Digital Signal Processing (DSP) is one of the fastest growing techniques in the electronics industry. The signal-rate system in digital signal processing has evolved the key of fastest speed in digital signal processor. Field Programmable Gate Array (FPGA) offers good solution for addressing the needs of high performance DSP systems. The focus of this paper is on the basic DSP functions, namely filtering signals to remove unwanted frequency bands. Multi-rate Digital Filters (MDFs) are the main theme to build bio-chip design in this paper. For different purposes DSP systems need to change the sampling rate of the signal to achieve some applications. This can be done using multi-rate system where designers can increase or decrease the operating sampling rate. This bio-chip has attractive features like, low requirement of the coefficient word lengths, significant saving in computation time and storage which results in a reduction in its dynamic power consumption. This paper introduces an efficient FPGA realization of multi-rate digital filter with narrow pass-band and narrow transition band to reduce noises and changing the frequency sampling rate by factor which is required according to application. This bio-chip works on bio-signals like EEG signal.