Apply pulse shaping by upsampling signal using raised cosine FIR filter
Comm Filters
The Raised Cosine Transmit Filter block upsamples and filters the input signal using a normal raised cosine FIR filter or a square root raised cosine FIR filter. The block's icon shows the filter's impulse response.
The Filter shape parameter determines which
type of filter the block uses; choices are Normal
and Square
root
.
The impulse response of a normal raised cosine filter with rolloff factor R and symbol period T is
$$h(t)=\frac{\mathrm{sin}(\pi t/T)}{(\pi t/T)}\cdot \frac{\mathrm{cos}(\pi Rt/T)}{(14{R}^{2}{t}^{2}/{T}^{2})}$$
The impulse response of a square root raised cosine filter with rolloff factor R is
$$h(t)=4R\frac{\mathrm{cos}\left((1+R)\pi t/T\right)+\frac{\mathrm{sin}\left((1R)\pi t/T\right)}{(4Rt/T)}}{\pi \sqrt{T}\left(1{(4Rt/T)}^{2}\right)}$$
The impulse response of a square root raised cosine filter convolved with itself is approximately equal to the impulse response of a normal raised cosine filter.
Because the ideal raised cosine filter has an infinite impulse response, the block truncates the impulse response to the number of symbols that the Filter span in symbols parameter specifies. The Filter span in symbols, N, and the Output samples per symbol, L, determine the length of the filter's impulse response, which is L * Filter span in symbols + 1.
The Rolloff factor parameter is the filter's rolloff factor. It must be a real number between 0 and 1. The rolloff factor determines the excess bandwidth of the filter. For example, a rolloff factor of .5 means that the bandwidth of the filter is 1.5 times the input sampling frequency.
The block normalizes the filter coefficients to unit energy. If you specify a Linear
amplitude filter gain other than 1
, then the block scales the
normalized filter coefficients using the gain value you specify.
The input must be a discretetime signal. This block accepts a column vector or matrix input signal. For information about the data types each block port supports, see the Supported Data Type table on this page.
The Rate options method and the value of the Output samples per symbol, L, parameter determine the characteristics of the output signal:
When you set the Rate options parameter
to Enforce singlerate processing
, the
input and output of the block have the same sample rate. To generate
the output while maintaining the input sample rate, the block resamples
the data in each column of the input such that the frame size of the
output (M_{o}) is L times
larger than that of the input (M_{o} = M_{i}*L),
where L represents the value of the Output
samples per symbol parameter.
When you set the Rate options parameter
to Allow multirate processing
, the input
and output of the block are the same size. However, the sample rate
of the output is L times faster than that of the
input (i.e. the output sample time is 1/L times the input sample time).
When the block is in multirate processing mode, you must also specify
a value for the Input processing parameter:
When you set the Input processing parameter
to Elements as channels (sample based)
,
the block treats an MbyL matrix
input as M*N independent channels,
and processes each channel over time. The output sample period (T_{so})
is L times shorter than the input sample period
(T_{so} = T_{si}/L),
while the input and output sizes remain identical.
When you set the Input processing parameter
to Columns as channels (frame based)
, the
block treats an M_{i}byN matrix
input as N independent channels. The block processes
each column of the input over time by keeping the frame size constant
(M_{i}=M_{o}),
while making the output frame period (T_{fo}) L times
shorter than the input frame period (T_{fo} = T_{fi}/L).
To examine or manipulate the coefficients of the filter that this block designs, select Export filter coefficients to workspace. Then set the Coefficient variable name parameter to the name of a variable that you want the block to create in the MATLAB^{®} workspace. Running the simulation causes the block to create the variable, overwriting any previous contents in case the variable already exists.
Specify the filter shape as Square root
or Normal
.
Specify the rolloff factor of the filter. Use a real number
between 0
and 1
.
Specify the number of symbols the filter spans as an even, integervalued
positive scalar. The default is 10
. Because the
ideal raised cosine filter has an infinite impulse response, the block
truncates the impulse response to the number of symbols that this
parameter specifies.
Specify the number of output samples for each input symbol. The default is 8. This property accepts an integervalued, positive scalar. The number of taps for the raised cosine filter equals the value of this parameter multiplied by the value of the Filter span in symbols parameter.
Specify a positive scalar value that the block uses to scale
the filter coefficients. By default, the block normalizes filter coefficients
to provide unit energy gain. If you specify a gain other than 1
,
the block scales the normalized filter coefficients using the gain
value you specify.
Specify how the block processes the input signal. You can set this parameter to one of the following options:
Columns as channels (frame based)
—
When you select this option, the block treats each column of the input
as a separate channel.
Elements as channels (sample based)
—
When you select this option, the block treats each element of the
input as a separate channel.
Specify the method by which the block should upsample and filter the input signal. You can select one of the following options:
Enforce singlerate processing
—
When you select this option, the block maintains the input sample
rate, and processes the signal by increasing the output frame size
by a factor of N. To select this option, you must
set the Input processing parameter to Columns
as channels (frame based)
.
Allow multirate processing
—
When you select this option, the block processes the signal such that
the output sample rate is N times faster than the
input sample rate.
Select this check box to create a variable in the MATLAB workspace that contains the filter coefficients.
If you click this button, then MATLAB launches the Filter
Visualization Tool, fvtool
, to analyze the raised
cosine filter whenever you apply any changes to the block's parameters.
If you launch fvtool
for the filter, and subsequently
change parameters in the mask, fvtool
will not
update. You will need to launch a new fvtool
in
order to see the new filter characteristics. Also note that if you
have launched fvtool
, then it will remain open
even after the model is closed.
Select the rounding mode for fixedpoint operations. The block uses the Rounding
mode when the result of a fixedpoint calculation does not map exactly to a number
representable by the data type and scaling storing the result. The filter coefficients do not
obey this parameter; they always round to Nearest
. For more
information, see Rounding Modes (DSP System Toolbox) or Rounding Mode: Simplest (FixedPoint Designer).
Select the overflow mode for fixedpoint operations. The filter coefficients do not obey this parameter; they are always saturated.
Choose how you specify the word length and the fraction length of the filter coefficients (numerator and/or denominator). See Filter Structure Diagrams (DSP System Toolbox) for illustrations depicting the use of the coefficient data types in this block:
When you select Same word length as input
,
the word length of the filter coefficients match that of the input
to the block. In this mode, the fraction length of the coefficients
is automatically set to the binarypoint only scaling that provides
you with the best precision possible given the value and word length
of the coefficients.
When you select Specify word length
,
you are able to enter the word length of the coefficients, in bits.
In this mode, the fraction length of the coefficients is automatically
set to the binarypoint only scaling that provides you with the best
precision possible given the value and word length of the coefficients.
When you select Binary point scaling
,
you are able to enter the word length and the fraction length of the
coefficients, in bits. If applicable, you are able to enter separate
fraction lengths for the numerator and denominator coefficients.
When you select Slope and bias scaling
,
you are able to enter the word length, in bits, and the slope of the
coefficients. If applicable, you are able to enter separate slopes
for the numerator and denominator coefficients. This block requires
poweroftwo slope and a bias of zero.
The filter coefficients do not obey the Rounding mode and the
Saturate on integer overflow parameters; they are always saturated and
rounded to Nearest
.
Use this parameter to specify how you would like to designate the product output word and fraction lengths. See Filter Structure Diagrams (DSP System Toolbox) and Multiplication Data Types (DSP System Toolbox) for illustrations depicting the use of the product output data type in this block:
When you select Same as input
,
these characteristics match those of the input to the block.
When you select Binary point scaling
,
you are able to enter the word length and the fraction length of the
product output, in bits.
When you select Slope and bias scaling
,
you are able to enter the word length, in bits, and the slope of the
product output. This block requires poweroftwo slope and a bias
of zero.
Use this parameter to specify how you would like to designate the accumulator word and fraction lengths. See Filter Structure Diagrams (DSP System Toolbox) and Multiplication Data Types (DSP System Toolbox) for illustrations depicting the use of the accumulator data type in this block:
When you select Same as input
,
these characteristics match those of the input to the block.
When you select Same as product output
,
these characteristics match those of the product output.
When you select Binary point scaling
,
you are able to enter the word length and the fraction length of the
accumulator, in bits.
When you select Slope and bias scaling
,
you are able to enter the word length, in bits, and the slope of the
accumulator. This block requires poweroftwo slope and a bias of
zero.
Choose how you specify the output word length and fraction length:
When you select Same as input
,
these characteristics match those of the input to the block.
When you select Same as accumulator
,
these characteristics match those of the accumulator.
When you select Binary point scaling
,
you are able to enter the word length and the fraction length of the
output, in bits.
When you select Slope and bias scaling
,
you are able to enter the word length, in bits, and the slope of the
output. This block requires poweroftwo slope and a bias of zero.
Select this parameter to prevent any fixedpoint scaling you specify in this block mask from being overridden by the autoscaling tool in the FixedPoint Tool.
This block supports HDL code generation using HDL Coder™. HDL Coder provides additional configuration options that affect HDL implementation and synthesized logic. For more information on implementations, properties, and restrictions for HDL code generation, see Raised Cosine Transmit Filter in the HDL Coder documentation.
Port  Supported Data Types 

In 

Out 
