Documentation

# dsp.FIRInterpolator

Polyphase FIR interpolator

## Description

The dsp.FIRInterpolator System object™ upsamples an input by the integer upsampling factor, L, followed by an FIR anti-imaging filter. The filter coefficients are scaled by the interpolation factor. A polyphase interpolation structure implements the filter. The resulting discrete-time signal has a sampling rate L times the original sampling rate.

To upsample an input:

1. Create the dsp.FIRInterpolator 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? (MATLAB).

## Creation

### Description

firinterp = dsp.FIRInterpolator returns an FIR interpolator, firinterp, which upsamples an input signal by a factor of 3 and applies an FIR filter to interpolate the output.

example

firinterp = dsp.FIRInterpolator(interpFactor,num) returns an FIR interpolator with the integer-valued InterpolationFactor property set to interpFactor and the Numerator property set to num.

firinterp = dsp.FIRInterpolator(___,Name,Value) returns an FIR interpolator object 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.

## Properties

expand all

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 (MATLAB).

Specify the integer factor, L, by which to increase the sampling rate of the input signal. The polyphase implementation uses L polyphase subfilters to compute convolutions at the lower sample rate. The FIR interpolator delays and interleaves these lower-rate convolutions to obtain the higher-rate output.

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

FIR filter coefficient source, specified as either:

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

• 'Input port' –– The numerator coefficients are specified as an input to the object algorithm.

Specify the numerator coefficients of the FIR anti-imaging filter as the coefficients of a polynomial in z–1. Indexing from zero, the filter coefficients are:

$H\left(z\right)=\sum _{n=0}^{N-1}b\left(n\right){z}^{-n}$

To act as an effective anti-imaging filter, the coefficients must correspond to a lowpass filter with a normalized cutoff frequency no greater than the reciprocal of the InterpolationFactor. The filter coefficients are scaled by the value of the InterpolationFactor property before filtering the signal. To form the L polyphase subfilters, Numerator is appended with zeros if necessary.

#### Dependencies

This property applies when NumeratorSource is set to 'Property'.

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

### Fixed-Point Properties

Flag to use full-precision rules for fixed-point arithmetic, specified as one of the following:

• true –– The object computes all internal arithmetic and output data types using the full-precision rules. These rules provide the most accurate fixed-point numerics. In this mode, other fixed-point properties do not apply. No quantization occurs within the object. Bits are added, as needed, to ensure that no roundoff or overflow occurs.

• false –– Fixed-point data types are controlled through individual fixed-point property settings.

For more information, see Full Precision for Fixed-Point System Objects and Set System Object Fixed-Point Properties.

Rounding method for fixed-point operations. For more details, see rounding mode.

#### Dependencies

This property is not visible and has no effect on the numerical results when the following conditions are met:

• FullPrecisionOverride set to true.

• FullPrecisionOverride set to false, ProductDataType set to 'Full precision', AccumulatorDataType set to 'Full precision', and OutputDataType set to 'Same as accumulator'.

Under these conditions, the object operates in full precision mode.

Overflow action for fixed-point operations, specified as one of the following:

• 'Wrap' –– The object wraps the result of its fixed-point operations.

• 'Saturate' –– The object saturates the result of its fixed-point operations.

For more details on overflow actions, see overflow mode for fixed-point operations.

#### Dependencies

This property is not visible and has no effect on the numerical results when the following conditions are met:

• FullPrecisionOverride set to true.

• FullPrecisionOverride set to false, OutputDataType set to 'Same as accumulator', ProductDataType set to 'Full precision', and AccumulatorDataType set to 'Full precision'

Under these conditions, the object operates in full precision mode.

Data type of the FIR filter coefficients, specified as:

• Same word length as input –– The word length of the coefficients is the same as that of the input. The fraction length is computed to give the best possible precision.

• Custom –– The coefficients data type is specified as a custom numeric type through the CustomCoefficientsDataType property.

Word and fraction lengths of the coefficients data type, specified as an autosigned numerictype with a word length of 16 and a fraction length of 15.

#### Dependencies

This property applies when you set the CoefficientsDataType property to Custom.

Data type of the product output in this object, specified as one of the following:

• 'Full precision' –– The product output data type has full precision.

• 'Same as input' –– The object specifies the product output data type to be the same as that of the input data type.

• 'Custom' –– The product output data type is specified as a custom numeric type through the CustomProductDataType property.

For more information on the product output data type, see Multiplication Data Types.

#### Dependencies

This property applies when you set FullPrecisionOverride to false.

Word and fraction lengths of the product data type, specified as an autosigned numeric type with a word length of 32 and a fraction length of 30.

#### Dependencies

This property applies only when you set FullPrecisionOverride to false and ProductDataType to 'Custom'.

Data type of an accumulation operation in this object, specified as one of the following:

• 'Full precision' –– The accumulation operation has full precision.

• 'Same as product' –– The object specifies the accumulator data type to be the same as that of the product output data type.

• 'Same as input' –– The object specifies the accumulator data type to be the same as that of the input data type.

• 'Custom' –– The accumulator data type is specified as a custom numeric type through the CustomAccumulatorDataType property.

#### Dependencies

This property applies when you set FullPrecisionOverride to false.

Word and fraction lengths of the accumulator data type, specified as an autosigned numeric type with a word length of 32 and a fraction length of 30.

#### Dependencies

This property applies only when you set FullPrecisionOverride to false and AccumulatorDataType to 'Custom'.

Data type of the object output, specified as one of the following:

• 'Same as accumulator' –– The output data type is the same as that of the accumulator output data type.

• 'Same as input' –– The output data type is the same as that of the input data type.

• 'Same as product' –– The output data type is the same as that of the product output data type.

• 'Custom' –– The output data type is specified as a custom numeric type through the CustomOutputDataType property.

#### Dependencies

This property applies when you set FullPrecisionOverride to false.

Word and fraction lengths of the output data type, specified as an autosigned numeric type with a word length of 16 and a fraction length of 15.

#### Dependencies

This property applies only when you set FullPrecisionOverride to false and OutputDataType to 'Custom'.

## Usage

### Description

example

y = firinterp(x) outputs the upsampled and filtered values, y, of the input signal, x.

y = firinterp(x,num) uses the FIR filter, num, to interpolate the input signal. This configuration is valid only when the 'NumeratorSource' property is set to 'Input port'.

### Input Arguments

expand all

Data input, specified as a vector or a matrix. A Ki-by-N input matrix is treated as N independent channels, and the System object interpolates each channel over the first dimension and generates a Ki*L-by-N output matrix, where L is the interpolation factor.

This object supports variable-size input and does not support complex unsigned fixed-point inputs.

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

FIR filter coefficients, specified as a row vector.

#### Dependencies

This input is accepted only when the 'NumeratorSource' property is set to 'Input port'.

Data Types: double
Complex Number Support: Yes

### Output Arguments

expand all

FIR interpolator output, returned as a vector or a matrix of size Ki*L-by-N, where L is the interpolation 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)

expand all

 freqz Frequency response of filter fvtool Visualize frequency response of DSP filters info Information about filter System object cost Estimate cost for implementing filter System objects polyphase Polyphase decomposition of multirate filter generatehdl Generate HDL code for quantized DSP filter (requires Filter Design HDL Coder) impz Impulse response of discrete-time filter System object coeffs Filter coefficients
 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

expand all

Note: If you are using R2016a or an earlier release, replace each call to the object with the equivalent step syntax. For example, obj(x) becomes step(obj,x).

Note: The dsp.AudioFileReader and audioDeviceWriter System objects are not supported in MATLAB Online.

This example shows how to double the sampling rate of an audio signal from 22.05 kHz to 44.1 kHz, and play the audio.

afr = dsp.AudioFileReader('OutputDataType',...
'single');
adw = audioDeviceWriter(44100);
firinterp = dsp.FIRInterpolator(2, ...
firpm(30, [0 0.45 0.55 1], [1 1 0 0]));

while ~isDone(afr)
frame = afr();
y = firinterp(frame);
adw(y);
end

pause(1);
release(afr);
release(adw);

## Algorithms

This object implements the algorithm, inputs, and outputs described on the FIR Interpolation block reference page. The object properties correspond to the block parameters, except:

• The FIRInterpolator object does not have a property that corresponds to the Input processing parameter of the FIR Interpolation block.

• The Rate options block parameter is not supported by the FIRInterpolator object.

Watch now