The design of cascade form FIR filters for discrete space implementation

When an FIR (finite-impulse response) filter with discrete valued coefficients is implemented in direct form, the peak of the amplitude response decreases with increasing filter length, but only up to certain length. Further reduction in peak ripple beyond that point cannot be realized easily without increasing the coefficient precision. It is shown that by cascading two direct-form FIR filters, each with coefficients that are sum or difference of two power-of-two terms, it is possible to achieve very small peak ripple