frequency response is the continuous Fourier transform of the impulse response. where is the (normalized) sinc function commonly used in digital signal processing. The Laplace transform transfer function of the ZOH is found by substituting s = i 2 π f: The fact that practical digital-to-analog converters (DAC) do not output a sequence of dirac impulses, xs(t) (that, if ideally low-pass filtered, would result in the unique underlying bandlimited signal before sampling), but instead output a sequence of rectangular pulses, xZOH(t) (a piecewise constant function), means that there is an inherent effect of the ZOH on the effective frequency response of the DAC, resulting in a mild roll-off of gain at the higher frequencies (a 3.9224 dB loss at the Nyquist frequency, corresponding to a gain of sinc(1/2) = 2/π). This drop is a consequence of the hold property of a conventional DAC, and is not due to the sample and hold that might precede a conventional analog-to-digital converter (ADC). See also Nyquist–Shannon sampling theorem First-order hold Discretization of linear state space models (assuming zero-order hold) References Digital signal processing Electrical engineering Control theory Signal processing