We propose a measurement feedback controller for a class of feedforward nonlinear systems under sensor noise. The sensor noise has unknown magnitude, frequency, and phase. Our proposed controller is coupled with a low-pass filter in such a way that the sensor noise is attenuated. We show that the controlled system results in bounded states whose ultimate bounds are inversely proportional to the minimum frequency of the sensor noise. Our result is further generalized to work in a case where the sensor noise is only required to have a Fourier transform with finite energy. Moreover, if the sensor noise enters only at partial states, depending on the location of the sensor noise, the ultimate bounds of the particular states can be made arbitrarily small via the gain factor of the controller.