Least squared error FIR filters with flat amplitude or group delay constraints

Finite impulse response lowpass filters with prescribed number of zeros at ω = π and either prescribed group delay flatness or prescribed amplitude flatness and linear phase are designed by minimizing a squared error. A simple orthogonal projection of least squared error filters (that are often available in closed form) onto a linear subspace determined via Thiran filters (for group delay flatness) and via Herrmann filters (for amplitude flatness) gives the desired filters.