The invention relates to representation of one and multidimensional signal vectors in multiple nonorthogonal domains and design of Vector Quantizers that can be chosen among these representations. There is presented a Vector Quantization technique in multiple nonorthogonal domains for both waveform and model based signal characterization. An iterative codebook accuracy enhancement algorithm, applicable to both waveform and model based Vector Quantization in multiple nonorthogonal domains, which yields further improvement in signal coding performance, is disclosed. Further, Vector Quantization in multiple nonorthogonal domains is applied to speech and exhibits clear performance improvements of reconstruction quality for the same bit rate compared to existing single domain Vector Quantization techniques. The technique disclosed herein can be easily extended to several other one and multidimensional signal classes.