Methods and apparatus for direct synthesis of RF signals using delta-sigma modulator

Methods and apparatus are provided for direct synthesis of RF signals using a delta-sigma modulator. An RF signal is synthesized from an input signal by quantizing the input signal using a quantizer, such as a one bit quantizer; determining a quantization error associated with the quantizer; generating an error prediction value using an error predictive filter, wherein the error predictive filter comprises one or more filter zeroes on a unit circle for one or more desired frequencies of f1, f2, . . . fn and one or more filter poles having a magnitude inside the unit circle and a frequency substantially equal to the one or more desired frequencies of f1, f2, . . . fn; and subtracting the error prediction value from the input signal. The filter poles have a magnitude that reduces a boost provided out-of-band.