A system includes a storage device containing machine instructions and a plurality of digital values of an oversampled sinuisoidal signal. The system also includes a core coupled to the storage. The core is configured to execute the machine instructions, wherein, when executed, the machine instructions cause the core to implement a sigma-delta modulator that retrieves the plurality of digital values from the storage device as input to the modulator. The sigma-delta modulator is configured compute an output bit stream. The system further includes an analog filter configured to receive the output bit stream from the core and to low-pass filter the output bit stream to produce a sinusoidal output signal.

Embodiments of circuits and methods are described below that may provide a modulator that has an enhanced signal-to-quantization-noise ratio (SQNR) for a given sampling frequency and bandwidth or that may enable a reduced sampling frequency for a target SQNR and bandwidth. In one or more embodiments, a modulator circuit may include a first modulator including an input and a first output, and including one or more feed-forward components; an output circuit including an input coupled to the first output and including an output, the output circuit including one of a noise-shaping circuit, a noise-shaped quantizer circuit, or an integrator and feed-forward component; and coefficients of the one or more feed-forward components of the first modulator and a transfer function of the output circuit provide a higher-order modulator with a first-order roll-off at high out-of-band frequencies.