A number of parallel modulation functions are configured to provide sigma-delta modulation on a plurality of low sampling rate signals, which are representative of a high sampling rate input signal. Resultant sigma-delta modulated signals from each of the modulation functions are combined in a multiplexing fashion to create a high sampling rate output signal. The modulation functions may be interdependent, wherein error signals from the modulation functions are provided to a parallel block digital filter, which will provide a processed error signal to feed back into the input of each modulation function. The processed error signal for a given modulation function may be a function of the error signals derived from multiple ones of the modulation functions. In one embodiment, there are N modulation functions, and the operating rate of the modulation functions is fs/N wherein the sampling rate of the high frequency output signal is fs.