dsp.FIRRateConverter

Perform polyphase FIR sample rate conversion

Description

The dsp.FIRRateConverter System object™ performs an efficient polyphase sample rate conversion using a rational factor L/M along the first dimension.

The FIR rate converter cascades an interpolator with a decimator. Conceptually, the rate converter (as shown in the schematic) consists of an upsampler, followed by a combined anti-imaging and anti-aliasing FIR filter, followed by a downsampler. The coefficients of the anti-imaging and anti-aliasing FIR filter can be specified through the Numerator property, or can be automatically designed by the object using the designMultirateFIR function. For an example, see Resample Signal Using FIR Rate Converter.

The upsampler increases the sample rate of the signal by a factor L and the downsampler reduces the sample rate of the signal by a factor M. Use upsampling and downsampling factors that are relatively prime or coprime. The resulting discrete-time signal has a sample rate that is L/M times the original sample rate.

Note that the actual object algorithm implements a polyphase structure, an efficient equivalent of the combined system depicted in the diagram. For more details, see Algorithms.

To perform sampling rate conversion:

1. Create the dsp.FIRRateConverter object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

firrc = dsp.FIRRateConverter

firrc = dsp.FIRRateConverter(L,M)

firrc = dsp.FIRRateConverter(L,M,'Auto')

firrc = dsp.FIRRateConverter(L,M,num)

firrc = dsp.FIRRateConverter(L,M,method)

firrc = dsp.FIRRateConverter(___,Name,Value)

firrc = dsp.FIRRateConverter(L,M,'legacy')

Description

firrc = dsp.FIRRateConverter returns an FIR sample rate converter object with an interpolation factor of 3 and a decimation factor of 2. The object designs the FIR filter coefficients using the designMultirateFIR(3,2) function.

firrc = dsp.FIRRateConverter(L,M) returns an FIR sample rate converter with the integer-valued InterpolationFactor property set to L and the DecimationFactor property set to M. The object designs its filter coefficients based on the rate conversion factors that you specify while creating the object, using the designMultirateFIR(L,M) function. The designed filter corresponds to a lowpass filter with normalized cutoff frequency no greater than min(π/L,π/M) in radial frequency units.

firrc = dsp.FIRRateConverter(L,M,'Auto') returns an FIR sample rate converter where the NumeratorSource property is set to 'Auto'. In this mode, every time there is an update in the rate conversion factors, the object redesigns the filter using the design method specified in DesignMethod.

firrc = dsp.FIRRateConverter(L,M,num) returns an FIR sample rate converter with the Numerator property set to num.

firrc = dsp.FIRRateConverter(L,M,method) returns an FIR sample rate converter with the DesignMethod property set to method. When you pass the design method as an input, the NumeratorSource property is automatically set to 'Auto'.

firrc = dsp.FIRRateConverter(___,Name,Value) returns an FIR sample rate converter with each specified property set to the specified value. Enclose each property name in quotes. You can use this syntax with any previous input argument combinations.

Example: firrc = dsp.FIRRateConverter('FullPrecisionOverride','false') enables the fixed-point data types to be controlled through the individual fixed-point property settings.

firrc = dsp.FIRRateConverter(L,M,'legacy') returns an FIR sample rate converter where the filter coefficients are designed using firpm(70,[0 0.28 0.32 1],[1 1 0 0]). The designed filter has a cutoff frequency of π/3 radians/sample.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

Main Properties

InterpolationFactor — Interpolation factor

3 (default) | positive integer

Interpolation factor L, specified as a positive integer.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

DecimationFactor — Decimation factor

2 (default) | positive integer

Decimation factor M, specified as a positive integer.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

NumeratorSource — FIR filter coefficient source

'Property' (default) | 'Auto'

FIR filter coefficient source, specified as one of the following:

• 'Property' –– The numerator coefficients are specified through the Numerator property.

• 'Auto' –– The numerator coefficients are designed automatically using the design method specified in DesignMethod.

Numerator — FIR filter coefficients

designMultirateFIR(L,M) (default) | row vector

Numerator coefficients of the FIR filter, specified as a row vector in powers of z^-1.

The following equation defines the transfer function of the filter:

$$H(z)={\displaystyle \sum _{n=0}^{N}b}(n)z^{-n}$$

The vector b = [b(0), b(1), …, b(N)] represents the vector of filter coefficients.

Use a lowpass filter with normalized cutoff frequency no greater than min(1/L,1/M), where L is the interpolation factor and M is the decimation factor. The gain of the lowpass filter should equal L, the interpolation factor. Choose the length of the filter to be a multiple of the interpolation factor. To design such a filter, use the designMultirateFIR function. For an example, see Resample Signal Using FIR Rate Converter. All initial filter states are zero.

Dependencies

This property is visible only when you set NumeratorSource to 'Property'.

When NumeratorSource is set to 'Auto', the numerator coefficients are automatically redesigned using the design method specified in DesignMethod. To access the filter coefficients in the automatic design mode, type objName.Numerator in the MATLAB^® command prompt.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

DesignMethod — Auto design method

'Kaiser' (default) | 'ZOH' | 'Linear'

Design method of the FIR filter coefficients, specified as one of the following:

• 'Kaiser' –– Kaiser method. Approximate combined anti-aliasing and anti-imaging lowpass filter using the designMultirateFIR function.

• 'ZOH' –– Zero order hold method. Hold the input sequence values.

• 'Linear' –– Linear interpolation method.

Dependencies

This property is visible only when you set the NumeratorSource property to 'Auto', or if you pass the 'auto' keyword as an input while creating the object.

Code Generation Properties

AllowArbitraryInputLength — Allow arbitrary input length in generated code

false (default) | true

Allow arbitrary frame length for fixed-size input signals in the generated code, specified as true or false. When you specify:

• true –– The input frame length does not have to be a multiple of the decimation factor. The output of the object in the generated code is a variable-size array.

• false –– The input frame length must be a multiple of the decimation factor.

When you specify variable-size signals, the input frame length can be arbitrary and the object ignores this property in the generated code. When you run this object in MATLAB, the object supports arbitrary input frame lengths for fixed-size and variable-size signals and this property does not affect the object behavior.

Data Types: logical

Fixed-Point Properties

FullPrecisionOverride — Full precision override for fixed-point arithmetic

true (default) | false

Specify whether to use full precision rules. If you set FullPrecisionOverride to true, which is the default, the object computes all internal arithmetic and output data types using full precision rules. These rules provide the most accurate fixed-point numerics. It also turns off the display of other fixed-point properties because they do not apply individually. These rules guarantee that no quantization occurs within the object. Bits are added, as needed, to ensure that no roundoff or overflow occurs. If you set FullPrecisionOverride to false, fixed-point data types are controlled through individual fixed-point property settings. For more information, see Full Precision for Fixed-Point System Objects.

RoundingMethod — Rounding method for fixed-point operations

Floor (default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero

Specify the rounding method as one of | Ceiling | Convergent | Floor | Nearest | Round | Simplest | Zero |.

Dependencies

This property applies only if the object is not in full precision mode.

OverflowAction — Overflow action for fixed-point operations

Wrap (default) | Saturate

Specify the overflow action as one of | Wrap | Saturate |.

Dependencies

This property applies only if the object is not in full precision mode.

CoefficientsDataType — Word and fraction lengths of filter coefficients

Same word length as input (default) | Custom

Specify the filter coefficient fixed-point data type as one of | Same word length as input | Custom |.

CustomCoefficientsDataType — Word and fraction lengths of filter coefficients

numerictype([],16,15) (default) | numerictype

Specify the filter coefficient fixed-point type as a numerictype (Fixed-Point Designer) object with a Signedness of Auto.

Dependencies

This property applies only when the CoefficientsDataType property is Custom.

ProductDataType — Product word and fraction lengths

Full precision (default) | Same as input | Custom

Specify the product fixed-point data type as one of | Full precision | Same as input | Custom |.

CustomProductDataType — Product word and fraction lengths

numerictype([],32,30) (default) | numerictype

Specify the product fixed-point type as a scaled numerictype (Fixed-Point Designer) object with a Signedness of Auto.

Dependencies

This property applies only when the ProductDataType property is Custom.

AccumulatorDataType — Accumulator word and fraction lengths

Full precision (default) | Same as product | Same as input | Custom

Specify the accumulator fixed-point data type as one of | Full precision | Same as product | Same as input | Custom |.

CustomAccumulatorDataType — Accumulator word and fraction lengths

numerictype([],32,30) (default) | numerictype

Specify the accumulator fixed-point type as a scaled numerictype (Fixed-Point Designer) object with a Signedness of Auto.

Dependencies

This property applies only when the AccumulatorDataType property is Custom.

OutputDataType — Output word and fraction lengths

Same as accumulator (default) | Same as product | Same as input | Custom

Specify the output fixed-point data type as one of | Same as accumulator | Same as product | Same as input | Custom |.

CustomOutputDataType — Output word and fraction lengths

numerictype([],16,15) (default) | numerictype

Specify the output fixed-point type as a scaled numerictype (Fixed-Point Designer) object with a Signedness of Auto.

Dependencies

This property applies only when the OutputDataType property is Custom.

Usage

Syntax

y = firrc(x)

Description

y = firrc(x) resamples the input x and returns the resampled signal y.

Input Arguments

x — Data input

column vector | matrix

Data input, specified as a column vector or a matrix of size P-by-Q. The columns in the input signal represent Q independent channels.

Under most conditions, the number of inputs rows P can be arbitrary and does not have to be a multiple of the DecimationFactor property. See this table for details.

Input Signal	When you Run Object in MATLAB	When you Generate Code Using MATLAB Coder™
Fixed-size	Object supports arbitrary input frame length	Object supports arbitrary input frame length when you set AllowArbitraryInputLength to true while generating code
Variable-size	Object supports arbitrary input frame length	Object supports arbitrary input frame length

Variable-size signals change in frame length once you lock the object while the fixed-size signals remain constant. When the object does not support arbitrary frame length, the input frame length must be a multiple of the DecimationFactor property.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fi
Complex Number Support: Yes

Output Arguments

y — Resampled output

column vector | matrix

Resampled output, returned as a column vector or a matrix. When the input is of size P-by-Q, and P is not a multiple of the decimation factor M, the output signal has an upper bound size of ceil(LP/M)-by-Q. If P is a multiple of the decimation factor, then the output is of size (LP/M)-by-Q.

The number of rows in the output signal is given by LP/M, where P is the number of input rows, L is the interpolation factor, and M is the decimation factor.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fi
Complex Number Support: Yes

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Specific to dsp.FIRRateConverter

freqz	Frequency response of discrete-time filter System object
fvtool	Visualize frequency response of DSP filters
info	Information about filter System object
cost	Estimate cost of implementing filter System object
coeffs	Returns the filter System object coefficients in a structure
polyphase	Polyphase decomposition of multirate filter
generatehdl	Generate HDL code for quantized DSP filter (requires Filter Design HDL Coder)
outputDelay	Determine output delay of single-rate or multirate filter

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Resample Signal Using FIR Rate Converter

Resample a 100 Hz sine wave signal by a factor of 3/2.

Create a dsp.SineWave object which generates a sinusoidal signal with 54 samples per frame, contains a tone at 100 Hz, and has a sample rate of 1250 Hz.

sine = dsp.SineWave(1,100,'SampleRate',1250,'SamplesPerFrame',54);

% Grab a frame
x = sine();

% Calculate input time vector 
tx = (0:length(x)-1)/sine.SampleRate; 

Design Default Filter

Create a dsp.FIRRateConverter object. The object uses a combined anti-imaging and anti-aliasing FIR filter. By default, this filter is designed using the designMultirateFIR function. The function designs the filter based on the rate conversion factors that you specify, and stores the coefficients in the Numerator property. For an interpolation factor of 3 and a decimation factor of 2, the object designs the coefficients using designMultirateFIR(3,2).

firrc = dsp.FIRRateConverter(3,2);

Resample by a Factor of 3/2

Resample the signal by a factor of 3/2.

y = firrc(x);

Plot the original and resampled signals. In order to plot the two signals on the same plot, you must account for the output delay of the FIR rate converter and the scaling introduced by the filter. Use the outputDelay function to compute the delay value introduced by the rate converter. Shift the output by this delay value.

Visualize the input and the resampled signals. The input and output values coincide every 3 output samples, and every other input sample, owing to the conversion rate of 3/2.

FsIn = sine.SampleRate;
[delay,FsOut] = outputDelay(firrc,FsIn=FsIn);
% Calculate output times for vector y in input units
ty = (0:length(y)-1)/FsOut-delay;

stem(tx,x,'filled',MarkerSize=4) 
hold on
stem(ty,y)
hold off
xlim([0.0 0.0145])
ylim([-1.5 1.5])
legend('Original input','Resampled')

Resample by a Factor of 5/3 in Automatic Filter Design Mode

Now change the interpolation factor to 5 and the decimation factor to 3. In order for the filter design to be updated automatically based on the new rate conversion factors, set the NumeratorSource property to 'Auto'. Alternately, you can pass the keyword 'auto' as an input while creating the object. The object then operates in the automatic filter design mode. Every time there is a change in the rate conversion factors, the object updates the filter design accordingly.

release(firrc)
firrc.NumeratorSource = 'Auto';
firrc.InterpolationFactor = 5;
firrc.DecimationFactor = 3

firrc = 
  dsp.FIRRateConverter with properties:

   Main
    InterpolationFactor: 5
       DecimationFactor: 3
        NumeratorSource: 'Auto'
           DesignMethod: 'Kaiser'

  Use get to show all properties

To access the filter coefficients in the automatic filter design mode, type firrc.Numerator in the MATLAB command prompt.

Resample the signal with the updated rate conversion values.

yAuto = firrc(x);

Plot the original and resampled signals. Recalculate the output delay and the output sample rate since the rate conversion factors have changed. Note that the input and output coincide every 3 input samples, and every 5 output samples, owing to the 5/3 conversion factor.

[delay,FsOut] = outputDelay(firrc,FsIn=FsIn);
% Calculate output times for vector yAuto in input units
tyAuto = (0:length(yAuto)-1)/FsOut-delay;

stem(tx,x,'filled',MarkerSize=4)
hold on
stem(tyAuto,yAuto,'r')
hold off
xlim([0.0 0.015])
ylim([-1.5 1.5])
legend('Original input','Resampled')

Specify Signal Interpolation Model

In the automatic design mode, you can also specify the underlying D/A signal interpolation model through the DesignMethod property.

Set DesignMethod to 'linear' and change the interpolation factor to 11.

release(firrc)
firrc.DesignMethod = 'linear';
firrc.InterpolationFactor = 11;

Resample the signal using the linear interpolation model.

yLinear = firrc(x);

Plot the original and resampled signals. The output samples lie on a piecewise-linear curve. Note that the input and output coincide every three input samples and every 11 output samples as expected from the ratio 11/3.

[delay,FsOut] = outputDelay(firrc,FsIn=FsIn);
% Calculate output times for vector yLinear in input units
tyLinear = (0:length(yLinear)-1)/FsOut-delay;

stem(tx,x,'filled',MarkerSize=4)
hold on
stem(tyLinear,yLinear)
plot(tyLinear,yLinear,Color=[1 0 0 0.3])
hold off
xlim([0.0 0.009])
ylim([-1.5 1.5])
legend('Original input','Resampled')

Resample and Play Audio Signal

Resample an audio signal from 48 kHz to 44 kHz and play the resampled signal using the audioDeviceWriter object.

Note: The audioDeviceWriter System object™ is not supported in MATLAB Online.

Create a dsp.AudioFileReader object. The object reads an audio file that has a sample rate of 48 kHz.

L = 11;
M = 12;
afr = dsp.AudioFileReader('audio48kHz.wav', ...
    'OutputDataType','single', ...
    'SamplesPerFrame',4*M);

Create a dsp.FIRRateConverter object with an interpolation factor of L = 11 and a decimation factor of M = 12 (the co-prime representation of the ratio $44\mathit{k}/48\mathit{k}$), a reasonable approximation of the standard 44.1 kHz rate. The object designs the filter using designMultirateFIR(11,12) and stores the coefficients in the Numerator property of the object.

firrc = dsp.FIRRateConverter(L,M)

firrc = 
  dsp.FIRRateConverter with properties:

   Main
    InterpolationFactor: 11
       DecimationFactor: 12
        NumeratorSource: 'Property'
              Numerator: [0 2.3076e-05 5.4790e-05 9.3620e-05 1.3665e-04 1.7959e-04 2.1699e-04 2.4263e-04 2.5004e-04 2.3320e-04 1.8731e-04 1.0959e-04 0 -1.3820e-04 -2.9809e-04 -4.6908e-04 -6.3723e-04 -7.8603e-04 -8.9751e-04 -9.5372e-04 ... ] (1x264 double)

  Use get to show all properties

Create an audioDeviceWriter object. Specify the sample rate to be 44100 Hz.

adw = audioDeviceWriter(44100);

Read the audio file, convert the sample rate of the audio signal, and play the resampled audio.

while ~isDone(afr)
    audio1 = afr();
    audio2 = firrc(audio1);
    adw(audio2);
end
release(afr)
release(adw)

Algorithms

The FIR rate converter is implemented efficiently using a polyphase structure.

To derive the polyphase structure, start with the transfer function of the FIR filter: This FIR filter is a combined anti-imaging and anti-aliasing filter.

$$H(z)=b_0+b_1{z}^{-1}+\mathrm{...}+b_N{z}^{-N}$$

N+1 is the length of the FIR filter.

You can rearrange this equation as follows:

$$H(z)=\begin{array}{c}\left(b_0+b_L{z}^{-L}+b_{2L}{z}^{-2L}+\mathrm{..}+b_{N-L+1}{z}^{-(N-L+1)}\right)+\\ z^{-1}\left(b_1+b_{L+1}{z}^{-L}+b_{2L+1}{z}^{-2L}+\mathrm{..}+b_{N-L+2}{z}^{-(N-L+1)}\right)+\\ \begin{array}{c}⋮\\ z^{-(L-1)}\left(b_{L-1}+b_{2L-1}{z}^{-L}+b_{3L-1}{z}^{-2L}+\mathrm{..}+b_N{z}^{-(N-L+1)}\right)\end{array}\end{array}$$

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

You can write this equation as:

$$H(z)=E_0(z^L)+z^{-1}{E}_1(z^L)+\mathrm{...}+z^{-(L-1)}{E}_{L-1}(z^L)$$

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

Conceptually, the FIR rate converter contains an upsampler, followed by a combined anti-imaging, anti-aliasing FIR filter H(z), which is followed by a downsampler.

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 the adder with a commutator switch. To account for the downsampler that follows, the switch moves in steps of size M. The switch receives the first sample from branch 0 and moves in the counter clockwise direction, each time skipping M−1 branches.

As an example, consider a rate converter with L set to 5 and M set to 3. The polyphase components are E₀(z), E₁(z), E₂(z), E₃(z), and E₄(z). The switch starts on the first branch 0, skips branches 1 and 2, receives the next sample from branch 3, then skips branches 4 and 0, receives the next sample from branch 2, and so on. The sequence of branches from which the switch receives the data sample is [0, 3, 1, 4, 2, 0, 3, 1, ….].

The rate converter implements the L/M conversion by first applying the interpolation factor L to the incoming data, and using the commutator switch at the end to receive only 1 in M samples, effectively accounting for the dowsampling factor M. Hence, the sample rate at the output of the FIR rate converter is Lfs/M.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

See System Objects in MATLAB Code Generation (MATLAB Coder).

HDL Code Generation

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

This object supports HDL code generation with the Filter Design HDL Coder™ product. For workflows and limitations, see Generate HDL Code for Filter System Objects (Filter Design HDL Coder).

Version History

Introduced in R2012a

R2022b: Support for arbitrary input frame length

Starting in R2022b, this object supports an input signal with an arbitrary frame length, so the input frame length does not have to be a multiple of the decimation factor.

When you generate code, to support arbitrary frame length for fixed-size signals, you must set the AllowArbitraryInputLength property to true while generating code.