In this paper, we propose a modular Constant Phase Element (CPE) emulator, the approximation order of which is electronically adjustable. In this way, the emulator provides a limited approximation error over a range of the parameter alpha, the order of the CPE. A fractional-order differentiator has been utilized in the emulator, which is realized by rational integer-order approximations implemented based on a lattice-type structure. The advantage of lattice-type implementation is the possibility of easily changing the order of approximation. It also provides the flexibility of compromising the approximation accuracy with power consumption. The emulator is accurate over five decades of frequency [0.1 Hz, 10 kHz] and provides electronic adjustability of the CPE capacitance, order, and operation frequency. The simulation results confirm the performance of the emulator. Two fractional band-pass filters (FBPF) are presented as an application of the CPE emulator, which are employed in electroencephalography (EEG) signal processing. One of the FBPFs is employed in extracting theta and alpha waves in the frequency range of 3-13 Hz; while the other filter is used for extracting the beta waves in the range of 13-30 Hz. The power consumption of the simulated FBPFs are 2.871 mu W and 1.836 mu W, respectively.