The Relationship between the WHT and the CIT

The Walsh-Hadamard Transform is an important signal transform that converts real input to real output, and it has found applications in many signal processing tasks. The Cosine Integer Transform is a recently developed transform and it shares the real-to-real conversion property of the Walsh-Hadamard Transform. Although these two transforms have different kernels, there exist relations between the two transforms. This paper attempts to study and mathematically formalize these relations.