Since from the block diagram, the coefficients of the FIR filter coefficients are optimized by the least squares error criterion, it belongs to the least squares FIR inverse filter or wiener filter.

In the process of truncating, we incur a total squared approximation error where M+1 is the length of the truncated filter.

FIR least square filters are also called as Wiener filters.

When ε is minimized with respect to the filter coefficients, we obtain the set of linear equations which are dependent on the auto correlation sequence of the signal h(n).

When ε is minimized with respect to the filter coefficients, we obtain the set of linear equations

The inverse to a linear time invariant system with impulse response h(n) is defined as the system whose impulse response is hI(n), satisfy the following condition h(n)*hI(n)=δ(n).

In most of the practical applications, it is desirable to restrict the inverse filter to be an FIR filter.

The inverse to a linear time invariant system with impulse response h(n) and system function H(z) is defined as the system whose impulse response is hI(n) and system function HI(z), satisfy the following condition

In many practical applications, it is desirable to restrict the inverse filter to be FIR. One of the simple method to get this requirement is to truncate hI(n).

We can use the least squares error criterion to optimize the M+1 coefficients of the FIR filter.