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The design of FIR filters by using Fourier series coefficients takes an important place in the use of digital speech and signal processing applications. Since the number of coefficients has to be chosen as finite, gain curves cannot be obtained exactly. The deviation on the gain curves of designed and actual networks has been partially eliminated by applying the window functions on the coefficients. After getting partial filter characteristics by partitioning the gain characteristics at bandwidth and associating these partial filters gives total gain curve about FIR filter design and this what we are trying to present.