This paper presents a set of sufficient conditions that ensure an arbitrary-order transfer function to exhibit a non-negative impulse response. Such conditions are given for both continuous-time and discrete-time systems. This set of sufficient conditions expose a simple geometric pole-zero pattern that can be easily employed for designing filters with a non-negative impulse response. Most of the existing work can be obtained as a special case of this work. This paper significantly extends the class of pole-zero patterns that are known to exhibit a non-negative impulse response, in both continuous-time and discretetime domains.
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