For some applications, the use of adaptive coefficients is required due to the fact that the parameters that need to be manipulated are not known in advance, such as the characteristics of some noisy signals. In such cases, adaptive filters are often used, which use feedback to adjust the filter coefficients as well as the frequency response.
Overall, the process of adaptation involves applying a value function to an algorithm that determines how to change the filter coefficients to reduce the cost of the next iteration of the process. The value function is a criterion for determining the optimal performance of the filter, such as the ability to reduce the noise component of the input signal.
Adaptive filters have become increasingly common as the performance of digital signal processors has increased, and today they are used in cellular phones and other communications devices, digital video recorders and digital cameras, and medical monitoring equipment.