7 Highpass filter transfer function

To obtain the transfer function of the high-pass filters, an equivalent low-pass analog prototype has to be designed first. Then the low-pass prototype transfer function can be mapped to the desired high-pass filter using s-domain frequency transformations. The mapping function that converts low-pass prototype into corresponding high-pass transfer function is given as

where is a low-pass prototype variable and is a high-pass variable. The same function (7.1) must be used to convert the high-pass filter specification into low-pass prototype specification.

The general procedure of obtaining the high-pass filter transfer function includes several steps:

  • Step 1:

    Generate specification for the desired high-pass filter, which includes 4 parameters:

  • Step 2:

    Convert the high-pass specification into the low-pass prototype specification using the mapping function (7.1)

    Note, that this conversion should be done with angular frequencies.

  • Step 3:

    Generate the low-pass prototype transfer function

  • Step 4:

    Map the low-pass prototype transfer function into the desired high-pass transfer function

Matheonics Technology Inc, 2009

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