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:
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Step 1:
Generate specification for the desired high-pass filter, which includes 4 parameters:
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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.
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Step 3:
Generate the low-pass prototype transfer function
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Step 4:
Map the low-pass prototype transfer function into the desired high-pass transfer function
