A new square wave transform based on the DCT

An efficient square wave transform (SWT) is presented. It is based on applying the signum function operator to the conventional discrete cosine transform (DCT) and is termed the signed DCT (SDCT). No order limits are imposed on the dimensions of the SDCT. Fast forward and backward transformation may be achieved. No multiplication operations or transcendental expressions are required. Analysis and simulations are introduced to show that the proposed SDCT maintains the good de-correlation and power compaction properties of the DCT. Simulation experiments are provided to justify the efficiency of the SDCT in signal processing applications such as system identification and image compression.