Discretetime, SOS, directform II filter
Refer to dfilt.df2sos
in Signal Processing Toolbox™ documentation.
hd = dfilt.df2sos(s)
returns
a discretetime, secondorder section, directform II filter object hd
,
with coefficients given in the s
matrix.
Make this filter a fixedpoint or singleprecision filter by
changing the value of the Arithmetic
property
for the filter hd
as follows:
To change to singleprecision filtering, enter
set(hd,'arithmetic','single');
To change to fixedpoint filtering, enter
set(hd,'arithmetic','fixed');
For more information about the property Arithmetic
,
refer to Arithmetic.
hd = dfilt.df2sos(b1,a1,b2,a2,...)
returns
a discretetime, secondorder section, directform II object, hd
,
with coefficients for the first section given in the b1
and a1
vectors,
for the second section given in the b2
and a2
vectors,
etc.
hd = dfilt.df2sos(...,g)
includes
a gain vector g
. The elements of g
are
the gains for each section. The maximum length of g
is
the number of sections plus one. If g
is not specified,
all gains default to one.
hd = dfilt.df2sos
returns
a default, discretetime, secondorder section, directform II filter
object, hd
. This filter passes the input through
to the output unchanged.
Note
The leading coefficient of the denominator 
The figure below shows the signal flow for the directform II
filter implemented with secondorder sections by dfilt.df2sos
.
To help you see how the filter processes the coefficients, input,
and states of the filter, as well as numerical operations, the figure
includes the locations of the formatting objects within the signal
flow.
To help you understand where and how the filter performs fixedpoint arithmetic during filtering, the figure shows various labels associated with data and functional elements in the filter. The following table describes each label in the signal flow and relates the label to the filter properties that are associated with it.
The labels use a common format — a prefix followed by the letters "frmt" (format). In this use, "frmt" means the word length and fraction length associated with the filter part referred to by the prefix.
For example, the InputFrmt label refers to the word length and
fraction length used to interpret the data input to the filter. The
frmt properties InputWordLength
and InputFracLength
(as
shown in the table) store the word length and the fraction length
in bits. Or consider NumFrmt, which refers to the word and fraction
lengths (CoeffWordLength
, NumFracLength
)
associated with representing filter numerator coefficients.
Signal Flow Label  Corresponding Word Length Property  Corresponding Fraction Length Property  Related Properties 

DenAccumFrmt 



DenFrmt 



DenProdFrmt 



InputFrmt 

 None 
NumAccumFrmt 



NumFrmt 



NumProdFrmt 



OutputFrmt 



ScaleValueFrmat 



SectionInputFormt 



SectionOutputFrmt 



StateFrmt 



Most important is the label position in the diagram, which identifies where the format applies.
As one example, look at the label DenProdFrmt, which always
follows a denominator coefficient multiplication element in the signal
flow. The label indicates that denominator coefficients leave the
multiplication element with the word length and fraction length associated
with product operations that include denominator coefficients. From
reviewing the table, you see that the DenProdFrmt refers to the properties ProdWordLength
, ProductMode
and DenProdFracLength
that
fully define the denominator format after multiply (or product) operations.
In this table you see the properties associated with secondorder
section implementation of directform II dfilt
objects.
Note The table lists all the properties that a filter can have. Many of the properties are dynamic, meaning they exist only in response to the settings of other properties. You might not see all of the listed properties all the time. To view all the properties for a filter at any time, use get(hd) where 
For further information about the properties of this filter
or any dfilt
object, refer to FixedPoint Filter Properties.
Property Name  Brief Description 

 Determines how the accumulator outputs stored values.
Choose from full precision ( 
 Sets the word length used to store data in the accumulator/buffer. 
 Defines the arithmetic the filter uses. Gives you the
options 
 Specifies whether to cast numeric data to the appropriate accumulator format (as shown in the signal flow diagrams) before performing sum operations. 
 Specifies whether the filter automatically chooses the
proper fraction length to represent filter coefficients without overflowing.
Turning this off by setting the value to 
 Specifies the word length to apply to filter coefficients. 
 Specifies the fraction length used to interpret data
in the accumulator used to hold the results of sum operations. You
can change the value for this property when you set 
 Set the fraction length the filter uses to interpret
denominator coefficients. 
 Specifies how the filter algorithm interprets the results
of product operations involving denominator coefficients. You can
change this property value when you set 
 Describes the signal flow for the filter object, including all of the active elements that perform operations during filtering—gains, delays, sums, products, and input/output. 
 Specifies the fraction length the filter uses to interpret input data. 
 Specifies the word length applied to interpret input data. 
 Specifies how the filter algorithm interprets the results
of addition operations involving numerator coefficients. You can change
the value of this property after you set 
 Sets the fraction length used to interpret the value of numerator coefficients. 
 Specifies how the filter algorithm interprets the results
of product operations involving numerator coefficients. Available
to be changed when you set 
 When true, the filter skips multiplicationbyone scaling. When false, the filter performs multiplicationbyone scaling. 
 Determines how the filter interprets the filter output
data. You can change the value of 
 Sets the mode the filter uses to scale the filtered data for output. You have the following choices:

 Determines the word length used for the output data. 
 Sets the mode used to respond to overflow conditions
in fixedpoint arithmetic. Choose from either 
 Determines how the filter handles the output of product
operations. Choose from full precision ( 
 Specifies the word length to use for multiplication operation
results. This property becomes writable (you can change the value)
when you set 
 Specifies whether to reset the filter states and memory
before each filtering operation. Lets you decide whether your filter
retains states from previous filtering runs. 
 Sets the mode the filter uses to quantize numeric values when the values lie between representable values for the data format (word and fraction lengths).
The choice you make affects only the accumulator and output arithmetic. Coefficient and input arithmetic always round. Finally, products never overflow — they maintain full precision. 
 Scale values work with SOS filters. Setting this property
controls how your filter interprets the scale values by setting the
fraction length. Only available when you disable 
 Scaling for the filter objects in SOS filters. 
 Tells the filter whether to set the stage input data format to minimize the occurrence of overflow conditions. 
 Lets you set the fraction length for section inputs in
SOS filters, if you set 
 Lets you set the word length for section inputs in SOS
filters, if you set 
 Tells the filter whether to set the section output data format to minimize the occurrence of overflow conditions. 
 Lets you set the fraction length for section outputs
in SOS filters, if you set 
 Lets you set the word length for section outputs in SOS
filters, if you set 
 Specifies whether the filter uses signed or unsigned fixedpoint coefficients. Only coefficients reflect this property setting. 
 Holds the filter coefficients as property values. Displays
the matrix in the format [sections x coefficients/section datatype]. A 
 When you set 
 This property contains the filter states before, during, and after filter operations. States act as filter memory between filtering runs or sessions. 
 Sets the word length used to represent the filter states. 
Specify a secondorder section, directform II dfilt
object
for a Butterworth filter converted to secondorder sections, with
the following code:
[z,p,k] = butter(30,0.5); [s,g] = zp2sos(z,p,k); hd = dfilt.df2sos(s,g); % Convert filter to fixedpoint hd.arithmetic='fixed';