Discrete

Hold Block

Sample-and-hold block. Zero-order hold (ZOH) holds the last sampled value. First-order hold (FOH) linearly interpolates between samples.

# Hold Block

Description

Sample-and-hold block that samples the input at regular intervals and holds or interpolates the value between samples.

Zero-Order Hold (ZOH):

y(t) = u(t_k)  for t_k ≤ t < t_{k+1}

First-Order Hold (FOH):

y(t) = u(t_k) + (u(t_k) - u(t_{k-1}))/T · (t - t_k)  for t_k ≤ t < t_{k+1}

where t_k = k · T and T is the sample time.

zoh: Zero-Order Hold — holds the last sampled value constant until the next sample (staircase output)
foh: First-Order Hold — linearly extrapolates between samples using the slope from the last two samples

Interval between samples (seconds). The block samples the input at multiples of this interval.

ZOH vs FOH: Zero-Order Hold produces a staircase output (common in DACs); First-Order Hold linearly extrapolates (smoother but can overshoot)
Sample time: Must be ≥ the simulation base timestep; values below the base step are clamped
Rate transition: Use Hold to bridge subsystems running at different sample rates
ZOH mode: Most numerically stable; recommended unless FOH's smoother output is explicitly needed
FOH mode: Requires two prior samples; initial behaviour differs on the first step after a rate transition