Designing fir filters with globally minimax-optimal magnitude response

A system for filtering a signal received by an electromagnetic receiver, the system comprising:

• a filter configuration unit for configuring a first filter of order N to be applied to the signal by determining coefficients h[n] of the first filter, where a target response of the first filter is specified by a target response function D(ω) and a variable Kdes indicative of a target ratio of an error in a set of passband frequencies ΩP and an error in a set of stopband frequencies ΩS of the first filter;
• and
• a digital filter for generating a filtered signal by applying the first filter to the signal,
• wherein the filter configuration unit is configured to determine the coefficients of the first filter by:
• iterating steps of i) setting a variable K indicative of a ratio of an error in the set of passband frequencies ΩP and an error in the set of stopband frequencies ΩS of a second filter of order 2N to a new value, and ii) determining coefficients g[n] of the second filter with a target response specified by the target response function D(ω) and the variable K, until a maximum passband error ΔP of a frequency response G(ejω) of the second filter satisfies a condition with respect to a comparison value based on the variables K and Kdes, and
• determining the coefficients h[n] of the first filter based on the coefficients g[n] of the second filter.