CIC Interpolation
Interpolate signal using cascaded integratorcomb filter
Libraries:
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 integratorcomb (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 FixedPoint 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 poweroftwo 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 adsp.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 fixedpoint 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:$$\text{WL}=\mathrm{ceil}\left({\mathrm{log}}_{2}\left(\frac{{\left(RM\right)}^{N}}{R}\right)\right)+I$$
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 inFull 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 fullprecision 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 singlerate 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 singlerate or multirate processing.
Rate options — Rate processing rule
Enforce singlerate processing
(default)  Allow multirate processing
Specify the rate processing rule for the block. You can select one of the following options:
Enforce singlerate 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 toElements as channels (sample based)
.
Filter object — Multirate filter object
dsp.CICInterpolator
System object
dsp.CICInterpolator
System objectSpecify 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 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

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 antiimaging filter. The CIC interpolation filter increases the sample rate of an input signal by an integer factor using a cascaded integratorcomb (CIC) filter.
In a more efficient implementation, the single rate CIC filter H(z) is factorized this way:
$$\begin{array}{l}H(z)={\left[{\displaystyle \sum _{k=0}^{RM1}{z}^{k}}\right]}^{N}=\frac{{(1{z}^{RM})}^{N}}{{(1{z}^{1})}^{N}}=\frac{{(1{z}^{RM})}^{N}}{1}\xb7\frac{1}{{(1{z}^{1})}^{N}}={H}_{\text{C}}{}^{N}(z)\xb7{H}_{\text{I}}{}^{N}(z)\\ \end{array}$$
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] MeyerBaese, 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™.
Note
For an HDLoptimized filter architecture with hardwarefriendly control signals, use the CIC Interpolator (DSP HDL Toolbox) block. The DSP HDL Toolbox™ block simulates the latency of the HDL algorithm in Simulink^{®}.
HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.
HDL Coder supports Coefficient source options Dialog parameters and Filter object.
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). 
AddPipelineRegisters  Insert a pipeline register between stages of computation in a filter. See also AddPipelineRegisters (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

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

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

Vector and frame inputs are not supported for HDL code generation.
When you select Dialog parameters, the Filter Structure option
Zerolatency interpolator
is not supported for HDL code generation. From the Filter Structure dropdown list, selectInterpolator
.When you use AddPipelineRegisters, delays in parallel paths are not automatically balanced. Manually add delays where required by your design.
FixedPoint Conversion
Design and simulate fixedpoint systems using FixedPoint Designer™.
If the input is fixed point, it must be a signed integer or a signed fixed point value with a poweroftwo slope and zero bias.
Version History
Introduced before R2006a
See Also
Functions
Objects
dsp.CICDecimator
dsp.CICInterpolator
dsp.FIRDecimator
dsp.FIRInterpolator
dsp.CICCompensationDecimator
dsp.CICCompensationInterpolator
dsp.FIRHalfbandDecimator
dsp.FIRHalfbandInterpolator
Blocks
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