FIR Decimation

Perform polyphase FIR decimation

Libraries:
DSP System Toolbox / Filtering / Multirate Filters
DSP System Toolbox HDL Support / Filtering

Description

The FIR Decimation block performs an efficient polyphase decimation using an integer downsampling factor M along the first dimension.

Conceptually, the FIR decimator (as shown in the schematic) consists of an anti-aliasing FIR filter followed by a downsampler. To design an FIR anti-aliasing filter, use the designMultirateFIR function.

The FIR filter filters the data in each channel of the input using a direct-form FIR filter. The downsampler that follows downsamples each channel of filtered data by taking every M-th sample and discarding the M – 1 samples that follow. M is the value of the decimation factor that you specify. The resulting discrete-time signal has a sample rate that is 1/M times the original sample rate.

Note that the actual block algorithm implements a direct-form FIR polyphase structure, an efficient equivalent of the combined system depicted in the diagram. For more details, see Algorithms.

Under specific conditions, this block also supports SIMD code generation. For details, see Code Generation.

Examples

FIR Decimation Using Single-Rate Processing

Use FIR Decimation block in single-rate processing mode.

• Open Model

FIR Decimation Using Multirate Frame-Based Processing

Use FIR Decimation block in multirate frame-based processing mode.

• Open Model

Polyphase Implementation of FIR Decimation Block

Polyphase implementation of the FIR decimator.

• Open Model

Two-Stage Multirate Narrow Lowpass Filter

Implement a two-stage multirate narrow band lowpass filter using FIR Decimation and FIR Interpolation blocks.

• Open Model

Ports

Input

In — Data input

vector | matrix

Specify the data input as a vector or a matrix of size P-by-Q. The columns in the input signal represent Q independent channels.

The block supports variable-size input signals (frame length changes during simulation) when you set Input processing to Columns as channels (frame based) and Rate options to Enforce single-rate processing. When the block accepts variable-size input signals, they can be of arbitrary frame length, that is, the input frame length does not have to be a multiple of the decimation factor. When you specify fixed-size signals, the frame length can be arbitrary under certain conditions. For more details, see Frame-Based Processing and Sample-Based Processing.

This port is unnamed until you set Coefficient source to Input port.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | fixed point
Complex Number Support: Yes

Num — Numerator coefficients

vector

Specify the numerator coefficients of the FIR filter as a vector.

The transfer function H(z) of the FIR filter is given by:

$$H(z)=b_0+b_1{z}^{-1}+\mathrm{...}+b_N{z}^{-N},$$

You can generate the FIR filter coefficient vector, b = [b₀, b₁, …, b_N], using one of the DSP System Toolbox™ filter design functions such as designMultirateFIR, firnyquist, firgr, or firceqrip.

To act as an effective anti-aliasing filter, the coefficients usually correspond to a lowpass filter with a normalized cutoff frequency no greater than 1/M, where M is the decimation factor. To design such a filter, use the designMultirateFIR function.

Coefficient values obtained through Num are tunable, that is, they can change during simulation, while their properties must remain constant.

The data type of the Num input must match the data type of the In input.

Dependencies

The Num input port appears when you set Coefficient source as Input port.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | fixed point
Complex Number Support: Yes

Output

Out — Decimator output

vector | matrix

Output of the FIR Decimator block, returned as a vector or a matrix.

When you set Rate options to:

• Enforce single-rate processing –– The block maintains the input sample rate and decimates the signal by decreasing the output frame size by a factor of M.

  The output has an upper bound size of ceil(P/M)-by-Q for an input of size P-by-Q.

• Allow multirate processing –– The block decimates the signal such that the output sample rate is M times slower than the input sample rate.

  The output frame size is the same as the input frame size.

For more details, see Frame-Based Processing and Sample-Based Processing.

This port is unnamed until you set Coefficient source to Input port.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | fixed point
Complex Number Support: Yes

Parameters

Coefficient source

Coefficient source — FIR filter coefficient source

Auto (default) | Dialog parameters | Input port | Filter object

Specify the FIR filter coefficient source as one of the following:

• Dialog parameters –– Specify the filter coefficients through the FIR filter coefficients parameter in the block dialog box.

• Input port –– Specify the filter coefficients through the Num input port.

• Filter object –– Specify the filter using a dsp.FIRDecimator System object™.

• Auto –– When you select Auto, the block designs an FIR decimator using the decimation factor that you specify in Decimation factor. The designMultirateFIR function designs the filter and returns the coefficients used by the block.

  For more information on the filter design, see Orfanidis [2].

Main Tab

FIR filter coefficients — Lowpass FIR filter coefficients

designMultirateFIR(1,2) (default) | vector

Specify the lowpass FIR filter coefficients, in descending powers of z, as a vector. By default, designMultirateFIR(1,2) computes the filter coefficients.

The transfer function H(z) of the FIR filter is given by:

$$H(z)=b_0+b_1{z}^{-1}+\mathrm{...}+b_N{z}^{-N},$$

You can generate the FIR filter coefficient vector, b = [b₀, b₁, …, b_N], using one of the DSP System Toolbox filter design functions such as designMultirateFIR, firnyquist, firgr, or firceqrip.

To act as an effective anti-aliasing filter, the coefficients usually correspond to a lowpass filter with a normalized cutoff frequency no greater than 1/M, where M is the decimation factor. To design such a filter, use the designMultirateFIR function.

The block internally initializes all filter states to zero.

Dependencies

This parameter appears only when you set the Coefficient source to Dialog parameters.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
Complex Number Support: Yes

Decimation factor — Decimation factor

2 (default) | positive scalar

Specify the integer factor M. The block decreases the sample rate of the input sequence by this factor.

Dependencies

This parameter appears only when you set the Coefficient source to Dialog parameters, Input port, or Auto.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Filter structure — FIR filter structure

Direct form (default) | Direct form transposed

Specify the FIR filter structure as either Direct form or Direct form transposed.

Dependencies

This parameter appears only when you set the Coefficient source to Dialog parameters, Input port, or Auto.

Filter object — Filter object

dsp.FIRDecimator

Specify the name of the multirate filter object that you want the block to implement. You must specify the filter as a dsp.FIRDecimator System object.

You can define the System object directly in the block dialog box. Alternatively, you can define the object in a MATLAB^® workspace variable and specify the variable in the block dialog box.

For information on creating System objects, see Define Basic System Objects.

Dependencies

This parameter appears only when you set the Coefficient source to Filter object.

Input processing — Method to process input signals

Columns as channels (frame based) (default) | Elements as channels (sample based)

Specify how the block should process the input. You can set this parameter to one of the following options:

• Columns as channels (frame based) — When you select this option, the block treats each column of the input as a separate channel.

• Elements as channels (sample based) — When you select this option, the block treats each element of the input as a separate channel.

Rate options — Method by which block decimates input

Enforce single-rate processing (default) | Allow multirate processing

Specify the method by which the block should decimate the input. You can select one of the following options:

• Enforce single-rate processing — When you select this option, the block maintains the input sample rate and decimates the signal by decreasing the output frame size by a factor of M. To select this option, you must set the Input processing parameter to Columns as channels (frame based).

  When you set the Rate options parameter to Enforce single-rate processing, you can use the FIR Decimation block inside triggered subsystems.

• Allow multirate processing — When you select this option, the block decimates the signal such that the output sample rate is M times slower than the input sample rate.

Allow arbitrary frame length for fixed-size input signals — Allow arbitrary frame length for fixed-size input signals

off (default) | on

Specify whether fixed-size input signals (whose size does not change during simulation) can have an arbitrary frame length, where the frame length does not have to be a multiple of the decimation factor. The block uses this parameter setting only for fixed-size input signals and ignores this parameter if the input has a variable-size.

When the input signal is a variable-size signal, the signal can have arbitrary frame length, that is, the frame length does not have to be a multiple of the decimation factor.

For fixed-size input signals, if you:

• Select the Allow arbitrary frame length for fixed-size input signals parameter, the frame length of the signal does not have to be a multiple of the decimation factor. If the input is not a multiple of the decimation factor, then the output is generally a variable-size signal. Therefore, to support arbitrary input size, the block must also support variable-size operations, which you can enable by selecting the Allow arbitrary frame length for fixed-size input signals parameter.

• Clear the Allow arbitrary frame length for fixed-size input signals parameter, the input frame length must be a multiple of the decimation factor.

Dependency

To enable this parameter, set Input processing to Columns as channels (frame based) and Rate options to Enforce single-rate processing.

Output buffer initial conditions — Initial conditions

0 (default) | scalar | matrix

When you set the FIR Decimation block to the frame-based processing mode, the block can exhibit one-frame latency. In the case of one-frame latency, this parameter specifies the output of the block until the first filtered input sample is available. Specify this parameter as a scalar value to be applied to all signal channels, or as a matrix containing one value for each channel.

Cases of one-frame latency can occur when the input frame size is greater than one, and you set the Input processing and Rate options parameters of the FIR Decimation block as follows:

• Input processing set to Columns as channels (frame based)

• Rate options set to Allow multirate processing

For more information on latency in the FIR Decimation block, see Latency.

Dependencies

This parameter appears only when you configure the block to perform multirate processing by setting Rate options to Allow multirate processing.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
Complex Number Support: Yes

View Filter Response — View filter response

button

Click on this button to open the Filter Visualization Tool (fvtool) and display the filter response of the filter defined in the block dialog box.

Data Types Tab

Rounding mode — Rounding mode

Floor (default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero

Select the rounding mode for fixed-point operations. The default is Floor. The filter coefficients do not obey this parameter and always round to Nearest.

Note

The Rounding mode and Saturate on integer overflow settings have no effect on numerical results when all the following conditions exist:

• Product output is Inherit: Inherit via internal rule

• Accumulator is Inherit: Inherit via internal rule

• Output is Inherit: Same as accumulator

With these data type settings, the block is effectively operating in the full-precision mode.

Saturate on integer overflow — Saturate on integer overflow

off (default) | on

When you select this parameter, the block saturates the result of its fixed-point operation. When you clear this parameter, the block wraps the result of its fixed-point operation. For details on saturate and wrap, see overflow mode for fixed-point operations.

Note

The Rounding mode and Saturate on integer overflow parameters have no effect on numeric results when all these conditions are met:

• Product output data type is Inherit: Inherit via internal rule.

• Accumulator data type is Inherit: Inherit via internal rule.

With these data type settings, the block operates in full-precision mode.

Coefficients Data Type — Coefficients data type

Inherit: Same word length as input (default) | fixdt(1,16) | fixdt(1,16,0)

Specify the coefficients data type. See Fixed-Point Data Types and Multiplication Data Types for illustrations depicting the use of the coefficients data type in this block.

You can set this parameter to one of the following:

• Inherit: Same word length as input

• fixdt(1,16,0) or fixdt(1,16) –– Specify a data type object.

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Coefficients parameter.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Dependencies

This parameter appears only when you set Coefficient source to Dialog parameters, Filter object, or Auto.

When Coefficient source is set to Filter object, Coefficients parameter is automatically set to Same word length as input.

Coefficients Minimum — Minimum value of filter coefficients

[] (default) | scalar

Specify the minimum value of the filter coefficients. The default value is [] (unspecified). Simulink^® software uses this value to perform automatic scaling of fixed-point data types.

Dependencies

This parameter appears only when you set Coefficient source to Dialog parameters or Auto.

Coefficients Maximum — Maximum value of filter coefficients

[] (default) | scalar

Specify the maximum value of the filter coefficients. The default value is [] (unspecified). Simulink software uses this value to perform automatic scaling of fixed-point data types.

Dependencies

This parameter appears only when you set Coefficient source to Dialog parameters or Auto.

Product output Data Type — Product output data type

Inherit: Inherit via internal rule (default) | Inherit: Same as input | fixdt(1,16,0)

Specify the product output data type. See Fixed-Point Data Types and Multiplication Data Types for illustrations depicting the use of the product output data type in this block.

You can set this parameter to one of the following:

• Inherit: Inherit via internal rule

  For more information on this rule, see Inherit via Internal Rule.

• Inherit: Same as input

• fixdt(1,16,0) –– Specify a data type object.

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Product output parameter.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Dependencies

When Coefficient source is set to Filter object, Product output parameter is automatically set to Full precision.

Accumulator Data Type — Accumulator data type

Inherit: Inherit via internal rule (default) | Inherit: Same as input | Inherit: Same as product output | fixdt(1,16,0)

Specify the accumulator data type. See Fixed-Point Data Types for illustrations depicting the use of the accumulator data type in this block.

You can set this parameter to one of the following:

• Inherit: Inherit via internal rule.

  For more information on this rule, see Inherit via Internal Rule.

• Inherit: Same as input

• Inherit: Same as product output

• fixdt(1,16,0) –– Specify a data type object.

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Accumulator parameter.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Dependencies

When Coefficient source is set to Filter object, Accumulator parameter is automatically set to Full precision.

Output Data Type — Output data type

Inherit: Same as accumulator (default) | Inherit: Same as input | Inherit: Same as product output | fixdt(1,16,0)

Specify the output data type. See Fixed-Point Data Types for illustrations depicting the use of the output data type in this block.

You can set it to one of the following:

• Inherit: Same as accumulator

• Inherit: Same as input

• Inherit: Same as product output

• fixdt(1,16,0) –– Specify a data type object.

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Output parameter.

See Control Data Types of Signals (Simulink) for more information.

Dependencies

When Coefficient source is set to Filter object, Output parameter is automatically set to Same as accumulator.

Output Minimum — Minimum value of block output

[] (default) | scalar

Specify the minimum value that the block should output. The default value is [] (unspecified). Simulink software uses this value to perform:

• Simulation range checking (see Specify Signal Ranges (Simulink))

• Automatic scaling of fixed-point data types

Dependencies

This parameter appears only when you set Coefficient source to Dialog parameters, Input port, or Auto.

Output Maximum — Maximum value of block output

[] (default) | scalar

Specify the maximum value that the block should output. The default value is [] (unspecified). Simulink software uses this value to perform:

• Simulation range checking (see Specify Signal Ranges (Simulink))

• Automatic scaling of fixed-point data types

Dependencies

This parameter appears only when you set Coefficient source to Dialog parameters, Input port, or Auto.

Lock data type settings against changes by the fixed-point tools — Prevent fixed-point tools from overriding data types

off (default) | on

Select this parameter to prevent the fixed-point tools from overriding the data types you specify in the block dialog box.

Block Characteristics

Data Types	double | fixed point | integer | single
Direct Feedthrough	no
Multidimensional Signals	no
Variable-Size Signals	yes
Zero-Crossing Detection	no

More About

Polyphase Subfilters

A polyphase implementation of an FIR decimator splits the lowpass FIR filter impulse response into M different subfilters, where M is the downsampling or decimation factor. For more details on the polyphase implementation, see Algorithms.

Let h(n) denote the FIR filter impulse response of length N+1 and x(n) the input signal. Decimating the filter output by a factor of M is equivalent to the downsampled convolution:

$$y(n)={\displaystyle \sum _{l=0}^{N}h}(l)x(nM-l)$$

The key to the efficiency of polyphase filtering is that specific input values are only multiplied by select values of the impulse response in the downsampled convolution. For example, letting M = 2, the input values x(0),x(2),x(4), ... are combined only with the filter coefficients h(0),h(2),h(4),..., and the input values x(1),x(3),x(5), ... are combined only with the filter coefficients h(1),h(3),h(5),.... By splitting the filter coefficients into two polyphase subfilters, no unnecessary computations are performed in the convolution. The outputs of the convolutions with the polyphase subfilters are interleaved and summed to yield the filter output.

The following code demonstrates how to construct the two polyphase subfilters for the default order 35 filter.

M = 2; 
Num = fir1(35,0.4);
FiltLength = length(Num);
Num = flipud(Num(:));

if (rem(FiltLength, M) ~= 0)
     nzeros = M - rem(FiltLength, M);
     Num = [zeros(nzeros,1); Num];  % Appending zeros
end

len = length(Num);
nrows = len / M;
PolyphaseFilt = flipud(reshape(Num, M, nrows).');

The columns of PolyphaseFilt are subfilters containing the two phases of the filter in Num. For a general downsampling factor of M, there are M phases and therefore M subfilters.

Frame-Based Processing

When you set the Input processing parameter to Columns as channels (frame based), the block resamples each column of the input over time. In this mode, the block can perform either single-rate or multirate processing. You can use the Rate options parameter to specify how the block resamples the input.

• When you set the Rate options parameter to Enforce single-rate processing, the input and output of the block have the same sample rate. To decimate the output while maintaining the input sample rate, the block resamples the data in each column of the input such that the frame length of the output has an upper bound size of ceil(P/M), where P is the input frame length and M is the decimation factor specified in the Decimation factor parameter.

  In this mode, if you input a fixed-size signal (frame length does not change during simulation) and select the Allow arbitrary frame length for fixed-size input signals parameter, the input frame length can be arbitrary and does not have to be a multiple of the decimation factor. If you clear the Allow arbitrary frame length for fixed-size input signals parameter, the input frame length must be a multiple of the decimation factor.

  In this mode, if you input a variable-size signal (frame length changes during simulation), the Allow arbitrary frame length for fixed-size input signals appears on the block dialog box but does not have any impact on the input frame length. You can input a variable-size signal of any frame length even if you do not select the Allow arbitrary frame length for fixed-size input signals parameter.

  This table summarizes the support for arbitrary input frame length when you set Input processing to Columns as channels (frame based) and Rate options to Enforce single-rate processing.

  Input Signal	Block Support for this Signal	Support for Arbitrary Input Frame Length	Input Size	Output Size
  Fixed-size input signal	Yes	When you select Allow arbitrary frame length for fixed-size input signals	P-by-Q	Upper bound size of ceil(P/M)-by-Q
  Variable-size input signal	Yes	Always	P-by-Q	Upper bound size of ceil(P/M)-by-Q

  For an example that shows single-rate FIR decimation, see FIR Decimation Using Single-Rate Processing.

• When you set the Rate options parameter to Allow multirate processing, the input and output of the FIR Decimation block are of the same size, but the sample rate of the output is M times slower than that of the input. In this mode, the block treats a P-by-Q matrix input as Q independent channels. The block decimates each column of the input over time by keeping the frame size constant, and making the output frame period (T_fo) M times longer than the input frame period (T_fo = M*T_fi).

  In this mode, the block accepts only fixed-size signals and these signals can have arbitrary frame length.

  This table summarizes the support for arbitrary input frame length when you set Input processing to Columns as channels (frame based) and Rate options to Allow multirate processing.

  Input Signal	Block Support for this Signal	Support for Arbitrary Input Frame Length	Input Size	Output Size
  Fixed-size input signal	Yes	Always	P-by-Q	P-by-Q
  Variable-size input signal	No	Not applicable	Not applicable	Not applicable

  See FIR Decimation Using Multirate Frame-Based Processing for an example that uses the FIR Decimation block in this mode.

Sample-Based Processing

When you set the Input processing parameter to Elements as channels (sample based), the block treats a P-by-Q matrix input as P*Q independent channels, and decimates each channel over time. The output sample period (T_so) is M times longer than the input sample period (T_so = M*T_si), and the input and output sizes are identical.

In this mode, the block accepts only fixed-size signals and these signals can have an arbitrary frame length.

This table summarizes the support for arbitrary input frame length when you set Input processing to Elements as channels (sample based). Rate options is automatically set to Allow multirate processing.

Input Signal	Block Support for this Signal	Support for Arbitrary Input Frame Length	Input Size	Output Size
Fixed-size input signal	Yes	Always	P-by-Q	P-by-Q
Variable-size input signal	No	Not applicable	Not applicable	Not applicable

Latency

When you use the FIR Decimation block in the sample-based processing mode, the block always has zero-tasking latency. Zero-tasking latency means that the block propagates the first filtered input sample (received at time t= 0) as the first output sample. That first output sample is then followed by filtered input samples M+1, 2M+1, and so on.

When you use the FIR Decimation block in the frame-based processing mode with a frame size greater than one, the block may exhibit one-frame latency. Cases of one-frame latency can occur when the input frame size is greater than one and you set the Input processing and Rate options parameters of the FIR Decimation block as follows:

• Input processing = Columns as channels (frame based)

• Rate options = Allow multirate processing

In cases of one-frame latency, you can define the value of the first P output rows by setting the Output buffer initial conditions parameter. The default value of the Output buffer initial conditions parameter is 0. However, you can enter a matrix containing one value for each channel of the input, or a scalar value to be applied to all channels. The first filtered input sample (first filtered row of the input matrix) appears in the output as sample P+1. That sample is then followed by filtered input samples M+1, 2M+1, and so on.

Note

For more information on latency and the Simulink tasking modes, see Excess Algorithmic Delay (Tasking Latency) and Time-Based Scheduling and Code Generation (Simulink Coder).

Fixed-Point Data Types

The following diagram shows the data types used within the FIR Decimation block for fixed-point signals.

This diagram shows that data is stored in the input buffer with the same data type and scaling as the input. The block stores filtered data and any initial conditions in the output buffer using the output data type and scaling that you set in the block dialog box.

When at least one of the inputs to the multiplier is real, the output of the multiplier is in the product output data type. When both inputs to the multiplier are complex, the result of the multiplication is in the accumulator data type. For details on the complex multiplication performed by this block, see Multiplication Data Types.

Note

When the block input is fixed point, all internal data types are signed fixed-point values.

Algorithms

The FIR decimation filter is implemented efficiently using a polyphase structure. For more details on polyphase filters, see Polyphase Subfilters.

To derive the polyphase structure, start with the transfer function of the FIR filter:

$$H(z)=b_0+b_1{z}^{-1}+\mathrm{...}+b_N{z}^{-N},$$

N+1 is the length of the FIR filter.

You can rearrange this equation as follows:

$$H(z)=\begin{array}{c}\left(b_0+b_M{z}^{-M}+b_{2M}{z}^{-2M}+\mathrm{..}+b_{N-M+1}{z}^{-(N-M+1)}\right)+\\ z^{-1}\left(b_1+b_{M+1}{z}^{-M}+b_{2M+1}{z}^{-2M}+\mathrm{..}+b_{N-M+2}{z}^{-(N-M+1)}\right)+\\ \begin{array}{c}⋮\\ z^{-(M-1)}\left(b_{M-1}+b_{2M-1}{z}^{-M}+b_{3M-1}{z}^{-2M}+\mathrm{..}+b_N{z}^{-(N-M+1)}\right)\end{array}\end{array}$$

M is the number of polyphase components, and its value equals the decimation factor that you specify.

You can write this equation as:

$$H(z)=E_0(z^M)+z^{-1}{E}_1(z^M)+\mathrm{...}+z^{-(M-1)}{E}_{M-1}(z^M)$$

E₀(z^M), E₁(z^M), ..., E_M-1(z^M) are the polyphase components of the FIR filter H(z).

Conceptually, the FIR decimation filter contains a lowpass FIR filter followed by a downsampler.

Replace H(z) with its polyphase representation.

Here is the multirate noble identity for decimation.

Applying the noble identity for decimation moves the downsampling operation to before the filtering operation. This move enables you to filter the signal at a lower rate.

You can replace the delays and the decimation factor at the input with a commutator switch. The switch starts on the first branch 0 and moves in the counterclockwise direction as shown in this diagram. The accumulator at the output receives the processed input samples from each branch of the polyphase structure and accumulates these processed samples until the switch goes to branch 0. When the switch goes to branch 0, the accumulator outputs the accumulated value.

When the first input sample is delivered, the switch feeds this input to the branch 0 and the decimator computes the first output value. As more input samples come in, the switch moves in the counter clockwise direction through branches M−1, M−2, and all the way up to branch 0, delivering one sample at a time to each branch. When the switch comes to branch 0, the decimator outputs the next set of output values. This process continues as data keeps coming in. Every time the switch comes to the branch 0, the decimator outputs y[m]. The decimator effectively outputs one sample for every M samples it receives. Hence the sample rate at the output of the FIR decimation filter is fs/M.

References

[1] Fliege, N. J. Multirate Digital Signal Processing: Multirate Systems, Filter Banks, Wavelets. West Sussex, England: John Wiley & Sons, 1994.

[2] Orfanidis, Sophocles J. Introduction to Signal Processing. Upper Saddle River, NJ: Prentice-Hall, 1996.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

Generated code relies on the memcpy or memset function (string.h) under certain conditions.

Generate SIMD code using Intel^® AVX2 code replacement library

Note

Requires Embedded Coder^® license

The FIR Decimation block supports SIMD code generation using Intel AVX2 code replacement library under these conditions:

• Filter structure is set to Direct form.

• Input processing is set to Columns as channels (frame based).

• Rate options is set to Enforce single-rate processing.

• Clear the Allow arbitrary frame length for fixed-size input signals parameter.

• Input signal is real-valued with real filter coefficients.

• Input signal is complex-valued with real or complex filter coefficients.

• Input signal has a data type of single or double.

To generate SIMD code from this block using this workflow, see Use Intel AVX2 Code Replacement Library to Generate SIMD Code from Simulink Blocks.

Generate SIMD code by leveraging target hardware instruction set extensions (since R2023a)

Note

Requires Simulink Coder™ or Embedded Coder license

You can generate SIMD code for the FIR Decimation block on all Intel platforms, ARM^® Cortex^®-A processors, and Apple silicon processors by using the model configuration parameter Leverage target hardware instruction set extensions under these conditions:

• You set Filter structure to Direct form for the FIR Decimation block

• You set Input processing to Columns as channels (frame based)

• Input signal is real-valued with real filter coefficients

• Input signal is complex-valued with real or complex filter coefficients.

• Data type of the input signal is single (ARM Cortex-A processors)

• Data type of the input signal is single or double (Intel platforms)

In addition, configure your model appropriately. In the Modeling tab of the Simulink model window, click Model Settings and configure these parameters under Code Generation.

• In the Optimization pane:

  • Provide a specific instruction set in the Leverage target hardware instruction set extensions parameter.

  • Select the Optimize reductions parameter.

  • Under Optimization levels, set Level to Maximum and Priority to Maximize execution speed.

• In the Interface pane, under Software environment, clear non-finite numbers.

To generate SIMD code from this block using this workflow, see Use Target Hardware Instruction Set Extensions to Generate SIMD Code from Simulink Blocks for Intel Platforms, Use Target Hardware Instruction Set Extensions to Generate SIMD Code from Simulink Blocks for Apple silicon, and Use Target Hardware Instruction Set Extensions to Generate SIMD Code from Simulink Blocks for ARM Cortex-A Processors.

For computationally intensive operations on supported blocks, SIMD intrinsics can significantly improve the performance of the generated code on Intel platforms. For more details, see Optimize Code for Reduction Operations by Using SIMD (Simulink Coder).

For more information on SIMD code generation in DSP System Toolbox, see SIMD Code Generation.

HDL Code Generation

Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.

HDL Architecture

The block has HDLDataPath as a default architecture. This architecture provides additional configuration options that affect HDL implementation and synthesized logic.

HDL Block Properties

HDL Block Properties	Description
InputPipeline	Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see InputPipeline (HDL Coder).
OutputPipeline	Number of output pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see OutputPipeline (HDL Coder).
ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is 0. For more details, see ConstrainedOutputPipeline (HDL Coder).
FlattenFilter	Remove hierarchy of Filter subsystem from generated HDL code. The default is auto. See FlattenHierarchy (HDL Coder).
DSPStyle	Synthesis attributes for multiplier mapping. The default is none. See also DSPStyle (HDL Coder).
SharingFactor	Number of functionally equivalent resources to map to a single shared resource. The default is 0. See also Resource Sharing (HDL Coder).
StreamingFactor	Number of parallel data paths, or vectors, that are time multiplexed to transform into serial, scalar data paths. The default is 0, which implements fully parallel data paths. See also Streaming (HDL Coder).
ConstMultiplierOptimization	Canonical signed digit (CSD) or factored CSD optimization. The default is none. See also ConstMultiplierOptimization (HDL Coder).
MultiplerArchitecture	Select the multipler architecture as linear or shiftadd. The default is linear. For more information, see HDL Code Generation section in Product, Matrix Multiply (Simulink).
MultiplierInputPipeline	Specify the number of pipeline stages to add at filter multiplier inputs. See also MultiplierInputPipeline (HDL Coder).
MultiplierOutputPipeline	Specify the number of pipeline stages to add at filter multiplier outputs. See also MultiplierOutputPipeline (HDL Coder).
AdderChainArchitecture	Select the adder architecture to generate linear chain or tree structure of adders to compute sum of elements. The default is tree. For more information, see HDL Code Generation section in Sum (Simulink).
AdderOutputPipeline	Number of output pipeline stages to insert in the generated code for addition operation. The default is 0. For more details, see OutputPipeline (HDL Coder).

Data Type Support

The block supports these data types for HDL code generation:

Input Port	Dimension	Fixed-Point	Floating-Point	Built-in Integers	Bus	Boolean	Enumerated	Complex Signal
In	Scalar Vector Matrix	Yes	Half Single Double	Yes	Yes	Yes	Yes	Yes

Optimizations

The block participates in these HDL optimizations to optimize the speed, and area.

Area Optimization

Optimization	Description
Resource Sharing (HDL Coder)	Resource sharing is an area optimization in which HDL Coder identifies multiple functionally equivalent resources and replaces them with a single resource.
Streaming (HDL Coder)	Streaming is an area optimization in which HDL Coder transforms a vector data path to a scalar data path (or to several smaller-sized vector data paths).

Speed Optimization

Optimization	Description
Distributed Pipelining (HDL Coder)	Distributed pipelining, or register retiming, is a speed optimization that moves existing delays in a design to reduce the critical path while preserving functional behavior.
Clock-Rate Pipelining (HDL Coder)	Clock-rate pipelining is an optimization framework in HDL Coder that allows other speed and area optimizations to introduce latency at the clock rate.
Adaptive Pipelining (HDL Coder)	Adaptive pipelining optimization creates patterns or combination of blocks with registers that can improve the achievable clock frequency and reduce the area usage on the FPGA boards by inserting pipeline registers to the blocks in your design.
Critical Path Estimation (HDL Coder)	To quickly identify the most likely critical path in your design, use Critical Path Estimation. Critical path estimation speeds up the iterative process of finding the critical path. To know blocks that are characterized in critical path estimation, see Characterized Blocks (HDL Coder).

Limitations and Considerations

The block has these limitations:

• You must set Initial conditions to zero. HDL code generation is not supported for nonzero initial states.

• When you select Dialog parameters, the following fixed-point options are not supported for HDL code generation:

  • Slope and Bias scaling

• Programmable coefficients are not supported.

• Frame-based input filters are not supported for:

  • Resettable and enabled subsystems

  • Complex input signals with complex coefficients. You can use either complex input signals and real coefficients, or complex coefficients and real input signals.

  • Sharing and streaming optimizations

To configure the FIR Decimation block for a frame-based input, use the following block settings:

Frame-based input

HDL Coder supports the use of vector inputs to FIR Decimation blocks, where each element of the vector represents a sample in time. You can use an input vector of up to 512 samples. The frame-based implementation supports fixed-point input and output data types, and uses full-precision internal data types. The output is a column vector of reduced size, corresponding to your decimation factor. You can use real input signals with real coefficients, complex input signals with real coefficients, or real input signals with complex coefficients. Connect a column vector signal to the FIR Decimation block input port. Specify Input processing as Columns as channels (frame based). Set Rate options to Enforce single-rate processing.

Note

For a FIR decimation filter with hardware-friendly control signals and simulation of HDL latency in Simulink, or for complex data with complex coefficients, use the FIR Decimator (DSP HDL Toolbox) block instead of this block.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced before R2006a

R2024b: Generate SIMD code for Apple silicon processors

In R2024b, if you have Embedded Coder, you can generate SIMD code for the FIR Decimation block for Apple silicon processors by using the model configuration parameter Leverage target hardware instruction set extensions. For more information, see Use Target Hardware Instruction Set Extensions to Generate SIMD Code from Simulink Blocks for Apple silicon.

R2024a: Generate SIMD code for ARM Cortex-A processors

In R2024a, if you have Embedded Coder, you can generate SIMD code for the FIR Decimation block for ARM Cortex-A processors by using the model configuration parameter Leverage target hardware instruction set extensions.

R2023b: Generate SIMD Code for Complex Signals

In R2023b, if you have Embedded Coder, you can generate SIMD code for the FIR Decimation block when the input signal is complex-valued by using the model configuration parameter Leverage target hardware instruction set extensions.

R2023a: Generate SIMD code for FIR Decimation block on all Intel platforms

In R2023a, if you have Embedded Coder, you can generate SIMD code for the FIR Decimation block on all Intel platforms by using the model configuration parameter Leverage target hardware instruction set extensions. Previously, you had to use a code replacement library to generate SIMD code. For more details, see Code Generation.

R2022b: Support for arbitrary input frame length

Starting in R2022b, this block supports input signals with arbitrary frame lengths when the:

• Input signal is a fixed-size signal (frame length does not change during simulation) and the block allows for multirate processing

• Input signal is a fixed-size signal, the block enforces single-rate processing, and you select the Allow arbitrary frame length for fixed-size input signals parameter

• Input signal is a variable-size signal (frame length changes during simulation)

When this block supports an arbitrary frame length input signal, the input frame length does not have to be a multiple of the decimation factor.

For more details, see Frame-Based Processing and Sample-Based Processing.