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dfilt.df1sos

Discrete-time, SOS direct-form I filter

Synopsis

Refer to dfilt.df1sos in Signal Processing Toolbox™ documentation.

Description

hd = dfilt.df1sos(s) returns a discrete-time, second-order section, direct-form I filter object hd, with coefficients given in the s matrix.

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.df1sos(b1,a1,b2,a2,...) returns a discrete-time, second-order section, direct-form I filter 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, and so on.

hd = dfilt.df1sos(...,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. When you do not specify g, all gains default to one.

hd = dfilt.df1sos returns a default, discrete-time, second-order section, direct-form I filter object, hd. This filter passes the input through to the output unchanged.

    Note   The leading coefficient of the denominator a(1) cannot be 0. To allow you to change the arithmetic setting to fixed or single, a(1) must be equal to 1.

Fixed-Point Filter Structure

The following figure shows the signal flow for the direct-form I filter implemented in second-order sections by dfilt.df1sos. 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 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 format properties InputWordLength and InputFracLength (as shown in the table) store the word length and the fraction length in bits. Similarly 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

AccumWordLength

DenAccumFracLength

AccumMode, CastBeforeSum

DenFrmt

CoeffWordLength

DenFracLength

CoeffAutoScale, Signed, Denominator

DenProdFrmt

CoeffWordLength

DenProdFracLength

ProductMode, ProductWordLength

DenStateFrmt

DenStateWordLength

DenStateFracLength

CastBeforeSum, States

InputFrmt

InputWordLength

InputFracLength

None

NumAccumFrmt

AccumWordLength

NumAccumFracLength

AccumMode, CastBeforeSum

NumFrmt

CoeffWordLength

NumFracLength

CoeffAutoScale, Signed, Numerator

NumProdFrmt

CoeffWordLength

NumProdFracLength

ProductWordLength, ProductMode

NumStateFrmt

NumStateWordLength

NumStateFracLength

States

OutputFrmt

OutputWordLength

OutputFracLength

OutputMode

ScaleValueFrmt

CoeffWordLength

ScaleValueFracLength

CoeffAutoScale, ScaleValues

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.

Properties

In this table you see the properties associated with SOS implementation of direct-form I 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.

Property Name

Brief Description

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 NumFracLength and DenFracLength properties to specify the precision used.

CoeffWordLength

Specifies the word length to apply to filter coefficients.

DenAccumFracLength

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 AccumMode to SpecifyPrecision.

DenFracLength

Set the fraction length the filter uses to interpret denominator coefficients. DenFracLength is always available, but it is read-only until you set CoeffAutoScale to false.

DenProdFracLength

Specifies how the filter algorithm interprets the results of product operations involving denominator coefficients. You can change this property value when you set ProductMode to SpecifyPrecision.

DenStateFracLength

Specifies the fraction length used to interpret the states associated with denominator coefficients in the filter.

DenStateWordLength

Specifies the word length used to represent the states associated with denominator coefficients in the filter.

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.

NumAccumFracLength

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 AccumMode to SpecifyPrecision.

NumFracLength

Sets the fraction length used to interpret the value of numerator coefficients.

NumStateFracLength

Specifies the fraction length used to interpret the states associated with numerator coefficient operations in the filter.

NumWordFracLength

Specifies the word length used to interpret the states associated with numerator coefficient operations in the filter.

OptimizeScaleValues

When true, the filter skips multiplication-by-one scaling. When false, the filter performs multiplication-by-one scaling.

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:

  • AvoidOverflow — directs the filter to set the output data word length and fraction length to avoid causing the data to overflow.

  • BestPrecision — directs the filter to set the output data word length and fraction length to maximize the precision in the output data.

  • SpecifyPrecision — lets you set the word and fraction lengths used by the output data from filtering.

OutputWordLength

Determines the word length applied for the output data.

OverflowMode

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.

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).

  • ceil - Round toward positive infinity.

  • convergent - Round to the closest representable integer. Ties round to the nearest even stored integer. This is the least biased of the methods available in this software.

  • fix - Round toward zero.

  • floor - Round toward negative infinity.

  • nearest - Round toward nearest. Ties round toward positive infinity.

  • round - Round toward nearest. Ties round toward negative infinity for negative numbers, and toward positive infinity for positive numbers.

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.

ScaleValueFracLength

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 AutoScaleMode by setting it to false.

ScaleValues

Scaling for the filter objects in SOS filters.

Signed

Specifies whether the filter uses signed or unsigned fixed-point coefficients. Only coefficients reflect this property setting.

SosMatrix

Holds the filter coefficients as property values. Displays the matrix in the format [sections x coefficients/section datatype]. A [15x6 double] SOS matrix represents a filter with 6 coefficients per section and 15 sections, using data type double to represent the coefficients.

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.

Examples

Specify a fixed-point, second-order section, direct-form I dfilt object with the following code:

b = [0.3 0.6 0.3];
a = [1 0 0.2];
hd = dfilt.df1sos(b,a);
% Convert to fixed-point filter
hd.arithmetic = 'fixed';

See Also

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