Sigma Healthcare is entering the U.K. market by partnering with London-based Greenlight Healthcare Ltd. Read more about the agreement: (Photo: Bloomberg)

Two Sigma Investments’ billionaire co-founder John Overdeck said the $723 million he is proposing to give his wife Laura to resolve their divorce is “fair” based on his compensation from and stake in the quantitative hedge fund.

Inside the feedback loop of a sigma-delta modulator it becomes something else: a high-pass filter that leaves the signal untouched and sweeps quantization noise out of the band of interest. 1 − z⁻¹ looks like nothing more than a discrete differentiator. The linearized first-order model reads Y(z) ≈ X(z) + (1 − z⁻¹)E(z), so the signal transfer function is identically one while the noise transfer function is exactly that difference operator. After a digital low-pass filter and decimation the remaining in-band error is vanishingly small, turning a crude one-bit quantizer into a high-resolution converter. The same operator raised to higher powers yields the modulators that now achieve twenty-bit accuracy in audio and sensor applications.