| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 1180419 | Chemometrics and Intelligent Laboratory Systems | 2015 | 8 Pages |
•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.
