What are filter banks and how are they designed?

Filter banks split signals into multiple frequency subbands (analysis) and reconstruct from subbands (synthesis). Perfect reconstruction (PR) requires synthesis filters exactly undo analysis effects. Types: Uniform filter banks (equal bandwidth subbands), Non-uniform (different bandwidths), and Tree-structured (cascaded for octave bands). Design conditions: Aliasing cancellation and Magnitude distortion elimination. QMF (Quadrature Mirror Filter) banks use H1(z) = H0(-z) relationship. Applications: Audio coding, subband adaptive filtering, wavelet transforms, and transmultiplexers. Modern designs use lattice structures or modulated filter banks for efficiency.