The low pass filters used by DPlot are composites of several filters using the linear equation shown in the Filter topic. This technique was first suggested by J.R.B. Whittlesey (see below).

A full description of filtering techniques is well beyond the scope of this documentation. For more information see the references at the end of this topic.

Four composite low-pass filters are constructed by combining the following components:

Operator |
to be Performed to |
Function |

S1 |
||

S2 |
||

S3 |
||

S4 |
||

S6 |
||

S8 |
||

SX |
||

R3 |
||

R6 |
||

R9 |
||

R12 |

In the above table x represents the input amplitudes, y represents the output.

Each of the 4 low-pass filter options applies several operators in sequence. The output from one operator is the input to the second operator. Each of the operators shown above amplifies the output, so that the original input is effectively multiplied by some factor. To compensate for this effect, DPlot multiplies the final output by the gain factors shown in the table below.

Low Pass Option |
Sequence |
Factor |

1 |
S1,SX,S2,R3 |
1/12 |

2 |
S1,SX,S2,S2,S4,R6 |
1/48 |

3 |
S1,SX,S3,S3,S6,R9 |
1/48 |

4 |
S1,SX,S2,S4,S4,S8,R12 |
1/96 |

For more information see:

Blackman, R.B. and Tukey, J.W., “The Measurement of Power Spectra, for the Point of View of Communications Engineering,” The Bell System Technical Journal, Vol 37, January and March 1958, pp 185-288, 485-569.

and

Whittlesey, J.R.B., “A Rapid Method of Digital Filtering,” Communications of the Association for Computing Machinery, Vol 7, No. 9, September 1964, pp 552-556.

Note: The Option 3 and 4 filter sequence is modified slightly from the above references to give an amplitude response of 1.0. The original filter designs might have exceeded 1.0. (That is, the output amplitude might have been greater than the input.)

Page url:
https://www.dplot.com/help/index.htm?helpid_lowpass.htm