comm.RaisedCosineReceiveFilter

Apply pulse shaping by decimating signal using raised-cosine FIR filter

Description

The comm.RaisedCosineReceiveFilter System object™ applies pulse shaping by decimating an input signal using a raised-cosine finite impulse response (FIR) filter. The FIR filter has (FilterSpanInSymbols × InputSamplesPerSymbol + 1) tap coefficients.

To apply pulse shaping by decimating an input signal using a raised-cosine FIR filter:

1. Create the comm.RaisedCosineReceiveFilter 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

rxfilter = comm.RaisedCosineReceiveFilter

rxfilter = comm.RaisedCosineReceiveFilter(Name,Value)

Description

rxfilter = comm.RaisedCosineReceiveFilter returns a raised-cosine FIR receive filter System object, which decimates the input signal using a raised-cosine FIR filter. The filter uses an efficient polyphase FIR decimation structure and has unit energy.

rxfilter = comm.RaisedCosineReceiveFilter(Name,Value) sets properties using one or more name-value pairs. Enclose each property name in quotes. For example, comm.RaisedCosineReceiveFilter('RolloffFactor',0.3) configures a raised-cosine receive filter System object with the roll-off factor set to 0.3.

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.

Shape — Filter shape

Square root (default) | Normal

Filter shape, specified as 'Square root' or 'Normal'.

Data Types: char | string

RolloffFactor — Roll-off factor

0.2 (default) | scalar in the range [0, 1]

Roll-off factor, specified as a scalar in the range [0, 1].

Data Types: double

FilterSpanInSymbols — Filter span in symbols

10 (default) | positive integer

Filter span in symbols, specified as a positive integer. The object truncates the infinite impulse response (IIR) of an ideal raised-cosine filter to an impulse response that spans the number of symbols specified by this property.

Data Types: double

InputSamplesPerSymbol — Input samples per symbol

8 (default) | positive integer

Input samples per symbol, specified as a positive integer.

Data Types: double

DecimationFactor — Decimation factor

8 (default) | integer

Decimation factor, specified as an integer in the range [1, InputSamplesPerSymbol]. This value must evenly divide into InputSamplesPerSymbol. The sampling rate of the output signal is reduced by the decimation factor such that length(Y)/length(X) is equal to DecimationFactor. For a matrix input signal, the number of input rows must be a multiple of the decimation factor.

Data Types: double

DecimationOffset — Decimation offset

0 (default) | integer

Decimation offset, specified as an integer in the range [0, (DecimationFactor − 1)]. This property specifies the number of filtered samples the object discards before downsampling.

Data Types: double

Gain — Linear filter gain

1 (default) | positive scalar

Linear filter gain, specified as a positive scalar. The object designs a raised-cosine filter that has unit energy and then applies the linear filter gain to obtain final tap coefficient values.

Data Types: double

Usage

Syntax

Y = rxfilter(X)

Description

Y = rxfilter(X) applies pulse shaping by decimating an input signal using a raised cosine FIR filter. The output consists of decimated signal values.

Input Arguments

X — Input signal

column vector | matrix

Input signal, specified as a column vector or a K_i-by-N matrix. K_i is the number of input samples per signal channel, and N is the number of signal channels.

For a K_i-by-N matrix input, the object processes columns of the input matrix as N independent channels.

This object accepts variable-size inputs. After the object is locked, you can change the size of each input channel, but you cannot change the number of channels. For more information, see Variable-Size Signal Support with System Objects.

Data Types: double | single
Complex Number Support: Yes

Output Arguments

Y — Output signal

column vector | matrix

Output signal, returned as a column vector or a K_o-by-N matrix. K_o is equal to K_i / DecimationFactor. K_i is the number of input samples per signal channel, and N is the number of signal channels.

The System object filters each channel over time and generates a K_o-by-N output matrix. The output signal is the same data type as the input signal.

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 comm.RaisedCosineReceiveFilter

info	Information about filter System object
coeffs	Coefficients for filters
cost	Computational cost of implementing filter System object
freqz	Frequency response of discrete-time filter
grpdelay	Group delay response of discrete-time filter
impz	Impulse response of discrete-time filter
order	Order of discrete-time filter System object

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

Filter Signal Using Root-Raised-Cosine Receive Filter

Filter the output of a square-root-raised-cosine (RRC) transmit filter by using a matched RRC receive filter. The input signal has eight samples per symbol.

Create an RRC transmit filter object, setting the number of output samples per symbol to 8.

 txfilter = comm.RaisedCosineTransmitFilter('OutputSamplesPerSymbol',8);

Create an RRC receive filter, setting the number of input samples per symbol to 8 and the decimation factor to 8.

rxfilter = comm.RaisedCosineReceiveFilter('InputSamplesPerSymbol',8, ...
    'DecimationFactor',8);

Use the coeffs function to determine the filter coefficients for both filters.

txCoef = coeffs(txfilter);
rxCoef = coeffs(rxfilter);

Display the magnitude responses of the two filters. The results show that the responses are the same. Here we use the freqz and plot functions to plot the magnitude responses. The Filter Analyzer app can also generate the filter responses.

[htx,f] = freqz(txfilter);
hrx = freqz(rxfilter);

plot(f/pi,mag2db(abs([htx hrx])))
ylabel("Magnitude (dB)")
xlabel("Normalized Frequency (\times\pi rad/sample)")
legend(["Tx" "Rx"]+" Filter")
grid
ylim([-65 15])

Generate a random bipolar signal. Interpolate the signal by using the RRC transmit filter object.

 preTx = 2*randi([0 1],100,1) - 1;
 y = txfilter(preTx);

Decimate the signal by using the RRC receive filter object.

 postRx = rxfilter(y);

The filter delay is equal to the filter span. Accounting for the filter delay, adjust the plotted samples to compare the pre-Tx filter signal with the post-Rx filter signal. Because the combined receive and the transmit RRC filters generate a matched filter pair, the two signals overlap one another.

delay = txfilter.FilterSpanInSymbols;
x = (1:(length(preTx)-delay));
plot(x,preTx(1:end-delay),x,postRx(delay+1:end))
legend('Pre-Tx filter','Post-Rx filter')

Specify Filter Span of Root-Raised-Cosine Receive Filter

Decimate a bipolar signal using a square-root-raised-cosine (RRC) filter whose impulse response is truncated to filter a span of six symbol durations.

Create a RRC transmit FIR filter, setting the filter span to six symbols. The object truncates the impulse response to six symbols.

txfilter = comm.RaisedCosineTransmitFilter(FilterSpanInSymbols=6);

Generate a random bipolar signal. Filter the signal by using the RRC transmit FIR filter object.

x = 2*randi([0 1],25,1) - 1;
y = txfilter(x);

Create a matched RRC receive filter object.

rxfilter = comm.RaisedCosineReceiveFilter(FilterSpanInSymbols=6);

Use impz to plot the impulse response of the receive filter.

impz(rxfilter)

Filter the output signal from the transmit filter by using the matched RRC receive filter object.

r = rxfilter(y);

Plot the interpolated signal. The results show a delay equal to the filter span (six symbols) before data passes through the filter.

stem(r)

Create Root-Raised-Cosine Receive Filter with Unity Passband Gain

Create a square-root-raised-cosine (RRC) receive filter object. Use freqz to plot the filter response. The results show that the linear filter gain is greater than unity. Specifically, the passband gain is more than 0 dB.

rxfilter = comm.RaisedCosineReceiveFilter;
freqz(rxfilter)

Use the coeffs object function to obtain the filter coefficients and adjust the filter gain to unit energy.

b = coeffs(rxfilter);

Because a filter with unity passband gain must have filter coefficients that sum to 1, set the linear filter gain to the inverse of the sum of the filter tap coefficients, b.Numerator.

rxfilter.Gain = 1/sum(b.Numerator);

Verify that the resulting filter coefficients sum to 1.

bNorm = coeffs(rxfilter);
sum(bNorm.Numerator)

ans = 
1.0000

Plot the filter frequency response. The results now show that the passband gain is 0 dB, which is unity gain.

freqz(rxfilter)

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).

The comm.RaisedCosineReceiveFilter System object supports SIMD code generation using Intel AVX2 technology under these conditions:

• Input signal is real-valued with real filter coefficients.

• Input signal is complex-valued with real or complex filter coefficients.

• Input signal has a data type of single or double.

The SIMD technology significantly improves the performance of the generated code. For details, see Generate SIMD Code from MATLAB Functions for Intel Platforms (Embedded Coder).

Version History

Introduced in R2013b