Smooth Block

Exponentially weighted moving average filter. Smooths noisy input signals using a specified averaging time.

Description

The Smooth block implements exponential smoothing (also known as a first-order low-pass filter). It is used to filter out noise or short-term fluctuations from a signal, focusing on the long-term trend.

Mathematical Model

d(Out)/dt = (In - Out) / T

The block computes the output $Out$ such that its rate of change is proportional to the discrepancy between the input $In$ and the current output, controlled by an averaging time $T$:

$$\frac{d(Out)}{dt} = \frac{In - Out}{T}$$

In terms of smoothing: $$Out_{n} = (1 - \alpha) \cdot Out_{n-1} + \alpha \cdot In_n$$ where $\alpha = \Delta t / T$.

Parameters

averagingTime

The time constant $T$ of the smoothing filter. A higher value means more smoothing but also more lag.

• Default: 1
• Tooltip: Time constant for the smoothing filter

initialValue

The starting value of the smoothed output at t=0.

• Default: 0
• Tooltip: Starting value of the smoothing output

Ports

in (Input)

The noisy or raw signal to be smoothed.

out (Output)

The resulting smoothed signal.

See Also

• Delay1: Mathematically identical, but conceptually used for delays instead of filtering.
• Integrator: A pure accumulator (averaging time = infinity).
• Gain: Can be used to manually scale signal components.