A nested mixed-radix DDSM can guarantee zero systematic frequency error when used as a divider controller in a fractional-N frequency synthesizer is described. This disclosure presents a nested cascaded mixed-radix DDSM architecture which can also guarantee zero systematic frequency error. In addition, the disclosure allows one to use higher order auxiliary modulators and shaped dither signal to eliminate feedthrough spurs completely. By increasing the number of levels in the cascade, the moduli of the individual modulator stages can be reduced, thereby increasing the speed of the synthesizer.

A method for differentiator-based compression of digital data includes (a) using a subtraction module, subtracting a predicted signal from a sample of an original signal to obtain an error signal, (b) using a quantization module, quantizing the error signal to obtain a quantized error signal, and (c) generating the predicted signal using a least means square (LMS)-based filtering method.

A quantizer includes: a quantizer capacitor having a first end and a second end; an input calculator that receives input voltages, sums the input voltages, and outputs the summed result to the first end of the quantizer capacitor; a scaler that receives reference voltages and a scale code, generates a scale voltage from the reference voltages depending on the scale code, and outputs the scale voltage to the second end of the quantizer capacitor; and a latch that stores an output voltage of the first end of the quantizer capacitor.

In accordance with embodiments of the present disclosure, a digital microphone system may include a microphone transducer and a digital processing system. The microphone transducer may be configured to generate an analog input signal indicative of audio sounds incident upon the microphone transducer. The digital processing system may be configured to convert the analog input signal into a first digital signal having a plurality (e.g., more than 3) of quantization levels, and in the digital domain, process the first digital signal to compress the first digital signal into a second digital signal having fewer quantization levels (e.g., +1, 0, 1) than that of the first digital signal.

A digital delta-sigma modulator (DDSM) is disclosed with an input signal x[n], an output signal y[n], a quantization error signal e[n] and a dither signal d[n], having an equation described in the z-domain by
Y(z)=STF(z)X(z)+DTF(z)D(z)NTF(z)E(z), wherein Y(z), X(z), D(z) and E(z) are z-transforms of the output signal, the input signal, the dither signal, and the quantization error signal, and wherein STF(z), DTF(z) and NTF(z) correspond to a transfer function of the input signal, a transfer function of the dither signal, and a transfer function of the quantization error signal, and wherein the transfer function of the quantization error signal is of the form: $\mathrm{NTF}\left(z\right)=A{z}^{-Q}\left(1-z^{-1}\right)\left(1+\underset{i=1}{\overset{K}{.Math.}}{c}_i{z}^{-i}\right),$ A, Q and K are constants, coefficients c.sub.i are real valued and c.sub.K0 and wherein at least one of the zeroes z.sub.j of $\left(1+\underset{i=1}{\overset{K}{.Math.}}{c}_i{z}^{-i}\right)$

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.