Non-integer order differentiation is changing application of traditional differentiation because it can achieve a continuous interpolation of the integer order differentiation. However, implementation of the non-integer order differentiation is much more complex than that of integer order differentiation. For this purpose, a Haar wavelet-based implementation method of non-integer order differentiation is proposed. The basic idea of the proposed method is to use the operational matrix to compute the noninteger order differentiation of a signal through expanding the signal by the Haar wavelets and constructing Haar wavelet operational matrix of the non-integer order differentiation. The effectiveness of the proposed method was verified by comparison of theoretical results and those obtained by another non-integer order differential filtering method. Finally, non-integer order differentiation was applied to enhance signal.

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