Information maximizing DAC noise shaping

DACs are usually defined as having a constant number of bits over a contiguous bandwidth. Signals in practice, however, frequently have an information or bit content which is not constant with frequency. As DAC power is a function of bits, this creates an opportunity to design a more power efficient DAC. This paper addresses this opportunity by deriving the optimal DAC bit resolution vs frequency shape for maximizing the information content in the channel output given a power constraint. An optimization method that works within the constraints of the delta sigma modulator is also developed as arbitrary noise shaping is not possible with a fixed delta sigma DAC architecture.