Farrow Rate Converter
Libraries:
DSP HDL Toolbox /
Signal Operations
Description
The Farrow Rate Converter block converts the sample rate of a signal by using FIR filters to implement a polynomial sinc approximation. A Farrow filter is an efficient rate converter when the rate conversion factor is a ratio of large integer decimation and interpolation factors. Specify the rate conversion factor by providing the input sample rate and the desired output sample rate. You can provide the rate conversion factor as a fixed parameter or as a timevarying input signal.
You can use this block with the default coefficients for most rate conversions. The default coefficients are a LaGrange interpolation that matches the Farrow Rate Converter block in DSP System Toolbox™. Or, you can specify a custom set of coefficients if the default does not meet your specifications.
The block provides a hardwarefriendly interface with input and output control signals. To provide a cycleaccurate simulation of the generated HDL code, the block models architectural latency including pipeline registers and multiplier optimizations.
Note
You can also generate HDL code for this hardwareoptimized algorithm, without creating a Simulink^{®} model, by using the DSP HDL IP Designer app. The app provides the same interface and configuration options as the Simulink block.
Examples
NFC Digital Downconverter
Design a high ratechange factor DDC for nearfield communications systems on FPGAs.
Fractional Delay Filters
Implement fractional delay filters for hardware, including a variable fractional delay filter that uses a Farrow algorithm.
Ports
Input
data — Input data
real or complex scalar
Input data, specified as a real or complex scalar. When the input data type is an integer type or a fixedpoint type, the block uses fixedpoint arithmetic for internal calculations.
The software supports double
and
single
data types for simulation, but not for HDL code generation.
Data Types: fixed point
 single
 double
 int8
 int16
 int32
 uint8
 uint16
 uint32
Complex Number Support: Yes
valid — Indicates valid input data
scalar
Control signal that indicates if the input data is valid.
When valid is 1
(true
), the block captures the
values from the input data port. When
valid is 0
(false
), the block ignores the
values from the input data
port.
Data Types: Boolean
rate — Rate change factor
scalar
Specify the rate change factor as a positive rational
value that is the ratio of the input sample rate and the
output sample rate,
F_{in}/F_{out}
.
There are no limits on the rate change factor.
When this input value changes, the block resets the internal phase accumulator. This reset means you can change the rate change factor from decimation to interpolation. For example, you can use this block to align data streams that have similar but varying sample clocks.
The block derives the data type of the internal
accumulator from the data type of this signal. The data
type of the rate change must have
at least one integer bit and one fractional bit. The
accumulator data type is
fixdt(1,fractionalWL+1,fractionalWL)
,
where fractionalWL is the fraction
length of the rate change data type. The
fractionalWL determines the
accuracy of the phase timing, but also increases the
critical path. When the rate change word length is large,
you can limit hardware resource use by fitting the
multiplicand data type to the DSP blocks on the
FPGA.
Dependencies
To enable this port, set the Rate change
source parameter to Input
port
.
Data Types: fixed point
reset — Clears internal states
scalar
Control signal that clears internal states. When
reset is 1
(true
), the block stops the
current calculation and clears internal states. When the
reset is 0
(false
) and the input
valid is 1
(true
), the block captures data
for processing.
For more reset considerations, see the Reset Signal section on the Hardware Control Signals page.
Dependencies
To enable this port, on the Control Ports tab, select Enable reset input port.
Data Types: Boolean
Output
data — Filtered output data
real or complex scalar
Filtered output data, returned as a real or complex scalar. When the input data type is a floatingpoint data type, the output data inherits the data type of the input data. When the input data type is an integer type or a fixedpoint type, the Output parameter on the Data Types tab controls the output data type.
Data Types: fixed point
 single
 double
Complex Number Support: Yes
valid — Indicates valid output data
scalar
Control signal that indicates if the data from the output
data port is valid. When
valid is 1
(true
), the block returns valid
data from the output data port. When
valid is 0
(false
), the values from the
output data port are not
valid.
Data Types: Boolean
ready — Indicates block is ready for new input data
scalar
Control signal that indicates that the block is ready for
new input data sample on the next cycle. When ready is 1
(true
), you can specify the
data and valid inputs for the next
time step. When ready is
0
(false
), the
block ignores any input data in the next time step.
Data Types: Boolean
Parameters
Main
Rate change source — Source of rate change
Property
(default)  Input port
You can enter a constant rate change as a parameter or provide a timevarying rate change by using an input port.
Selecting Input port
enables
the rate port on the block.
Rate change (fsin/fsout) — Rate change factor
147/160
(default)  positive real scalar
Specify the rate change factor as a ratio of the input
sample rate and the output sample rate,
F_{in}/F_{out}
,
or provide a positive rational value. There are no limits
on the rate change factor. Specify the data type for this
value by using the RateChange
parameter on the Data Types
tab.
Dependencies
To enable this parameter, set Rate change
source to
Property
.
Coefficients matrix — FIR filter coefficients
[1/6 1/2 1/3 0;1/2 1 1/2
1;1/2 1/2 1 0;1/6 0 1/6 0]
(default)  matrix of real values
Specify FIR filter coefficients as an MbyN matrix of real values, where N is the number of filters and M is the number of coefficients in each filter. N must be less than six. The block implements a polynomial of order N – 1. The default value is a special closedform LaGrange solution that accomplishes most rate changes.
Filter structure — HDL filter architecture
Direct form
systolic
(default)  Direct form transposed
This block implements the FIR filter stages by using the same architectures as the Discrete FIR Filter block. Specify the HDL filter architecture as one of these structures:
Direct form systolic
— This architecture provides a fully parallel filter implementation that makes efficient use of Intel^{®} and Xilinx^{®} DSP blocks. For architecture details, see Fully Parallel Systolic Architecture.Direct form transposed
— This architecture is a fully parallel implementation that is suitable for FPGA and ASIC applications. For architecture and performance details, see Fully Parallel Transposed Architecture.
All implementations share multipliers for symmetric and antisymmetric coefficients and remove multipliers for zerovalued coefficients.
Minimum number of cycles between valid input samples — Serialization requirement for input timing
1
(default)  positive integer
Serialization requirement for input timing, specified as a
positive integer. This parameter represents
N, the minimum number of cycles
between valid input samples. To implement a fully serial
architecture, set Minimum number of cycles
between valid input samples greater than
the filter length, L, or to
Inf
.
When this parameter is greater than one, the block implements each FIR subfilter as a partlyserial architecture that shares the multipliers in time.
Dependencies
To enable this parameter, set Filter
structure to Direct form
systolic
.
Data Types
Rounding mode — Rounding mode for typecasting the output
Floor
(default)  Ceiling
 Convergent
 Nearest
 Round
 Zero
Rounding mode for typecasting the output to the data type specified by the Output parameter. When the input data type is a floatingpoint data type, the block ignores this parameter. For more details, see Rounding Modes.
Saturate on integer overflow — Overflow handling for typecasting the output
off
(default)  on
Overflow handling for typecasting the output to the data type specified by the Output parameter. When the input data type is a floatingpoint data type, the block ignores this parameter. For more details, see Overflow Handling.
Coefficients — Data type of filter coefficients
Inherit: Same word length as
input
(default)  <data type
expression>
The block casts the filter coefficients to this data type. The quantization rounds to the nearest representable value and saturates on overflow. When the input data type is a floatingpoint data type, the block ignores this parameter.
The recommended data type for this parameter is
Inherit: Same word length as
input
. When selecting this data type,
consider the size supported by the DSP blocks on your
target FPGA.
RateChange — Data type of rate change factor
fixdt(1,16)
(default)  <data type
expression>
The block casts the Rate change
(fsin/fsout) parameter value to this data
type and uses this data type to derive the data type for
the internal accumulator. The accumulator data type is
fixdt(1,fractionalWL+1,fractionalWL)
,
where fractionalWL is the fraction
length of the rate change data type. The quantization
rounds to the nearest representable value and saturates on
overflow. When the input data type is a floatingpoint
data type, the block ignores this parameter.
This data type must have enough integer bits to represent
the fsIn/fsOut
value. If the data type
specified does not have enough integer bits, the block
returns an error. The default setting does not specify a
number of fractional bits, so the block can compute the
necessary integer bits. This data type
must have at least one integer bit
and one fractional bit.
The
fractional part of this data type determines the accuracy
of the phase timing, but also increases the critical path.
When the rate change word length is large, you can limit
hardware resources by fitting the multiplicand data type
to the DSP blocks on the FPGA.
Dependencies
To enable this parameter, set Rate change
source to
Property
.
Multiplicand — Data type of multiplicand
Inherit: Inherit via internal
rule
(default)  <data type
expression>
The block casts the output of the accumulator to this data type. The quantization rounds to the nearest representable value and saturates on overflow. When the input data type is a floatingpoint data type, the block ignores this parameter. When the rate change word length is large, you can limit hardware resource use by controlling the multiplicand data type. When selecting this data type, consider the size supported by the DSP blocks on your target FPGA.
Output — Data type of filter output
Inherit: same as first
input
(default)  <data type
expression>
The block casts the output of each filter stage to this data type. The quantization uses the settings of the Rounding mode and Overflow mode parameters. When the input data type is a floatingpoint data type, the block ignores this parameter.
Control Ports
Enable reset input port — Option to enable reset input port
off
(default)  on
Select this check box to enable the reset input port. The reset signal implements a local synchronous reset of the data path registers.
For more reset considerations, see the Reset Signal section on the Hardware Control Signals page.
Use HDL global reset — Option to connect data path registers to generated HDL global reset signal
off
(default)  on
Select this check box to connect the generated HDL global reset signal to the data path registers. This parameter does not change the appearance of the block or modify simulation behavior in Simulink. When you clear this check box, the generated HDL global reset clears only the control path registers. The generated HDL global reset can be synchronous or asynchronous depending on the HDL Code Generation > Global Settings > Reset type parameter in the model Configuration Parameters.
For more reset considerations, see the Reset Signal section on the Hardware Control Signals page.
Algorithms
The Farrow Rate Converter block uses Horner’s rule to compute samples from the polynomial. The polynomial is implemented with several FIR filters. Each FIR filter is an instance of the Discrete FIR Filter block. For details of filter architectures and resource optimization, see FIR Filter Architectures for FPGAs and ASICs. When Minimum number of cycles between valid input samples is greater than one, the block implements each FIR subfilter as a partlyserial architecture that shares the multipliers in time.
This diagram shows the Farrow architecture for a fourstage filter. There are four
FIR filters. The output of each filter is added to the result of the previous
stage, cast to the output data type, then multiplied by the current value of the
accumulator. The accumulator operates on the fractional part of the rate change,
and uses a data type derived from the rate change data type. The accumulator data
type is
fixdt(1,fractionalWL+1,fractionalWL)
,
where fractionalWL is the fraction length of the rate change
data type.
When you set the coefficient data type to Same as input
wordlength
, each subfilter computes the best precision data
type based on its coefficients. As a result, each filter can have a different
output data type. To maintain full precision when you set the output data type to
Full precision
, the block casts the output of
each subfilter to the highest precision data type of all the subfilter data
types.
The table shows the coefficient data type and output data type for each subfilter
when using the default Farrow coefficients, and an input data type of
fixdt(1,18,14)
.
Coefficient Value  Coefficient Data Type  Subfilter Output Data Type 

1/6 1/2 1/2 1/6  fixdt(1,18,17)  fixdt(1,36,31) 
1/2 1 1/2 0  fixdt(1,18,17)  fixdt(1,36,31) 
1/3 1/2 1 1/6  fixdt(1,18,16)  fixdt(1,35,30) 
0 1 0 0  fixdt(1,18,16)  fixdt(1,34,30) 
In this case, the full precision data type is fixdt(1,36,31)
.
Performance
This table shows postsynthesis resource utilization for the HDL code
generated for the default coefficients and rate change settings, with 16bit
input and 16bit coefficients. The synthesis targets a Xilinx ZC706 (XC7Z045ffg9002) FPGA. The Global HDL reset
type parameter is Synchronous
and Minimize clock enables is selected. The
reset port is not enabled, so only control path
registers are connected to the generated global HDL reset.
Resource  Uses 

LUT  394 
FF  604 
BRAM  0 
Xilinx LogiCORE DSP48  13 
After place and route, the maximum clock frequency of the design is 495 MHz.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
This block supports C/C++ code generation for Simulink accelerator and rapid accelerator modes and for DPI component 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.
This block has one default HDL architecture.
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

Version History
Introduced in R2022aR2022b: Partly serial filter architecture
The block now has the Minimum number of cycles between valid input samples parameter to enable resource sharing with a partly serial systolic architecture. The internal FIR filter for each filter stage is implemented with a partly serial systolic filter with the sharing factor that you specify.
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