# dsp.FIRHalfbandInterpolator

Halfband interpolator

## Description

The dsp.FIRHalfbandInterpolator System object™ performs efficient polyphase interpolation of the input signal using an upsampling factor of two. You can use dsp.FIRHalfbandInterpolator to implement the synthesis portion of a two-band filter bank to synthesize a signal from lowpass and highpass subbands. dsp.FIRHalfbandInterpolator uses an FIR equiripple design or a Kaiser window design to construct the halfband filters and a polyphase implementation to filter the input. For more details, see Algorithms.

To upsample and interpolate your data:

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

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

## Creation

### Description

firhalfbandinterp = dsp.FIRHalfbandInterpolator returns a FIR halfband interpolation filter, firhalfbandinterp, with the default settings. Under the default settings, the System object upsamples and interpolates the input data using a halfband frequency of 11025 Hz, a transition width of 4.1 kHz, and a stopband attenuation of 80 dB. The design method is set to "Auto".

example

firhalfbandinterp = dsp.FIRHalfbandInterpolator(Name=Value) returns a halfband interpolator, with additional properties specified by one or more Name=Value pair arguments.

Example: firhalfbandinterp = dsp.FIRHalfbandInterpolator(Specification="Filter order and stopband attenuation") creates an FIR halfband interpolator object with filter order set to 52 and stopband attenuation set to 80 dB.

## Properties

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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.

Filter design parameters, specified as a character vector. When you set Specification to one of the following, you choose two of the three available design parameters to design the FIR Halfband filter.

• "Transition width and stopband attenuation" –– Transition width and stopband attenuation are the design parameters.

• "Filter order and stopband attenuation" –– Filter order and stopband attenuation are the design parameters.

• "Filter order and transition width" –– Filter order and transition width are the design parameters.

The filter is designed using optimal equiripple filter design method.

When you set Specification to "Coefficients", you specify the halfband filter coefficients directly through the Numerator property.

Filter order, specified as an even positive integer.

#### Dependencies

This property applies when you set Specification to either "Filter order and stopband attenuation" or "Filter order and transition width".

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

Stopband attenuation in dB, specified as a positive real scalar.

#### Dependencies

This property applies when you set Specification to either "Filter order and stopband attenuation" or "Transition width and stopband attenuation".

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

Transition width in Hz, specified as a positive real scalar. The value of the transition width in Hz must be less than 1/2 the input sample rate.

#### Dependencies

This property applies when you set Specification to either "Transition width and stopband attenuation" or "Filter order and transition width".

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

FIR halfband filter coefficients, specified as a row vector. The coefficients must comply with the FIR halfband impulse response format. For details on this format, see Halfband Filters and FIR Halfband Filter Design. If half the order of the filter, (length(Numerator) - 1)/2 is even, every other coefficient starting from the first coefficient must be a zero except for the center coefficient which must be a 1.0. If half the order of the filter is odd, the sequence of alternating zeros with a 1.0 at the center starts at the second coefficient.

#### Dependencies

This property applies when you set Specification to "Coefficients".

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

Specify the filter design method as one of the following:

• "Auto" –– The algorithm automatically chooses the filter design method depending on the filter design parameters. The algorithm uses the equiripple or the Kaiser window method to design the filter.

If the design constraints are very tight, such as very high stopband attenuation or very narrow transition width, then the algorithm automatically chooses the Kaiser method, as this method is optimal for designing filters with very tight specifications. However, if the design constraints are not tight, then the algorithm chooses the equiripple method.

When you set the DesignMethod property to "Auto", you can determine the method used by the algorithm by examining the passband and stopband ripple characteristics of the designed filter. If the object used the equiripple method, the passband and stopband ripples of the designed filter have a constant amplitude in the frequency response. If the filter design method the object chooses in the "Auto" mode is not suitable for your application, manually specify the DesignMethod as "Equiripple" or "Kaiser".

• "Equiripple" –– The algorithm uses the equiripple method.

• "Kaiser" –– The algorithm uses the Kaiser window method.

For more details on these two methods, see Algorithms.

#### Dependencies

To enable this property, set Specification to "Transition width and stopband attenuation", "Filter order and stopband attenuation", or "Filter order and transition width".

Data Types: char | string

Input sample rate in Hz, specified as a positive real scalar. The input sample rate defaults to 44100 Hz. If you specify a transition width as one of your filter design parameters, the transition width cannot exceed 1/2 the input sample rate.

Data Types: single | double

Synthesis filter bank, specified as either false or true. If this property is false, dsp.FIRHalfbandInterpolator is an interpolation filter for a single vector- or matrix-valued input when you call the algorithm. If this property is true, dsp.FIRHalfbandInterpolator is a synthesis filter bank and the algorithm accepts two inputs, the lowpass and highpass subbands to synthesize.

### Fixed-Point Properties

Word and fraction lengths of coefficients, specified as a signed or unsigned numerictype object. The default, numerictype(1,16) corresponds to a signed numeric type object with 16-bit coefficients and a fraction length determined based on the coefficient values, to give the best possible precision.

This property is not tunable.

Word length of the output is same as the word length of the input. Fraction length of the output is computed such that the entire dynamic range of the output can be represented without overflow. For details on how the fraction length of the output is computed, see Fixed-Point Precision Rules for Avoiding Overflow in FIR Filters.

Rounding method for output fixed-point operations, specified as a character vector. For more information on the rounding modes, see Precision and Range.

## Usage

### Description

example

y = firhalfbandinterp(x1) upsamples by two and interpolates the input signal x1 using the FIR halfband interpolator, firhalfbandinterp.

example

y = firhalfbandinterp(x1,x2) implements a halfband synthesis filter bank for the inputs x1 and x2. x1 is the lowpass output of a halfband analysis filter bank and x2 is the highpass output of a halfband analysis filter bank. dsp.FIRHalfbandInterpolator implements a synthesis filter bank only when the FilterBankInputPort property is set to true.

### Input Arguments

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Data input to the FIR halfband interpolator, specified as a column vector or a matrix. This signal is the lowpass output of a halfband analysis filter bank. If the input signal is a matrix, each column of the matrix is treated as an independent channel.

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

Second data input to the synthesis filter bank, specified as a column vector or a matrix. This signal is the highpass output of a halfband analysis filter bank. If the input signal is a matrix, each column of the matrix is treated as an independent channel.

The size, data type, and complexity of both the inputs must be the same.

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

### Output Arguments

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Output of the interpolator, returned as a column vector or a matrix. The number of rows in the interpolator output is twice the number of rows in the input signal.

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)

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 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
 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

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Create two lowpass halfband interpolation filters for upsampling data to 44.1 kHz. The design method in the first filter is set to "Equiripple" and in the second filter is set to "Kaiser".

Specify a filter order of 52 and a transition width of 4.1 kHz.

Fs = 44.1e3;
InputSampleRate = Fs/2;
Order = 52;
TW = 4.1e3;
filterspec = "Filter order and transition width";

firhalfbandinterpEqui = dsp.FIRHalfbandInterpolator(...
Specification=filterspec,FilterOrder=Order,...
TransitionWidth=TW,DesignMethod="Equiripple",...
SampleRate=InputSampleRate);

firhalfbandinterpKaiser = dsp.FIRHalfbandInterpolator(...
Specification=filterspec,FilterOrder=Order,...
TransitionWidth=TW,DesignMethod="Kaiser",...
SampleRate=InputSampleRate);

Plot the impulse response of both the filters. The zeroth-order coefficient is delayed 26 samples, which is equal to the group delay of the filter. This yields a causal halfband filter.

hfvt = fvtool(firhalfbandinterpEqui,firhalfbandinterpKaiser,...
Analysis="Impulse");
legend(hfvt,{'Equiripple','Kaiser'})

Plot the magnitude and phase response.

If the filter specifications are tight, say a very high filter order with a very narrow transition width, the filter designed using the "Kaiser" method converges more effectively.

hvftMag = fvtool(firhalfbandinterpEqui,firhalfbandinterpKaiser,...
Analysis="Magnitude");
legend(hvftMag,{'Equiripple','Kaiser'})

hvftPhase = fvtool(firhalfbandinterpEqui,firhalfbandinterpKaiser,...
Analysis="Phase");
legend(hvftPhase,{'Equiripple','Kaiser'})

Use a halfband analysis filter bank and interpolation filter to extract the low frequency subband from a speech signal.

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 audioDeviceWriter System object™ is not supported in MATLAB Online.

Set up the audio file reader, the analysis filter bank, audio device writer, and interpolation filter. The sample rate of the audio data is 22050 Hz. The order of the halfband filter is 52, with a transition width of 2 kHz.

Set the design method to "Auto". This mode chooses one of the filter design methods, equiripple or Kaiser, based on the design parameters of the filter.

"speech_dft.mp3",...
SamplesPerFrame=1024);

filtSpec = "Filter order and transition width";
Order = 52;
TW = 2000;

firhalfbanddecim = dsp.FIRHalfbandDecimator(...
Specification=filtSpec,...
FilterOrder=Order,...
TransitionWidth=TW,...
DesignMethod="Auto",...
SampleRate=afr.SampleRate);

firhalfbandinterp = dsp.FIRHalfbandInterpolator(...
Specification=filtSpec,...
FilterOrder=Order,...
TransitionWidth=TW,...
DesignMethod="Auto",...
SampleRate=afr.SampleRate/2);

View the magnitude response of the halfband filter.

fvtool(firhalfbanddecim)

Read the speech signal from the audio file in frames of 1024 samples. Filter the speech signal into lowpass and highpass subbands with a halfband frequency of 5512.5 Hz. Reconstruct a lowpass approximation of the speech signal by interpolating the lowpass subband. Play the filtered output.

while ~isDone(afr)
audioframe = afr();
xlo = firhalfbanddecim(audioframe);
ylow = firhalfbandinterp(xlo);
end

Wait until the audio file is played to the end, then close the input file and release the audio output resource.

release(afr);

Use a halfband decimator and interpolator to implement a two-channel filter bank. This example uses an audio file input and shows that the power spectrum of the filter bank output does not differ significantly from the input.

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 audioDeviceWriter System object™ is not supported in MATLAB Online.

Set up the audio file reader and device writer. Construct the FIR halfband decimator and interpolator. Finally, set up the spectrum analyzer to display the power spectra of the filter-bank input and output.

AP = audioDeviceWriter(SampleRate=AF.SampleRate);

filterspec = "Filter order and transition width";
Order = 52;
TW = 2000;

firhalfbanddecim = dsp.FIRHalfbandDecimator(...
Specification=filterspec,FilterOrder=Order,...
TransitionWidth=TW,DesignMethod="Auto",...
SampleRate=AF.SampleRate);

firhalfbandinterp = dsp.FIRHalfbandInterpolator(...
Specification=filterspec,FilterOrder=Order,...
TransitionWidth=TW,SampleRate=AF.SampleRate/2,...
DesignMethod="Auto",...
FilterBankInputPort=true);

SpecAna = spectrumAnalyzer(SampleRate=AF.SampleRate,...
PlotAsTwoSidedSpectrum=false,...
ShowLegend=true,...
ChannelNames={'Input signal','Filtered output signal'});

Read the audio 1024 samples at a time. Filter the input to obtain the lowpass and highpass subband signals decimated by a factor of two. This is the analysis filter bank. Use the halfband interpolator as the synthesis filter bank. Display the running power spectrum of the audio input and the output of the synthesis filter bank. Play the output.

while ~isDone(AF)
audioInput = AF();
[xlo,xhigh] = firhalfbanddecim(audioInput);
audioOutput = firhalfbandinterp(xlo,xhigh);
spectrumInput = [audioInput audioOutput];
SpecAna(spectrumInput);
AP(audioOutput);
end

release(AF);
release(AP);
release(SpecAna);

Create a half-band interpolation filter for data sampled at 44.1 kHz. The filter order is 52 with a transition width of 4.1 kHz. Use the filter to upsample and interpolate a multichannel input.

Set the design method to "Auto". This mode chooses one of the filter design methods, equiripple or Kaiser, based on the specified filter design parameters.

Fs = 44.1e3;
filterspec = "Filter order and transition width";
Order = 52;
TW = 4.1e3;
firhalfbandinterp = dsp.FIRHalfbandInterpolator(...
Specification=filterspec,...
FilterOrder=Order,...
TransitionWidth=TW,...
DesignMethod="Auto",...
SampleRate=Fs);
x = randn(1024,4);
y = firhalfbandinterp(x);

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## References

[1] Harris, F.J. Multirate Signal Processing for Communication Systems, Prentice Hall, 2004, pp. 208–209.

## Version History

Introduced in R2014b