An area efficient real time implementation of dual tree complex wavelet transform in field programmable gate arrays

Biomedical signals (BSs), which give information about the normal condition and also the inherent irregularities of our body, are expected to have non-stationary character due to the time-varying behavior of physiological systems. The Fourier transform and the short time Fourier transform are the widely used frequency and time-frequency analysis methods for extracting information from BSs with fixed frequency and time-frequency resolution respectively. However, in order to derive relevant information from non-stationary BSs, an appropriate analysis method which exhibits adjustable time-frequency resolution is needed. The wavelet transform (WT) can be used as a mathematical microscope in which the time-frequency resolution can be adjusted according to the different parts of the signal. The discrete wavelet transform (DWT) is a fast and discretized implementation for classical WT. Due to the aliasing, lack of directionality and shift-variance disadvantages, the DWT exhibits limited performance in the process of BSs. In literature, an improved version of the DWT, which is named as Dual Tree Complex Wavelet Transform (DTCWT), is employed in the analysis of BSs with great success. In this study, considering the improvements in embedded system technology and the needs for wavelet based real-time feature extraction or de-noising systems in portable medical devices, the DTCWT is implemented as a sub-system in field programmable gate arrays. In proposed hardware architecture, for every data input-channel, DTCWT is implemented by using only one adder and one multiplier. Additionally, considering the multi-channel outputs of biomedical data acquisition systems, this architecture is designed with the capability of running in parallel for N channels.