> For the complete documentation index, see [llms.txt](https://yams.yassrobotics.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://yams.yassrobotics.com/api-reference/c++-reference/math/derivative-time-filter.md).

# DerivativeTimeFilter

**Namespace:** `yams::math` **Java equivalent:** [Java DerivativeTimeFilter](/api-reference/java-reference/math/derivative-time-filter.md)

`DerivativeTimeFilter` computes a numerical derivative of a signal and applies a debounce filter to suppress transient spikes.

***

## Constructors

```cpp
DerivativeTimeFilter(double initial, units::second_t debouncerPeriod)
explicit DerivativeTimeFilter(units::second_t debouncerPeriod)  // initial = 0.0
```

| Parameter         | Description                                                           |
| ----------------- | --------------------------------------------------------------------- |
| `initial`         | Initial value of the signal. Defaults to `0.0` if omitted.            |
| `debouncerPeriod` | Duration the debounce filter holds a spike before passing it through. |

***

## Methods

```cpp
double Derivative(double current, units::second_t dt)
double Derivative(double current)
```

| Overload                  | Description                                                                         |
| ------------------------- | ----------------------------------------------------------------------------------- |
| `Derivative(current, dt)` | Computes derivative using an explicit time step `dt`.                               |
| `Derivative(current)`     | Computes derivative using the FPGA timestamp; `dt` is measured since the last call. |

Returns the filtered derivative value.

***

## Example

```cpp
math::DerivativeTimeFilter filter{20_ms};

// In periodic (called every 20 ms):
double velocity = filter.Derivative(encoder.GetPosition());
```

{% hint style="info" %}
Use the explicit `dt` overload in simulation or when calling at non-uniform intervals. Use the FPGA overload in robot periodic methods where real wall-clock time is authoritative.
{% endhint %}