Fast Convolution Algorithm for Real-Valued Finite Length Sequences

The Fast Fourier Transform (FFT)-based convolution is the most popular fast convolution algorithm. In past work, we developed the Discrete Hirschman Transform (DHT)-based convolution. When compared to the FFT-based convolution, our DHT-based convolution can reduce the computational complexity by a third. Recently, we developed a comprehensive DFT algorithm where every calculation is natively real-valued (RV) dot products. In this paper, we first apply the natively real-valued DFT to linear convolution. We call this method the RV-based convolution. The arithmetic analysis reveals that it efficiently reduces the operation counts. The algorithm is fast regardless of length.