A New Orthogonal Transform for Signal Coding

This paper deals with the concept of orthogonal transformation and proposes a new orthogonal, unitary transformation called the “Modified Hermite Transformation’’ (MHT), and its extension which is called the “Modular Modified Hermite Transformation” (MMHT). The MHT algorithm, which is an efficient algorithm, is explored and explained extensively. The MHT is compared to the well-known Discrete Cosine Transform (DCT) for various AR (1) input signal source models using the performance criterion of gain over PCM, denoted by NGrc. The MHT algorithm requires only 2N real multiplications or divisions for a transformation of a signal block of N samples. The MHT algorithm is also used for the inverse transformation, IMHT. The MHT algorithm makes this new transform very attractive. It is efficient computationally and comparable to the industry standard, the DCT, for the AR(1) source models with positive correlation coefficients; it is somewhat better than the DCT for negative correlation coefficients.