A method of approximate fractional order differentiation with noise immunity

• We present a method of differentiation with noise immunity.
• Arbitrary fractional order differentiation (FOD) of a signal was realized.
• The integer order differentiation is just a special case of the FOD.
• The proposed method is used to enhance signal.

In order to successfully apply differentiation to quantitative analytical applications, it is important to develop a method of differentiation with noise immunity to optimize the signal-to-noise ratio. Therefore, a direct method for the approximate fractional order differentiation (FOD) of a noised signal is proposed. Using the proposed method, arbitrary order differentiation of a signal can be realized by the convolution between the fractional order differentiation of the Gaussian function and the noised signal, and the integer order differentiation is just a special case of the FOD. The proposed method is verified by comparing the FOD of the noise and noise-free peak-signals. Moreover, the proposed method is used to enhance a mass spectrum signal and locate the position of each peak.