### Rate Estimation (Rooftop) Filter

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

The Rate Estimation (Rooftop) Filter block 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 > eMotor > 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.