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Finite duration Impulse Response (FIR) filter has found its widespread applications in the field of communication as well as digital signal processing because of its attractive features, such as, linear phase response, assured stability etc. In modern digital or mobile communication system, transmitting pulse-shaping filters are more commonly realized by FIR filter. However, such a filter requires quite a large number of filter coefficients as compared to an Infinite duration Impulse Response (IIR) filter and hence leads to greater computational complexity. In this paper, an efficient algorithm has been proposed for the minimization of the number of coefficients of standard Raised Cosine (RC) pulse-shaping filter of different lengths, without affecting its performance to a great extent. The performance of the designed filter has been studied in terms of its impulse response as well as magnitude response. The designed FIR filter has also been used as a pulse-shaping filter in a Quadrature Phase Shift Keying (QPSK) modulated system and its performance has been studied in terms of the system Bit Error Rate (BER) value. From the simulation results it has been established that the newly proposed filter provides a significant reduction in the number of tap coefficients without much degradation in its performance.