The new Mersenne number transform (NMNT) has proved to be an important number theoretic transform (NTT) used for error-free calculation of convolutions and correlations. Its main feature is that for a suitable Mersenne prime number (p), the allowed power-of-two transform lengths can be very large. In this paper, efficient radix-2 2 decimation-in-time and in-frequency algorithms for fast calculation of the NMNT are developed by deriving the appropriate mathematical relations in finite field and applying principles of the twiddle factor unscrambling technique. The proposed algorithms achieve both the regularity of radix-2 algorithm and the efficiency of radix-4 algorithm and can be applied to any powers of two transform lengths with simple bit reversing for ordering the output sequence. Consequently, the proposed algorithms possess the desirable properties such as simplicity and inplace computation. The validity of the proposed algorithms has been verified through examples involving large integer multiplication and digital filtering applications, using both the NMNT and the developed algorithms. Keywords-Number theoretic transforms (NTTs), new Mersenne number transform (NMNT), radix-2 2 algorithm.

This paper presents a new algorithm for fast calculation of the discrete Hartley transform (DHT) based on decimation-in-time (DIT) approach. The proposed radix-2^2 fast Hartley transform (FHT) DIT algorithm has a regular butterfly structure that provides flexibility of different powers-of-two transform lengths, substantially reducing the arithmetic complexity with simple bit reversing for ordering the output sequence. The algorithm is developed through the three-dimensional linear index map and by integrating two stages of the signal flow graph together into a single butterfly. The algorithm is implemented and its computational complexity has been analysed and compared with the existing FHT algorithms, showing that it is significantly reduce the structural complexity with a better indexing scheme that is suitable for efficient implementation.

With the increase of the complexion in the power distribution system, it is very possible that several kinds of power quality disturbances are happened in a power distribution system simultaneously.This paper proposes a unified power quality conditioner (UPQC) including a series and a shunt active power filter (APF) to compensate harmonics in both the distorted supply voltage and nonlinear load current. In the series APF control scheme, a proportional-integral (PI) controller, meanwhile a PI controller and are designed in the shunt APF control scheme to relieve harmonic currents produced by nonlinear loads. The DC voltage is maintained constant using Two degree of freedom proportional integral voltage controller (2DoFPI). The performance of the proposed UPQC is significantly improved compared to the conventional control strategy. The feasibility of the proposed UPQC control scheme is validated through the simulations. Keyword:2DoFPI controller Series active filter Shunt active filter UPQC Voltage regulator

In real-time signal processing applications, the discrete version of the transform introduced by Hartley (DHT) has been proved to be an efficient substitute to the discrete Fourier transform (DFT). A new algorithm for fast calculations of the DHT (FHT) based on radix -2/4/8 method is introduced in this paper. In comparison with the split radix FHT algorithm, the proposed algorithm has a comparable arithmetic complexity, but preserves the regularity and the simple butterfly structure of the radix-2 algorithm. The development of the algorithm is motivated by firstly deriving a new radix-2/8 FHT algorithm and then cascading it with the radix-4 and radix-2 FHT algorithms. The arithmetic complexity of the developed algorithm has been implemented and analyzed by calculating the number of real additions and multiplications for different transform lengths. Comparisons with the existing FHT algorithms have shown that this algorithm can be considered as a good compromise between structural and arithmetic complexity.

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