FIR Interpolation

Perform polyphase FIR interpolation

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

Description

The FIR Interpolation block performs an efficient polyphase interpolation using an integer upsampling factor L along the first dimension.

Conceptually, the FIR interpolator (as shown in the schematic) consists of an upsampler followed by an FIR anti-imaging filter, which is usually an approximation of an ideal band-limited interpolation filter. To design an FIR anti-imaging filter, use the designMultirateFIR function. The upsampler upsamples each channel of the input to a higher rate by inserting L–1 zeros between samples. The FIR filter that follows filters each channel of the upsampled data. The resulting discrete-time signal has a sample rate that is L times the original sample rate.

FIR interpolator contains an upsampler followed by an anti-imaging FIR filter.

However, 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.

You can use the FIR Interpolation block inside triggered subsystems when you set the Rate options parameter to Enforce single-rate processing.

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

Examples

FIR Interpolation Using Single-Rate Processing

Use FIR Interpolation block in single-rate processing mode.

Open Model

FIR Interpolation Using Multirate Frame-Based Processing

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

Open Model

Polyphase Implementation of FIR Interpolation Block

Polyphase implementation of the FIR interpolator.

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

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In — Data input
vector | matrix

Specify the data input as a vector or a matrix.

When you set Input processing to Columns as channels (frame based) and Rate options to Enforce single-rate processing, the input can be a variable-size signal. That is, the frame size (number of rows) and the number of channels (columns) of the signal can change during simulation.

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

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:

$H (z) = b_{0} + b_{1} z^{- 1} + ... + b_{N} z^{- N},$

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-imaging filter, the coefficients usually correspond to a lowpass filter with a normalized cutoff frequency no greater than the reciprocal of the interpolation factor. To design such a filter, use the designMultirateFIR function.

Coefficient values are tunable. That is, their values can change during simulation while their properties such as size, data type, and complexity cannot change.

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.

Output

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Out — Interpolator output
vector | matrix

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

When Rate options is set to:

Enforce single-rate processing — When you select this option, the block maintains the input sample rate, and interpolates the signal by increasing the output frame size by a factor of L.
Allow multirate processing — When you select this option, the block interpolates the signal such that the output sample rate is L times faster than the input sample rate.

When the input is a variable-size signal, the output is also a variable-size signal.

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

Parameters

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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.FIRInterpolator System object™.
Auto –– When you select Auto, the block designs an FIR interpolator using the interpolation factor you specify in Interpolation 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(3,1)` (default) | vector

Specify the numerator coefficients of the FIR filter transfer function H(z).

$H (z) = b_{0} + b_{1} z^{- 1} + ... + b_{N} z^{- N},$

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.

The block internally initializes all filter states to zero.

Dependencies

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

Interpolation factor — Interpolation factor
`3` (default) | positive scalar

Specify the integer factor L. The block increases 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.

Filter object — Filter object
`dsp.FIRInterpolator`

Specify the name of the multirate filter object that you want the block to implement. You must specify the filter as a dsp.FIRInterpolator 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 interpolates input
`Enforce single-rate processing` (default) | `Allow multirate processing`

Specify the method by which the block should interpolate 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 interpolates the signal by increasing the output frame size by a factor of L. To select this option, you must set the Input processing parameter to Columns as channels (frame based).
Allow multirate processing — When you select this option, the block interpolates the signal such that the output sample rate is L times faster than the input sample rate.

Output buffer initial conditions — Initial conditions
`0` (default) | scalar | matrix

When you set the Rate options parameter to Allow multirate processing and run your models in Simulink^® MultiTasking mode, the block exhibits latency. The amount of latency for multirate, multitasking operation depends on how you set the Input processing parameter.

Input processing	Latency
`Elements as channels (sample based)`	L samples
`Columns as channels (frame based)`	L frames (K_i samples per frame)

When the block exhibits latency, the default initial condition is zero. Alternatively, you can use the Output buffer initial conditions parameter to specify a matrix of initial conditions containing one value for each channel or a scalar initial condition that the block applies to all channels. The block divides the Output buffer initial conditions by the Interpolation factor and outputs the scaled initial conditions until the first filtered input sample becomes available.

Output buffer initial conditions are stored in the output data type and scaling.

See Latency for more information about latency in the FIR Interpolation block.

Dependencies

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

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 the 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

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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 interpolate the output while maintaining the input sample rate, the block resamples the data in each column of the input such that the frame size of the output (K_o) is L times larger than that of the input (K_o = K_i*L).
For an example of single-rate FIR Interpolation, see FIR Interpolation Using Single-Rate Processing.
When you set the Rate options parameter to Allow multirate processing, the input and output of the FIR Interpolation block are the same size. However, the sample rate of the output is L times faster than that of the input. In this mode, the block treats a K_i-by-N matrix input as N independent channels. The block interpolates each column of the input over time by keeping the frame size constant (K_i=K_o), while making the output frame period (T_fo) L times shorter than the input frame period (T_fo = T_fi/L).
See FIR Interpolation Using Multirate Frame-Based Processing for an example that uses the FIR Interpolation 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 interpolates each channel over time. The output sample period (T_so) is L times shorter than the input sample period (T_so = T_si/L), while the input and output sizes remain identical.

Latency

When you run your models in the Simulink SingleTasking mode or set the Input processing parameter to Columns as channels (frame based) and the Rate options parameter to Enforce single-rate processing, the FIR Interpolation 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 L–1 interpolated values, the second filtered input sample, and so on.

The only time the FIR Interpolation block exhibits latency is when you set the Rate options parameter set to Allow multirate processing and run your models in the Simulink MultiTasking mode. The amount of latency for a multirate, multitasking operation depends on how you set the Input processing parameter.

Input processing	Latency
`Elements as channels (sample based)`	L samples
`Columns as channels (frame based)`	L frames (K_i samples per frame)

When the block exhibits latency, the default initial condition is zero. Alternatively, you can use the Output buffer initial conditions parameter to specify a matrix of initial conditions containing one value for each channel or a scalar initial condition that the block applies to all channels. The block scales the Output buffer initial conditions by the Interpolation factor and outputs the scaled initial conditions until the first filtered input sample becomes available.

When the block is in the sample-based processing mode, the block outputs the scaled initial conditions at the start of each channel, followed immediately by the first filtered input sample, then L–1 interpolated values, and so on.

When the block is in the frame-based processing mode and using the default initial condition of zero, the first K_i*L output rows contain zeros, where K_i is the input frame size. The first filtered input sample (first filtered row of the input matrix) appears in the output as sample K_i*L+1. That value is then followed by L–1 interpolated values, the second filtered input sample, 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 Interpolation block for fixed-point signals.

This diagram shows that input 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.

Algorithms

The FIR interpolation filter is implemented efficiently using a polyphase structure.

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

$H (z) = b_{0} + b_{1} z^{- 1} + ... + b_{N} z^{- N},$

N+1 is the length of the FIR filter.

You can rearrange this equation as follows:

$H (z) = \begin{matrix} (b_{0} + b_{L} z^{- L} + b_{2 L} z^{- 2 L} + .. + b_{N - L + 1} z^{- (N - L + 1)}) + \\ z^{- 1} (b_{1} + b_{L + 1} z^{- L} + b_{2 L + 1} z^{- 2 L} + .. + b_{N - L + 2} z^{- (N - L + 1)}) + \\ \begin{matrix} ⋮ \\ z^{- (L - 1)} (b_{L - 1} + b_{2 L - 1} z^{- L} + b_{3 L - 1} z^{- 2 L} + .. + b_{N} z^{- (N - L + 1)}) \end{matrix} \end{matrix}$

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

You can write this equation as:

$H (z) = E_{0} (z^{L}) + z^{- 1} E_{1} (z^{L}) + ... + z^{- (L - 1)} E_{L - 1} (z^{L})$

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

Conceptually, the FIR interpolation filter contains an upsampler followed by an FIR lowpass filter H(z).

FIR interpolator contains an upsampler followed by an anti-imaging FIR filter.

Replace H(z) with its polyphase representation.

Here is the multirate noble identity for interpolation.

Applying the noble identity for interpolation moves the upsampling operation to after the filtering operation. This move enables you to filter the signal at a lower rate.

You can replace the upsampling operator, delay block, and adder with a commutator switch. The switch starts on the first branch 0 and moves in the counterclockwise direction, each time receiving one sample from each branch. The interpolator effectively outputs L samples for every one input sample it receives. Hence the sample rate at the output of the FIR interpolation filter is Lfs.

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 Interpolation block supports SIMD code generation using Intel AVX2 code replacement library under these conditions:

Input processing is set to Columns as channels (frame based).
Rate options is set to Enforce single-rate processing.
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 Interpolation 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 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).
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

Input Port

Dimension

Fixed-Point

Floating-Point

Built-in Integers

Bus

Boolean

Enumerated

Complex Signal

Scalar

Vector

Matrix

Yes

Half

Single

Double

Yes

Block Parameter Configuration

These block parameter configurations are incompatible with HDL code generation.

Block Parameter	Limitations
Rate options	Parameter value `Enforce single-rate processing` is not supported.
Input processing	Parameter value `Columns as channels (frame based)` is not supported.
Coefficient source	Parameter value `Input port` is not supported.

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

You must set Initial conditions to zero. HDL code generation is not supported for nonzero initial states.
Frame inputs and outputs are not supported for HDL code generation.
When you select Dialog parameters, the following fixed-point options are not supported for HDL code generation:
- Coefficients: Slope and Bias scaling

Note

For an HDL-optimized filter architecture with hardware-friendly control signals that supports vector input and output data, use the FIR Interpolator (DSP HDL Toolbox) block. The DSP HDL Toolbox™ block simulates the latency of the HDL algorithm in Simulink.

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

Version History

Introduced before R2006a

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R2024b: Generate SIMD code for Apple silicon processors

In R2024b, if you have Embedded Coder, you can generate SIMD code for the FIR Interpolation 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 Interpolation 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 Interpolation 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 Interpolation block on all Intel platforms

In R2023a, if you have Embedded Coder license, you can generate SIMD code for the FIR Interpolation 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.

FIR Interpolation

Description

Examples

FIR Interpolation Using Single-Rate Processing

FIR Interpolation Using Multirate Frame-Based Processing

Polyphase Implementation of FIR Interpolation Block

Two-Stage Multirate Narrow Lowpass Filter

Ports

Input

In — Data input vector | matrix

Num — Numerator coefficients vector

Dependencies

Output

Out — Interpolator output vector | matrix

Parameters

Coefficient source — FIR filter coefficient source Auto (default) | Dialog parameters | Input port | Filter object

FIR filter coefficients — Lowpass FIR filter coefficients designMultirateFIR(3,1) (default) | vector

Dependencies

Interpolation factor — Interpolation factor 3 (default) | positive scalar

Dependencies

Filter object — Filter object dsp.FIRInterpolator

Dependencies

Input processing — Method to process input signals Columns as channels (frame based) (default) | Elements as channels (sample based)

Rate options — Method by which block interpolates input Enforce single-rate processing (default) | Allow multirate processing

Output buffer initial conditions — Initial conditions 0 (default) | scalar | matrix

Dependencies

View Filter Response — View filter response button

Rounding mode — Rounding mode Floor (default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero

Saturate on integer overflow — Saturate on integer overflow off (default) | on

Coefficients Data Type — Coefficients data type Inherit: Same word length as input (default) | fixdt(1,16) | fixdt(1,16,0)

Dependencies

Coefficients Minimum — Minimum value of filter coefficients [] (default) | scalar

Dependencies

Coefficients Maximum — Maximum value of filter coefficients [] (default) | scalar

Dependencies

Product output Data Type — Product output data type Inherit: Inherit via internal rule (default) | Inherit: Same as input | fixdt(1,16,0)

Dependencies

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)

Dependencies

Output Data Type — Output data type Inherit: Same as accumulator (default) | Inherit: Same as input | Inherit: Same as product output | fixdt(1,16,0)

Dependencies

Output Minimum — Minimum value of block output [] (default) | scalar

Dependencies

Output Maximum — Maximum value of block output [] (default) | scalar

Dependencies

Lock data type settings against changes by the fixed-point tools — Prevent fixed-point tools from overriding data types off (default) | on

Block Characteristics

More About

Frame-Based Processing

Sample-Based Processing

Latency

Fixed-Point Data Types

Algorithms

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

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

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

Version History

R2024b: Generate SIMD code for Apple silicon processors

R2024a: Generate SIMD code for ARM Cortex-A processors

R2023b: Generate SIMD Code for Complex Signals

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

See Also

Functions

Objects

Blocks

In — Data input
vector | matrix

Num — Numerator coefficients
vector

Out — Interpolator output
vector | matrix

Coefficient source — FIR filter coefficient source
Auto (default) | Dialog parameters | Input port | Filter object

FIR filter coefficients — Lowpass FIR filter coefficients
`designMultirateFIR(3,1)` (default) | vector

Interpolation factor — Interpolation factor
`3` (default) | positive scalar

Filter object — Filter object
`dsp.FIRInterpolator`

Input processing — Method to process input signals
`Columns as channels (frame based)` (default) | `Elements as channels (sample based)`

Rate options — Method by which block interpolates input
`Enforce single-rate processing` (default) | `Allow multirate processing`

Output buffer initial conditions — Initial conditions
`0` (default) | scalar | matrix

View Filter Response — View filter response
button

Rounding mode — Rounding mode
`Floor` (default) | `Ceiling` | `Convergent` | `Nearest` | `Round` | `Simplest` | `Zero`

Saturate on integer overflow — Saturate on integer overflow
`off` (default) | `on`

Coefficients Data Type — Coefficients data type
`Inherit: Same word length as input` (default) | `fixdt(1,16)` | `fixdt(1,16,0)`

Coefficients Minimum — Minimum value of filter coefficients
`[]` (default) | scalar

Coefficients Maximum — Maximum value of filter coefficients
`[]` (default) | scalar

Product output Data Type — Product output data type
`Inherit: Inherit via internal rule` (default) | `Inherit: Same as input` | `fixdt(1,16,0)`

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)`

Output Data Type — Output data type
`Inherit: Same as accumulator` (default) | `Inherit: Same as input` | `Inherit: Same as product output` | `fixdt(1,16,0)`

Output Minimum — Minimum value of block output
`[]` (default) | scalar

Output Maximum — Maximum value of block output
`[]` (default) | scalar

Lock data type settings against changes by the fixed-point tools — Prevent fixed-point tools from overriding data types
`off` (default) | `on`

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

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

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