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In this paper, we present a fundamental result of polynomial signal processing. We show that a system annihilates any polynomial input signals up to a given degree if and only if the derivatives of the frequency response of the system vanish. A direct consequence of the result is that the maximally flat filters are ideal for polynomial signals. Our result interprets maximally flat filters in the time...
In this paper, the closed-form design of finite impulse response (FIR) digital differentiators (DD) with fractional delay (FD) using interlaced sampling (IS) method is proposed. Typically, design of FIR DDs with real impulse responses suffers from the difficulty of approximation within the high frequency band. The issue arises from the fact that the desired frequency response is complex and the designed...
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