A complex grating is approximated by a sequence of uniform segments, and analyzed by connecting the segments with the well-known Transfer Matrix Method. This gives the designer the information needed to test and optimize grating designs. Applications WDM add/drop, narrow and broadband fiber and waveguide filters Fiber Bragg reflectors EDFA gain flattening elements Dispersion compensators for fiber communications Sideband suppression using grating apodization Fiber and waveguide sensors Long Period Gratings with coupling to cladding modes