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

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

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

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 Interpolation Filter.

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:

  $$\text{WL}=\mathrm{ceil}\left({\log }_2\left(\frac{{\left(RM\right)}^N}{R}\right)\right)+I$$

  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

CIC Filter

CIC filters are an optimized class of linear phase FIR filters composed of a comb part and an integrator part.

The CIC interpolation filter is conceptually given by an upsampler followed by a single rate CIC filter, H(z), which is a lowpass anti-imaging filter. The CIC interpolation filter increases the sample rate of an input signal by an integer factor using a cascaded integrator-comb (CIC) filter.

In a more efficient implementation, the single rate CIC filter H(z) is factorized this way:

$$\begin{array}{l}H(z)={\left[{\displaystyle \sum _{k=0}^{RM-1}{z}^{-k}}\right]}^N=\frac{{(1-z^{-RM})}^N}{{(1-z^{-1})}^N}=\frac{{(1-z^{-RM})}^N}{1}·\frac{1}{{(1-z^{-1})}^N}=H_{\text{C}}{}^N(z)·H_{\text{I}}{}^N(z)\\ \end{array}$$

where,

• H_C is the transfer function of the N sections of the cascaded comb filters, each with a width of RM.

• H_I is the transfer function of the integrator part of the filter containing N stages of integrators.

• 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.

In the overall multirate realization, the algorithm applies the noble identity for interpolation and moves the rate change factor, R, to follow after the N sections of the cascaded comb filters.

The transfer function of the resulting filter is given by the following equation:

$$H(z)=\frac{{\left(1-z^{-M}\right)}^N}{{\left(1-z^{-1}\right)}^N}.$$

For a block diagram that shows the multirate implementation, see Algorithms.

Algorithms

CIC Interpolation Filter

The CIC interpolation filter in More About is realized as a cascade of N sections of comb filters followed by a rate change by a factor R, followed by N sections of cascaded integrators.

This diagram shows two sections of cascaded comb filters and two sections of cascaded integrators. The unit delay in the integrator portion of the CIC filter can be located in either the feedforward or the feedback path. These two configurations yield identical filter frequency response. However, the numerical outputs from these two configurations are different due to the latency. This algorithm puts the unit delay in the feedforward path of the integrator since it is a preferred configuration 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 the memcpy or memset function (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 a power-of-two slope and zero bias.

Version History

Introduced before R2006a