Goal:
:To design FIR filter in the MSE sense, we minimize the mean square error between the filter we obtained and the desired filter.
:: , where is sampling frequency, is the spectrum of the filter we obtained, and is the spectrum of the desired filter.

Method:
:Given an N-point FIR filter , and .
:Step 1: Suppose even symmetric. Then, the discrete time Fourier transform of is defined as
::
:Step 2: Calculate mean square error.
::
::Therefore,
::
:Step 3: Minimize