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.