Apply pulse shaping by interpolating signal using raised-cosine FIR filter
System object™ applies pulse shaping by interpolating an input signal using a raised
cosine finite impulse response (FIR) filter. The FIR filter has
OutputSamplesPerSymbol + 1) tap coefficients.
To apply pulse shaping by interpolating an input signal using a raised cosine FIR filter:
comm.RaisedCosineTransmitFilterobject and set its properties.
Call the object with arguments, as if it were a function.
To learn more about how System objects work, see What Are System Objects?
returns a raised cosine transmit FIR filter System object, which interpolates an input signal using a raised cosine FIR
filter. The filter uses an efficient polyphase FIR interpolation structure and
has unit energy.
txfilter = comm.RaisedCosineTransmitFilter
sets properties using one or more name-value pairs. Enclose each property name
in quotes. For example,
txfilter = comm.RaisedCosineTransmitFilter(Name,Value)
configures a raised cosine transmit filter System object with the filter span set to 15 symbols.
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) |
Filter shape, specified as
'Square root' or
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].
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.
OutputSamplesPerSymbol — Output samples per symbol
8 (default) | positive integer
Output samples per symbol, specified as a positive integer.
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.
x — Input signal
column vector | matrix
Input signal, specified as a column vector or a Ki-by-N matrix. Ki is the number of input samples per signal channel, and N is the number of signal channels.
For a Ki-by-N matrix input, the object processes columns of the input matrix as N independent channels.
Complex Number Support: Yes
y — Output signal
column vector | matrix
Output signal, returned as a column vector or a
matrix. Ko is equal to
Ki is the number of input
samples per signal channel, and N is the number of
The object interpolates and filters each channel over the first dimension and then generates a Ko-by-N output matrix. The output signal is the same data type as the input signal.
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
|Information about filter System object|
|Coefficients for filters|
|Computational cost of implementing filter System object|
|Frequency response of discrete-time filter|
|Plot frequency response of filter|
|Group delay response of discrete-time filter|
|Impulse response of discrete-time filter|
|Order of discrete-time filter System object|
Interpolate Signal Using Square-Root-Raised-Cosine Filter
Interpolate a signal using square-root-raised-cosine (SRRC) transmit filter object and display the spectrum of the filtered signal.
Create random bipolar symbols at a symbol rate of 1e6 symbols per second.
data = 2*randi([0 1],1e6,1) - 1;
Create a SRRC transmit filter object. The default sets the filter to a square-root shape and the number of samples per symbol to 8.
txfilter = comm.RaisedCosineTransmitFilter
txfilter = comm.RaisedCosineTransmitFilter with properties: Shape: 'Square root' RolloffFactor: 0.2000 FilterSpanInSymbols: 10 OutputSamplesPerSymbol: 8 Gain: 1
Filter the data by using the SRRC filter.
filteredData = txfilter(data);
Create a spectrum analyzer object with an 8e6 sampling rate. This sampling rate matches the sampling rate of the filtered signal.
spectrumAnalyzer = spectrumAnalyzer(SampleRate=8e6);
View the spectrum of the filtered signal by using the spectrum analyzer object.
Examine Effect of Filter Span on Magnitude Response
Create interpolated signals from a square-root-raised-cosine (SRRC) filter with various filter spans. Examine the magnitude response of the various filter designs.
Create SRRC filter objects setting various filter spans. Use the
coeffs object function to obtain the filter coefficients.
txfilt2 = comm.RaisedCosineTransmitFilter('FilterSpanInSymbols',2); txfilt4 = comm.RaisedCosineTransmitFilter('FilterSpanInSymbols',4); txfilt6 = comm.RaisedCosineTransmitFilter('FilterSpanInSymbols',6); txfilt8 = comm.RaisedCosineTransmitFilter('FilterSpanInSymbols',8); txfilt16 = comm.RaisedCosineTransmitFilter('FilterSpanInSymbols',16); taps2 = coeffs(txfilt2).Numerator; taps4 = coeffs(txfilt4).Numerator; taps6 = coeffs(txfilt6).Numerator; taps8 = coeffs(txfilt8).Numerator; taps16 = coeffs(txfilt16).Numerator;
Launch the filter visualization tool to show the magnitude response for various filter spans. Specify a sample rate of 1 kHz. Display the two-sided centered response.
fvt = fvtool(taps2,1,taps4,1,taps8,1,taps16,1); fvt.Fs = 1e3; fvt.FrequencyRange = '[-Fs/2, Fs/2)'; legend(fvt,'Span 2 symbols','Span 4 symbols', ... 'Span 8 symbols','Span 10 symbols')
Create Square-Root-Raised-Cosine Transmit Filter with Unity Passband Gain
Create a square-root-raised-cosine (SRRC) transmit filter System object™, and then plot the filter response. The results show that the linear filter gain is greater than unity. Specifically, the passband gain is greater than 0 dB.
txfilter = comm.RaisedCosineTransmitFilter; fvtool(txfilter)
Obtain the filter coefficients by using the
coeffs object function and adjust the filter gain to unit energy.
b = coeffs(txfilter);
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,
txfilter.Gain = 1/sum(b.Numerator);
Verify that the resulting filter coefficients sum to 1.
bNorm = coeffs(txfilter); sum(bNorm.Numerator)
ans = 1.0000
Plot the filter frequency response again. The results now show that the passband gain is 0 dB, which is unity gain.
Examine Polyphase Matrix of RRC Filter
When you create a multirate filter that uses polyphase decomposition, the
polyphase function lets you analyze the component filters individually by returning the components as rows in a matrix. Using
polyphase with an output argument returns a matrix containing the polyphase decomposition with individual rows defining each subfilter.
rcfilter = comm.RaisedCosineTransmitFilter; p = polyphase(rcfilter)
p = 8×11 -0.0060 0.0097 -0.0133 0.0165 -0.0186 0.3729 -0.0186 0.0165 -0.0133 0.0097 -0.0060 -0.0051 0.0058 -0.0041 -0.0029 0.0297 0.3621 -0.0524 0.0301 -0.0190 0.0112 0 -0.0029 -0.0000 0.0075 -0.0255 0.0892 0.3308 -0.0707 0.0368 -0.0206 0.0105 0 0.0004 -0.0068 0.0196 -0.0477 0.1552 0.2823 -0.0742 0.0364 -0.0184 0.0079 0 0.0043 -0.0134 0.0300 -0.0653 0.2218 0.2218 -0.0653 0.0300 -0.0134 0.0043 0 0.0079 -0.0184 0.0364 -0.0742 0.2823 0.1552 -0.0477 0.0196 -0.0068 0.0004 0 0.0105 -0.0206 0.0368 -0.0707 0.3308 0.0892 -0.0255 0.0075 -0.0000 -0.0029 0 0.0112 -0.0190 0.0301 -0.0524 0.3621 0.0297 -0.0029 -0.0041 0.0058 -0.0051 0
polyphase without an output argument opens the Filter Visualization Tool, ready for you to use the analysis capabilities of the tool to investigate the filter. The Filter Analysis Using FVTool shows the coefficients of the subfilters. To see the magnitude response of the subfilters, click on the
Magnitude Response button on the Filter Analysis Using FVTool toolstrip.
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).
System object supports SIMD code generation using Intel AVX2 technology under these
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
The SIMD technology significantly improves the performance of the generated code. For details, see Generate SIMD Code for MATLAB Functions (Embedded Coder).
Introduced in R2013b