#### Rate Estimation (Rooftop) Filter

**Category:****
**eMotors >** **Other Tools
>** **Filters

The Rate Estimation (Rooftop) Filter block <tbs. will the parentheses be removed>
provides a band limited derivative of a signal by band-pass
filtering. This method of obtaining the derivative is optimal in a sense that it
maximizes derivative bandwidth as a compromise to upper band noise attenuation.
The rooftop filter is a 2-pole band pass filter in which the poles at p rad/sec
are equal. If the filter is scaled by p^{2}, the low frequency band of
the filter well below the filter poles corresponds to the response of a pure
derivative with gain equal to ω and a phase shift of plus 90^{o}. As the
frequency nears p rad/sec, phase shift becomes less than 90^{ o} and the
derivative response is diminished. Frequency content above p rad/sec is
attenuated at –20 dB/decade. A general rule is to select the filter pole 30
times larger than the highest frequency at which derivative response is to be
applied. Pole selection provides a trade-off between derivative bandwidth and
higher frequency noise attenuation.

**Clock Frequency:** Defines the processor rate for rate
estimation in hertz.

**Filter Pole:** Defines the center frequency of the
rooftop filter in hertz. Select a frequency 30 times larger than the highest
frequency for estimation of derivative.

#### Example

**Diagram name: **Rate Estimation Roof Top Filter

**Location: **Examples > eMotors > Filters

The following example demonstrates how to use a rooftop
filter to limit the rate on a signal. The rooftop filter is first used to
determine the derivative (rad/sec) of the angular displacement input signal
(rad). The rate is limited, and then converted back to radians by integration.
The resulting signal shows limiting when the input signal exceeds the rate
limit.