Filter Design Toolbox Reference Guide

dfilt.dffirt

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Discrete-time, direct-form FIR transposed filter

Syntax

Refer to dfilt.dffirt in Signal Processing Toolbox.

Description

hd = dfilt.dffirt(b) returns a discrete-time, direct-form FIR transposed filter object hd, with numerator coefficients b.

Make this filter a fixed-point or single-precision filter by changing the value of the Arithmetic property for the filter hd as follows:

To change to single-precision filtering, enter
```
set(hd,'arithmetic','single');
```
To change to fixed-point filtering, enter
```
set(hd,'arithmetic','fixed');
```

For more information about the property Arithmetic, refer to Arithmetic.

hd = dfilt.dffirt returns a default, discrete-time, direct-form FIR transposed filter object hd, with b = 1. This filter passes the input through to the output unchanged.

Fixed-Point Filter Structure

The following figure shows the signal flow for the transposed direct-form FIR filter implemented by dfilt.dffirt. 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.

Notes About the Signal Flow Diagram

To help you understand where and how the filter performs fixed-point 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`	None
InputFormat	`InputWordLength`	`InputFracLength`	None
NumFormat	`CoeffWordLength`	`NumFracLength`	`CoeffAutoScale`, `Signed`, `Numerator`
OutputFormat	`OutputWordLength`	`OutputFracLength`	None
ProductFormat	`ProductWordLength`	`ProductFracLength`	None

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 and ProductWordLength that fully define the coefficient format after multiply (or product) operations.

Properties

In this table you see the properties associated with the transposed direct-form FIR 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 Fixed-Point Filter Properties.

Name	Values	Description
`AccumFracLength`	Any positive or negative integer number of bits [30]	Specifies the fraction length used to interpret data output by the accumulator.
`AccumWordLength`	Any integer number of bits[34]	Sets the word length used to store data in the accumulator.
`Arithmetic`	fixed for fixed-point filters	Setting this to `fixed` allows you to modify other filter properties to customize your fixed-point filter.
`CoeffAutoScale`	[true], false	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 `NumFracLength` property value to specify the precision used.
`CoeffWordLength`	Any integer number of bits [16]	Specifies the word length to apply to filter coefficients.
`FilterInternals`	[FullPrecision], SpecifyPrecision	Controls whether the filter automatically sets the output word and fraction lengths, product word and fraction lengths, and the accumulator word and fraction lengths to maintain the best precision results during filtering. The default value, `FullPrecision`, sets automatic word and fraction length determination by the filter. `SpecifyPrecision` makes the output and accumulator-related properties available so you can set your own word and fraction lengths for them.
`InputFracLength`	Any positive or negative integer number of bits [15]	Specifies the fraction length the filter uses to interpret input data.
`InputWordLength`	Any integer number of bits [16]	Specifies the word length applied to interpret input data.
`NumFracLength`	Any positive or negative integer number of bits [`14`]	Sets the fraction length used to interpret the numerator coefficients.
`OutputFracLength`	Any positive or negative integer number of bits [30]	Determines how the filter interprets the filter output data. You can change the value of `OutputFracLength` when you set `FilerInternals` to `SpecifyPrecision`.
`OutputWordLength`	Any integer number of bits [34]	Determines the word length used for the output data. You make this property editable by setting `FilterInternals` to `SpecifyPrecision`.
`OverflowMode`	saturate, [wrap]	Sets the mode used to respond to overflow conditions in fixed-point 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.
`RoundMode`	[convergent], `ceil`,`fix`,`floor`, `round`	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). `convergent` — Round up to the next allowable quantized value. `ceil` — Round to the nearest allowable quantized value. Numbers that are exactly halfway between the two nearest allowable quantized values are rounded up only if the least significant bit (after rounding) would be set to `1`. `fix` — Round negative numbers up and positive numbers down to the next allowable quantized value. `floor` — Round down to the next allowable quantized value. `round` — Round to the nearest allowable quantized value. Numbers that are halfway between the two nearest allowable quantized values are rounded up. 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`	[true], false	Specifies whether the filter uses signed or unsigned fixed-point coefficients. Only coefficients reflect this property setting.
`States`	`fi` object to match the filter arithmetic setting	Contains the filter states before, during, and after filter operations. States act as filter memory between filtering runs or sessions. Notice that the states use `fi` objects, with the associated properties from those objects. For details, refer to fixed-point objects in Fixed-Point Toolbox documentation or in the online Help system.

Examples

Specify a second-order direct-form FIR transposed filter structure for a dfilt object, hd, with the following code:

b = [0.05 0.9 0.05];
hd = dfilt.dffirt(b)
 
hd =
 
     FilterStructure: 'Direct-Form FIR Transposed'
          Arithmetic: 'double'
           Numerator: [0.0500 0.9000 0.0500]
    PersistentMemory: false

Now use the filter property Arithmetic to change the filter to fixed-point format.

set(hd,'arithmetic','fixed')
hd
 
hd =
 
     FilterStructure: 'Direct-Form FIR Transposed'
          Arithmetic: 'fixed'
           Numerator: [0.0500 0.9000 0.0500]
    PersistentMemory: false
 
     CoeffWordLength: 16             
      CoeffAutoScale: true           
              Signed: true           
                                     
     InputWordLength: 16             
     InputFracLength: 15             
                                     
     FilterInternals: 'FullPrecision'
                                     
hd.filterInternals='specifyPrecision'
 
hd =
 
     FilterStructure: 'Direct-Form FIR Transposed'
          Arithmetic: 'fixed'
           Numerator: [0.0500 0.9000 0.0500]
    PersistentMemory: false
 
     CoeffWordLength: 16                
      CoeffAutoScale: true              
              Signed: true              
                                        
     InputWordLength: 16                
     InputFracLength: 15                
                                        
     FilterInternals: 'SpecifyPrecision'
                                        
    OutputWordLength: 34                
    OutputFracLength: 30                
                                        
   ProductWordLength: 32                
   ProductFracLength: 30                
                                        
     AccumWordLength: 34                
     AccumFracLength: 30                
                                        
           RoundMode: 'convergent'      
        OverflowMode: 'wrap'