Filter arrangement with a linear phase characteristic, and method to develop such a filter arrangement
View Patent ↗A filter arrangement with a linear phase characteristic having first filter cascade coupled to second filter. The first filter is an analog or digital filter designed so that its amplitude characteristic meets a predefined amplitude specification. The second filter is implemented as the anti-causal version of a fictive digital all-pass filter that is designed so that its phase characteristic, up to a linear function of frequency, equals the phase characteristic of the first filter.
1. A filter arrangement with a linear phase characteristic comprising:
a first filter having an amplitude characteristic that meets a predefined amplitude specification and having a phase characteristic that is a non-linear function of frequency; and
a second filter, cascade coupled to said first filter, said second filter having a phase characteristic that is substantially equal to the sum of a linear function of frequency and the opposite phase characteristic of said first filter,
wherein said second filter is an anti-causal version of a fictive digital all-pass filter having a phase characteristic that is substantially equal to the sum of a linear function of frequency and said phase characteristic of said first filter.
2. The filter arrangement according to claim 1 , wherein said first filter is an analog filter.
3. The filter arrangement according to claim 1 , wherein said first filter is a digital filter.
4. A method to develop a filter arrangement with a linear phase characteristic, wherein the method comprises:
designing a first filter so that its amplitude characteristic meets a predefined amplitude specification;
implementing said first filter;
determining a phase characteristic of said first filter, said phase characteristic being a non-linear function of frequency;
implementing a second filter so that its phase characteristic is substantially equal to the sum of a linear function of frequency and the opposite phase characteristic of said first filter; and
cascade coupling said first filter and said second filter, wherein
implementing said second filter comprises:
designing a fictive digital all-pass filter so that its phase characteristic is substantially equal to the sum of a linear function of frequency and equal said phase characteristic of said first filter; and
implementing said second filter as an anti-causal version of said fictive digital all-pass filter.