In linear-phase filter design, we assumed symmetry of our filter coefficients [ ]

- The filter frequency response became a
*sum of cosines*(``zero phase'') - The matrix was real
- The desired magnitude response was real
- The final zero-phase filter could be right-shifted samples to get a corresponding causal linear-phase FIR filter

- is complex
- is complex
- We still want (our filter coefficients) to be real

If we try to use '
' or `pinv` in Matlab, we will generally
get a complex result for

Summarizing our problem:

where, , , and

Hence we have,

which can be written as:

or

which is written in terms of only *real* variables.

Hence, we can use the standard least squares solvers in Matlab and end
up with a *real* solution.

**Related paper**

``Design of Fractional Delay Filters Using Convex Optimization'' (Mohonk-97, Music 421 handout):

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