When the signal being filtered changes, this is less useful, because a filter with fixed coefficients is optimised only for a specific signal. Fixed coefficients are also less useful when one is unsure as to what one is filtering (i.e. the desired frequency response of the filter is unknown)
In these situations it is common to use an Adaptive filter, which uses feedback to refine the values of the filter coefficients and hence its frequency response.
Generally speaking, this involves the use of a cost function, which is a criterion for optimum performance of the filter (I.e. minimise the noise component).
As the power of digital signal processors has increased, adaptive filters have become much more common, and are now routinely used in devices such as mobile phones and other communication devices, as well as medical monitoring equipment, etc.
Suppose a hospital is recording a heart beat (an ECG), which is being corrupted by 50Hz noise (i.e. the power supply in Australia). One way to remove this is to use a filter to remove the noise at 50Hz.
However, due to slight variations in the power supply to the hospital, the exact frequency of the power supply might (hypothetically) wander between 47Hz and 53Hz. Thus in order to remove this, all these frequencies must be removed - which will degrade the quality of the ECG being recorded (because there is a loss of information).
To circumvent this, an adaptive filter could be used. This would take input both from the patient and from the power supply directly, and is able to track the actual frequency of the noise as it fluctuates. This generally allows for a filter with a smaller 'rejection band' (the frequencies it removes), which means that the quality of the output signal is better.Example