Suppose an electronic low-pass filter (a circuit) is to be designed to reduce measurement noise from a sensor. The output of the sensor will be connected to the input of the filter, and the output of the filter will be used by the controller in a control system. In this problem we don't concern ourselves with the whole control system, but only with the filter.
Suppose it is desired that any noise in the sensor output with frequency higher than 100 Hz is reduced at least by a factor of 10 by the filter. It is also desired that any component in the sensor output with frequency lower than 10 Hz is untouched by the filter. Convert these specifications to frequency domain. That is, if F(s) is the filter's transfer function from its input to its output, what properties should F(j!) satisfy to meet the desired properties?