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System Simulator >
System Component Models >
Digital Filters >
Root Raised Cosine Filter (RRCF)

Root Raised Cosine Filter (RRCF)

Property	Description	Units	Default	Range/Type
FC	3 dB Cutoff_Frequency	Hz	50	(0, Inf)/Real
BETA	Rolloff factor	None	0.5	[0, 1]/Real
FILT_LENGTH	Number of filter coefficients	None	16	[9, Inf]/Integer
TRAN	0 = Discard transient samples, 1 = Retain samples	None	0	[0, 1]/Integer
RIN	Input impedance	Ohm	Inf	(0, Inf]/Real
ROUT	Output impedance	Ohm	0	[0, Inf)/Real
Ports
Input	Input signal (real)
Output	Output signal (real)

Notes

2. This is a lowpass filter model which has the following transfer function:

H(f) = 1, for 0 £ |f| £ (1 - BETA)* FC

H(f) =sqrt (0.5 * (1 - sin (pi * (|f| - FC)/(2 * FC * BETA))))
for (1 - BETA) * FC £ |f| £ (1 + BETA) * FC

H(f) = 0, for |f| ³ (1 + BETA) * FC
where FC is the 3 dB cutoff frequency and BETA is the rolloff factor.

3. The impulse response of the filter is obtained by implementing the above function in the FFT domain (taking the input sampling frequency (FS) into consideration) and then using an inverse FFT of length FFTL. This length is given by

FFTL = Minimum power of 2 larger than 2 x FILT_LENGTH.

Upon finding the impulse response, the filter is made causal by delaying the impulse response. For a more accurate impulse response, the user must make sure
FILT_LENGTH 5.0(FS/(1+BETA)FC
and to avoid aliasing, the user must ensure that
FS => 2 ^.(1+ BETA) FC

4. The model will not issue warning messages if these conditions are not met.

Netlist Form

RRCF:Name 1 2 FC=val BETA=val FILT_LENGTH=val [Rin=val] [Rout=val] [TRAN=val]

Netlist Example

RRCF:1 1 2 FC=100KHZ BETA=.75 FILT_LENGTH=32

References

1. J. G. Proakis, Digital Communications, McGraw-Hill, 1989.

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