuates the signal. The default is 2 (6.0206 dB). This property is tunable. 

Peak or dip gain of the filter in dB Specify the filter's peak or dip gain in dB. A positive
value boosts the signal. A negative value attenuates the signal. The
default is 

Quality factor of the parametric EQ filter Specify the Quality factor (Q factor) of the filter. The Q factor
is defined as the center frequency divided by the bandwidth. A higher
Q factor corresponds to a narrower peak or dip. This property is only
applicable if 

Input sample rate Specify the sample rate of the input as a finite numeric scalar,
in Hz. The default is 
getBandwidth  Convert quality factor or bandwidth coefficient to bandwidth in Hz 
getCenterFrequency  Convert center frequency coefficient to frequency in Hz 
getOctaveBandwidth  Measure bandwidth of parametric equalizer filter in octaves 
getPeakGain  Convert peak or notch gain from dB to absolute units 
getPeakGaindB  Convert peak or notch gain from absolute units to dB 
getQualityFactor  Convert bandwidth to quality factor 
reset  Reset states of ParametricEQFilter object 
step  Filter input with ParametricEQFilter object 
tf  Compute transfer function 
Common to All System Objects  

clone  Create System object with same property values 
getNumInputs  Expected number of inputs to a System object 
getNumOutputs  Expected number of outputs of a System object 
isLocked  Check locked states of a System object (logical) 
release  Allow System object property value changes 
The parametric equalizer is formed by a linear combination of
a peak and a notch filter. See the Algorithm section
of dsp.NotchPeakFilter
for
details.
$$H(z)={H}_{notch}(z)+G{H}_{peak}(z)$$
Here is a graph of the two cases (boost and cut) of the magnitude squared of the transfer functions:
The transfer function can be written as:
$$\begin{array}{l}H(z)=\frac{(\frac{1+{G}_{\gamma}}{1+\gamma})2(\frac{\mathrm{cos}{\omega}_{0}}{1+\gamma}){z}^{1}+(\frac{1{G}_{\gamma}}{1+\gamma}){z}^{2}}{12(\frac{\mathrm{cos}{\omega}_{0}}{1+\gamma}){z}^{1}+(\frac{1\gamma}{1+\gamma}){z}^{2}}\\ where\\ \gamma =\mathrm{tan}(\frac{\Delta \omega}{2})\\ and\\ {G}_{B}{}^{2}=\frac{1+{G}^{2}}{2}\end{array}$$
G is the parametric equalizer gain, and G_{B} is the bandwidth gain, that is, the gain level at which the bandwidth Δω is measured.
The dsp.NotchPeakFilter
that
does most of the work is implemented in a decoupled way so that the
center frequency can be tuned independently from the bandwidth. Note
that the Q factor is defined as center frequency/bandwidth.
[1] Orfanidis, Sophocles J. Introduction to Signal Processing Upper Saddle River, NJ: PrenticeHall, 1996
Parametric EQ Filter  DSP System Toolbox 
iirparameq  DSP System Toolbox 