Window functions have been successfully used in various areas such as filtering, beam forming and multirate signal processing. Due to available closed form expressions, the role of windows is economical. One of the key applications is the design of FIR filters. These filters are used in decimators and interpolators which are the basic building blocks for any multirate system and filterbank. In present scenario, a system with an improved performance, better quality, little error is the prime requirement. With this objective FIR multirate filters are designed using window functions. These functions can be used to design half-band filters where fifty percent filter coefficients result with zero value. With bandpass filters more than seventy percent zero valued coefficients are obtained if they preserved the concept of half-band symmetry. On the basis of error criterion filterbanks are of two types, viz., pseudo filterbanks and perfect reconstructed filterbanks. A new linear optimization algorithm is applied to obtain the pseudo filterbanks. Lag windows can be used to design energy efficient filters called compaction filters. The compaction gain is very near to optimal ones.