Orthogonality-Preserving Analog Signal Construction From a Finite Sequence

Orthogonal signal sets play a central role in many digital communication and radar use cases, among others. While these important signal sets are readily defined in the digital domain, practical implementations transmit and receive signals in the analog domain. Interestingly, the commonly applied sinc interpolation does not preserve orthogonality for signals defined over a finite-length time slot. In this letter, we propose a novel construction technique for mapping discrete-time signals onto continuous-time signals which preserves scalar products and signal orthogonality while satisfying the Nyquist criterion in the presence of matched filtering at the receiver. Our construction technique can be efficiently implemented using a fast Fourier transform.