Could anyone suggest the most computationally efficient method for finding amplitude at a given frequency having a noisy wide band signal.
To be more specific about a task. I have some physical dynamical system. I'm introducing sinusoidal input with exact frequency and amplitude. And looking for the amplitude at the same frequency on the output signal. While output signal is subject to noise and affected by other physical inputs at the same time.
This is required to detect some aspects of physical model. Experiments shows that this kind of test is sensitive to physical changes I want to detect.
Also I quite limited in resources. I only have small 32 bit MCU that is capable only of fixed-point arithmetic. Or very slow emulated floating point. That's why I'm asking about most effective solutions to the task.