Synthesis of two-dimensional pseudo white-noise signal with low peak factor

This letter presents a new systematic approach for generating two-dimensional (2-D) signals having both a low peak factor (crest factor) and a flat power spectrum. The flat power spectrum provides zero auto-correlation, except for the zero shift. The proposed synthesis method is a systematic scheme, not a search method, and produces a 2-D signal of size (2n₁+1)(4n₁+1)×(2n₂+1)² for an arbitrary pair of integers n₁ and n₂. The peak factor of the proposed signal is equal to √1+1/(4n₁+1) times the peak factor of a single trigonometric function.