RaisedCosine

VisualSim.simulators.sdf.lib
Class RaisedCosine

• public class RaisedCosine
• extends FIR

This actor implements an FIR filter with a raised cosine or square-root raised cosine frequency response. The excess bandwidth is given by excessBW and the symbol interval (in number of samples) by interpolation (which by default is 16). The length of the filter (the number of taps) is given by length.

For the ordinary raised cosine response, the impulse response of the filter would ideally be

  sin(pi n/T)   cos(alpha pi n/T)
  h(n) = ----------- * -----------------
  pi n/T      1-(2 alpha n/T)2
 

where alpha is excessBW and T is the interpolation factor. However, this pulse is centered at zero, and we can only implement causal filters in the SDF domain in VisualSim. Hence, the impulse response is actually

  g(n) = h(n - M)
 

where M = length/2 if length is even, and M = (length+1)/2 if length is odd. The impulse response is simply truncated outside this range, so the impulse response will generally not be symmetric if length is even because it will have one more sample to the left than to the right of center. Unless this extra sample is zero, the filter will not have linear phase if length is even.

For the ordinary raised cosine response, the distance (in number of samples) from the center to the first zero crossing is given by symbolInterval. For the square-root raised cosine response, a cascade of two identical square-root raised cosine filters would be equivalent to a single ordinary raised cosine filter.

The impulse response of the square-root raised cosine pulse is given by

  4 alpha(cos((1+alpha)pi n/T)+Tsin((1-alpha)pi n/T)/(4n alpha/T))
  h(n) = -----------------------------------------------------------------
  pi sqrt(T)(1-(4 alpha n/T)2)
 

This impulse response convolved with itself will, in principle, be equal to a raised cosine pulse. However, because of the abrupt rectangular windowing of the pulse, with low excess bandwidth, this ideal is not closely approximated except for very long filters.

The output sample rate is interpolation times the input. This is set by default to 16 because in digital communication systems this pulse is used for the line coding of symbols, and upsampling is necessary. Typically, the value of interpolation is the same as that of symbolInterval, at least when the filter is being used as a transmit pulse shaper.

References

[1] E. A. Lee and D. G. Messerschmitt, Digital Communication, Kluwer Academic Publishers, Boston, 1988.

[2] I. Korn, Digital Communications, Van Nostrand Reinhold, New York, 1985.

• Since:
• VisualSim0.2

excessBW

public VisualSim.data.expr.Parameter excessBW

• The excess bandwidth. This contains a DoubleToken, and by default it has value 1.0.

length

public VisualSim.data.expr.Parameter length

• The length of the pulse. This contains an IntToken, and by default it has value 64.

root

public VisualSim.data.expr.Parameter root

• If true, use the square root of the raised cosine instead of the raised cosine. This contains a BooleanToken, and by default it has value false.

symbolInterval

public VisualSim.data.expr.Parameter symbolInterval

• The symbol interval, which is the number of samples to the first zero crossing on each side of the main lobe. Its value is an IntToken, and by default it has value 16.

decimation

public VisualSim.data.expr.Parameter decimation

• Decimation is to reduce the sampling rate of the signal.The decimation ratio of the filter. This must contain an IntToken, and by default it has value one. No negative or Zero values.
  

decimationPhase

public VisualSim.data.expr.Parameter decimationPhase

• The decimation phase of the filter. This must contain an IntToken, and by default it has value zero.

interpolation

public VisualSim.data.expr.Parameter interpolation

• The interpolation ratio of the filter. This must contain an IntToken, and by default it has value one.

Created with the Personal Edition of HelpNDoc: Easily create EPub books