For an efficient and optimized digital FIR filter design, there are two methods available broadly, Equiripple filter design & Least Squares filter design. A general method for designing a filter is also Frequency Sampled FIR design but it is not an optimized design
The basic knowledge I have is that Equiripple filter, as the name suggests, has equal ripples in passband & stopband, which means the signal distortion that happens at the edge of the passband due to presence of a large ripple is avoided in Equiripple design BUT, Equiripple design has a large transition band, thus limiting the total passband width.
On the other hand, in a Least Squares design, the transition band width is smaller than for Equiripple design, hence the passband width is more, but the passband ripple are not equi-ripple & exhibit a spike at the passband edge due to Gibbs phenomenon, which causes signal distortion at the edge.
My question is can somebody present or quote the all the differences & advantages over other, in a technical language, for the Equiripple design vs Least squares design of digital low pass FIR filter.