Documentation 
Discretetime, lattice, autoregressive filter
Refer to dfilt.latticear in Signal Processing Toolbox™ documentation.
hd = dfilt.latticear(k) returns a discretetime, lattice autoregressive filter object hd, with lattice coefficients, k.
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.latticear returns a default, discretetime, lattice autoregressive filter object hd, with k=[ ]. This filter passes the input through to the output unchanged.
The following figure shows the signal flow for the autoregressive lattice filter implemented by dfilt.latticear. 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 word "format." In this use, "format" means the word length and fraction length associated with the filter part referred to by the prefix.
For example, the InputFormat label refers to the word length and fraction length used to interpret the data input to the filter. The format properties InputWordLength and InputFracLength (as shown in the table) store the word length and the fraction length in bits. Or consider NumFormat, 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 

AccumFormat  AccumWordLength  AccumFracLength  AccumMode 
InputFormat  InputWordLength  InputFracLength  None 
LatticeFormat  CoeffWordLength  LatticeFracLength  CoeffAutoScale 
OutputFormat  OutputWordLength  OutputFracLength  OutputMode 
ProductFormat  ProductWordLength  ProductFracLength  ProductMode 
StateFormat  StateWordLength  StateFracLength  States 
Most important is the label position in the diagram, which identifies where the format applies.
As one example, look at the label ProductFormat, which always follows a coefficient multiplication element in the signal flow. The label indicates that coefficients leave the multiplication element with the word length and fraction length associated with product operations that include coefficients. From reviewing the table, you see that the ProductFormat refers to the properties ProductFracLength, ProductWordLength, and ProductMode that fully define the coefficient format after multiply (or product) operations.
In this table you see the properties associated with the autoregressive lattice implementation of 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 hd is a filter. 
For further information about the properties of this filter or any dfilt object, refer to FixedPoint Filter Properties.
Property Name  Brief Description 

AccumFracLength  Specifies the fraction length used to interpret data output by the accumulator. This is a property of FIR filters and lattice filters. IIR filters have two similar properties — DenAccumFracLength and NumAccumFracLength — that let you set the precision for numerator and denominator operations separately. 
AccumMode  Determines how the accumulator outputs stored values. Choose from full precision (FullPrecision), or whether to keep the most significant bits (KeepMSB) or least significant bits (KeepLSB) when output results need shorter word length than the accumulator supports. To let you set the word length and the precision (the fraction length) used by the output from the accumulator, set AccumMode to SpecifyPrecision. 
AccumWordLength  Sets the word length used to store data in the accumulator/buffer. 
Arithmetic  Defines the arithmetic the filter uses. Gives you the options double, single, and fixed. In short, this property defines the operating mode for your filter. 
CastBeforeSum  Specifies whether to cast numeric data to the appropriate accumulator format (as shown in the signal flow diagrams) before performing sum operations. 
CoeffAutoScale  Specifies whether the filter automatically chooses the proper fraction length to represent filter coefficients without overflowing. Turning this off by setting the value to false enables you to change the LatticeFracLength to specify the precision used. 
CoeffWordLength  Specifies the word length to apply to filter coefficients. 
FilterStructure  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. 
InputFracLength  Specifies the fraction length the filter uses to interpret input data. 
InputWordLength  Specifies the word length applied to interpret input data. 
Lattice  Any lattice structure coefficients. 
LatticeFracLength  Sets the fraction length applied to the lattice coefficients. 
OutputFracLength  Determines how the filter interprets the filter output data. You can change the value of OutputFracLength when you set OutputMode to SpecifyPrecision. 
OutputMode  Sets the mode the filter uses to scale the filtered data for output. You have the following choices:

OutputWordLength  Determines the word length used for the output data. 
OverflowMode  Sets the mode used to respond to overflow conditions in fixedpoint arithmetic. Choose from either saturate (limit the output to the largest positive or negative representable value) or wrap (set overflowing values to the nearest representable value using modular arithmetic). The choice you make affects only the accumulator and output arithmetic. Coefficient and input arithmetic always saturates. Finally, products never overflow — they maintain full precision. 
ProductFracLength  For the output from a product operation, this sets the fraction length used to interpret the data. This property becomes writable (you can change the value) when you set ProductMode to SpecifyPrecision. 
ProductMode  Determines how the filter handles the output of product operations. Choose from full precision (FullPrecision), or whether to keep the most significant bit (KeepMSB) or least significant bit (KeepLSB) in the result when you need to shorten the data words. For you to be able to set the precision (the fraction length) used by the output from the multiplies, you set ProductMode to SpecifyPrecision. 
ProductWordLength  Specifies the word length to use for multiplication operation results. This property becomes writable (you can change the value) when you set ProductMode to SpecifyPrecision. 
PersistentMemory  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. False is the default setting. 
RoundMode  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. 
Signed  Specifies whether the filter uses signed or unsigned fixedpoint coefficients. Only coefficients reflect this property setting. 
StateFracLength  When you set StateAutoScale to false, you enable the StateFracLength property that lets you set the fraction length applied to interpret the filter states. 
States  This property contains the filter states before, during, and after filter operations. States act as filter memory between filtering runs or sessions. The states use fi objects, with the associated properties from those objects. For details, refer to filtstates in Signal Processing Toolbox documentation or in the Help system. 
StateWordLength  Sets the word length used to represent the filter states. 
Specify a thirdorder lattice autoregressive filter structure for a dfilt object, hd, with the following code that creates a fixedpoint filter.
k = [.66 .7 .44];
hd1=dfilt.latticear(k);
hd1.arithmetic='fixed';
specifyall(hd1);
dfilt  dfilt.latticeallpass  dfilt.latticearma  dfilt.latticemamax  dfilt.latticemamin