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 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 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 and Multiplication Data Types 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 and Multiplication Data Types 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.
Port  Supported Data Types 

In 

Out 
