In this section, we consider the minimax dB linear phase lowpass FIR filter design,

Note that this problem has infinite constraints. Subsequently, we discretize the frequency parameter to obtain a finite-constraint approximation. Moreover, there is a nonlinear term in the first part of the constraints. To convert it to a second order cone constraint, we introduce such that

for and

Now, we obtain the problem in SOCP form,

where , We use the following data in our test cases.

**Example 5.** Given
,
, and
We descretize the frequency parameter
by the uniform step
We choose
as our test samples.

More details about this problem and the interior point approach can be found in [19].