Finite Impulse Response Filters for Stagger-Period Signals, their Designs and Applications

Those theories of conventional filters for uniform-period signals do not apply to the analysis and design of the finite impulse response (FIR) filters for stagger-period signals. In this paper, we defined the fundamental concepts related to the stagger-period signals, derived the calculating equations, and described the time-variant property of the stagger-period filter; we proposed the Fourier transform pair between the frequency and impulse responses of this type filter, and proved the inverse of each other. Then, we discussed the design methods of stagger-period frequency-selective FIR filters, including lowpass, bandpass, and high-pass, presented the staggered windowing philosophies, illustrated different windows’ effectiveness, and described the principles and designs of optimized stagger-period high-pass filters with the match algorithm. As applications, we introduced three staggered optimization algorithms: eigenvalue, match, and linear prediction; and discussed performances of the filters designed for a moving target indication (MTI) radar. The stagger-period MTI filters not only extended the blind speed of flying targets, but also had an optimized improvement factor. Finally, we proposed a mathematical programming to search the best period code, which makes this type filter’s velocity response flattened. Meanwhile, we compared properties of the stagger-period to uniform-period filters, and provided with some examples to illustrate the theories and designs.