CIC Interpolation

Interpolate signal using cascaded integrator-comb filter

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

Description

The CIC Interpolation block performs a sample rate increase (interpolation) on an input signal by an integer factor. cascaded integrator-comb (CIC) filters are a class of linear phase FIR filters that consist of a comb part and an integrator part.

The CIC Interpolation block requires a Fixed-Point Designer™ license.

Ports

Input

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`Port_1` — Input signal
vector | matrix

Data input, specified as a vector or matrix. If the input is fixed point, it must be signed integer or signed fixed point with power-of-two slope and zero bias.

Data Types: int8 | int16 | int32 | int64 | fixed point
Complex Number Support: Yes

Output

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`Port_1` — CIC interpolated output
vector | matrix

CIC interpolated output, returned as a vector or a matrix. The data type of the output is determined by the settings in the block dialog. The complexity of the output matches that of the input. The number of output rows is R✕Num, where R is the interpolation factor and Num is the number of input rows.

Data Types: int8 | int16 | int32 | int64 | fixed point
Complex Number Support: Yes

Parameters

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`Coefficient source` — Source of filter information
`Dialog parameters` (default) | `Filter object`

Source of the filter information, specified as one of the following:

Dialog parameters — Enter information about the filter, such as Interpolation factor (R), Differential delay (M) and Number of sections (N), in the block dialog.
Filter object — Specify the filter using a dsp.CICInterpolator System object™.

`Interpolation factor (R)` — Interpolation factor
`2` (default) | integer

Interpolation factor of the filter, specified as an integer greater than 1.

Dependencies

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

`Differential Delay (M)` — Differential delay
`1` (default) | positive integer

Specify the differential delay of the comb part of the filter, M, as a positive integer. For more details, see CIC Filter Structure.

Dependencies

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

`Number of sections (N)` — Number of filter sections
`2` (default) | positive integer

Specify the number of filter sections. The number you specify determines the number of sections in either the comb part of the filter or the integrator part of the filter. This value does not represent the total number of sections in the comb and integrator parts combined.

Dependencies

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

`Data type specification mode` — Specify word length and fraction length of filter sections and output
`Full precision` (default) | `Minimum section word lengths` | `Specify word lengths` | `Binary point scaling`

Choose how you specify the fixed-point word length and fraction length of the filter sections and/or output:

Full precision — The word and fraction lengths of the filter sections and outputs are automatically selected for you. The output and last section word lengths (WL) are set to:

$WL = ceil (\log_{2} (\frac{{(R M)}^{N}}{R})) + I$
where,
- I –– Input word length
- M –– Differential delay
- N –– Number of sections
- R –– Interpolation factor
The other section word lengths are set to accommodate the bit growth, as described in Hogenauer's paper [1]. All fraction lengths are set to the input fraction length.
Minimum section word lengths — Specify the word length of the filter output in the Output word length parameter. The word lengths of the filter sections are set in the same way as in Full precision mode.
The section fraction lengths are set to the input fraction length. The output fraction length is set to the input fraction length minus the difference between the last section word length and the output word length.
Specify word lengths — Specify the word lengths of the filter sections and output in the Section word lengths and Output word length parameters. The fraction lengths of the filter sections are set such that the spread between word length and fraction length is the same as in full-precision mode. The output fraction length is set to the input fraction length minus the difference between the last section word length and the output word length.
Binary point scaling — Specify the word and fraction lengths of the filter sections and output in the Section word lengths, Section fraction lengths, Output word length, and Output fraction length parameters.

Dependencies

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

`Section word lengths` — Word length of filter sections
[`16 16 16 16`] (default) | scalar | row vector

Word lengths of filter sections, specified as a scalar or a vector of length equal to 2N, where N is the number of filter sections. The section word length must be in the range [2, 128].

Dependencies

This parameter appears when you set Coefficient source to Dialog parameters and Data type specification mode to either Specify word lengths or Binary point scaling.

`Section fraction lengths` — Fraction length of filter sections
`0` (default) | integer

Fraction lengths of filter sections, specified as an integer.

Dependencies

This parameter appears when you set Coefficient source to Dialog parameters and Data type specification mode to Binary point scaling.

`Output word length` — Word length of filter output
`32` (default) | integer

Word length of the filter output, specified as an integer in the range [2, 128].

Dependencies

This parameter appears when you set Coefficient source to Dialog parameters and Data type specification mode to any option other than Full precision.

`Output fraction length` — Fraction length of filter output
`0` (default) | integer

Fraction length of the filter output, specified as an integer.

Dependencies

This parameter appears when you set Coefficient source to Dialog parameters and Data type specification mode to Binary point scaling.

`Input processing` — Method of processing input
`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) — The block treats each column of the input as a separate channel. In this mode, the block always performs single-rate processing.
Elements as channels (sample based) — The block treats each element of the input as a separate channel. In this mode, the input to the block must be a scalar or a vector. You can use the Rate options parameter to specify whether the block performs single-rate or multirate processing.

`Rate options` — Rate processing rule
`Enforce single-rate processing` (default) | `Allow multirate processing`

Specify the rate processing rule for the block. You can select one of the following options:

Enforce single-rate processing — The block maintains the sample rate of the input.
Allow multirate processing — The block produces an output with a sample rate that is R times faster than the input sample rate. To select this option, you must set the Input processing parameter to Elements as channels (sample based).

`Filter object` — Multirate filter object
`dsp.CICInterpolator System object`

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

You can define the System object in the block dialog or in a MATLAB^® workspace variable.

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

Dependencies

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

`View Filter Response` — View filter response
button

This button opens the Filter Visualization Tool (fvtool) from the Signal Processing Toolbox™ product and displays the filter response of the filter defined in the block. For more information on FVTool, see the Signal Processing Toolbox documentation.

Note

If you specify a filter in the Filter object parameter, you must apply the filter by clicking the Apply button before using the View Filter Response button.

Block Characteristics

Data Types	`fixed point` \| `integer`
Direct Feedthrough	`no`
Multidimensional Signals	`no`
Variable-Size Signals	`no`
Zero-Crossing Detection	`no`

More About

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CIC Interpolation Filter

The transfer function of a CIC interpolator filter is

$\begin{array}{l} H (z) = {[\sum_{k = 0}^{R M - 1} z^{- k}]}^{N} = \frac{{(1 - z^{- R M})}^{N}}{{(1 - z^{- 1})}^{N}} = \frac{{(1 - z^{- R M})}^{N}}{1} \cdot \frac{1}{{(1 - z^{- 1})}^{N}} = H_{C}^{N} (z) \cdot H_{I}^{N} (z) \end{array}$

where

H_I is the transfer function of the integrator part of the filter.
H_C is the transfer function of the comb part of the filter.
N is the number of sections. The number of sections in a CIC filter is defined as the number of sections in either the comb part or the integrator part of the filter. This value does not represent the total number of sections throughout the entire filter.
R is the interpolation factor.
M is the differential delay.

CIC Filter Structure

The CIC Interpolation block has the following CIC filter structure. The structure consists of N sections of cascaded comb filters, followed by a rate change by a factor R, followed by N sections of cascaded integrators [1] .

The unit delay in the integrator portion of the CIC Filter can be located in either the feed-forward or the feedback path. These two configurations yield an identical filter frequency response. However, the numerical outputs from these two configurations are different due to the latency. This block puts the unit delay in the feed-forward path of the integrator because that configuration is preferred for HDL implementation.

References

[1] Hogenauer, E.B. “An Economical Class of Digital Filters for Decimation and Interpolation” IEEE Transactions on Acoustics, Speech and Signal Processing. Vol. 29, Number 2, 1981, pp. 155–162, 1981.

[2] Meyer-Baese, U. Digital Signal Processing with Field Programmable Gate Arrays. New York: Springer Verlag, 2001.

[3] Harris, Fredric J., Multirate Signal Processing for Communication Systems. Upper Saddle River, NJ: Prentice Hall PTR, 2004.

Extended Capabilities

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

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

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

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

HDL Coder supports Coefficient source options Dialog parameters and Filter object.

AddPipelineRegisters Support

When you use AddPipelineRegisters, registers are placed based on the filter structure. The pipeline register placement determines the latency.

Pipeline Register Placement	Latency (clock cycles)
A pipeline register is added between the comb stages of the differentiators.	`NS`, the number of sections (at the input side).

HDL Filter Properties

AddPipelineRegisters

Insert a pipeline register between stages of computation in a filter. See also AddPipelineRegisters (HDL Coder).

HDL Block Properties

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).
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).

Restrictions

Vector and frame inputs are not supported for HDL code generation.
When you select Dialog parameters, the Filter Structure option Zero-latency interpolator is not supported for HDL code generation. From the Filter Structure drop-down list, select Interpolator.
When you use AddPipelineRegisters, delays in parallel paths are not automatically balanced. Manually add delays where required by your design.

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

If the input is fixed point, it must be signed integer or signed fixed point with power-of-two slope and zero bias.

Documentation

CIC Interpolation

Description

Ports

Input

Port_1 — Input signal vector | matrix

Output

Port_1 — CIC interpolated output vector | matrix

Parameters

Coefficient source — Source of filter information Dialog parameters (default) | Filter object

Interpolation factor (R) — Interpolation factor 2 (default) | integer

Dependencies

Differential Delay (M) — Differential delay 1 (default) | positive integer

Dependencies

Number of sections (N) — Number of filter sections 2 (default) | positive integer

Dependencies

Data type specification mode — Specify word length and fraction length of filter sections and output Full precision (default) | Minimum section word lengths | Specify word lengths | Binary point scaling

Dependencies

Section word lengths — Word length of filter sections [16 16 16 16] (default) | scalar | row vector

Dependencies

Section fraction lengths — Fraction length of filter sections 0 (default) | integer

Dependencies

Output word length — Word length of filter output 32 (default) | integer

Dependencies

Output fraction length — Fraction length of filter output 0 (default) | integer

Dependencies

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

Rate options — Rate processing rule Enforce single-rate processing (default) | Allow multirate processing

Filter object — Multirate filter object dsp.CICInterpolator System object

Dependencies

View Filter Response — View filter response button

Block Characteristics

More About

CIC Interpolation Filter

CIC Filter Structure

References

Extended Capabilities

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

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

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

See Also

Functions

Objects

Blocks

DSP System Toolbox Documentation

Support

`Port_1` — Input signal
vector | matrix

`Port_1` — CIC interpolated output
vector | matrix

`Coefficient source` — Source of filter information
`Dialog parameters` (default) | `Filter object`

`Interpolation factor (R)` — Interpolation factor
`2` (default) | integer

`Differential Delay (M)` — Differential delay
`1` (default) | positive integer

`Number of sections (N)` — Number of filter sections
`2` (default) | positive integer

`Data type specification mode` — Specify word length and fraction length of filter sections and output
`Full precision` (default) | `Minimum section word lengths` | `Specify word lengths` | `Binary point scaling`

`Section word lengths` — Word length of filter sections
[`16 16 16 16`] (default) | scalar | row vector

`Section fraction lengths` — Fraction length of filter sections
`0` (default) | integer

`Output word length` — Word length of filter output
`32` (default) | integer

`Output fraction length` — Fraction length of filter output
`0` (default) | integer

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

`Rate options` — Rate processing rule
`Enforce single-rate processing` (default) | `Allow multirate processing`

`Filter object` — Multirate filter object
`dsp.CICInterpolator System object`

`View Filter Response` — View filter response
button

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

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

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