Summary

Rick Lyons presents a compact processing scheme that implements a digital differentiator, a Hilbert transformer, and a half-band filter simultaneously. The paper explains the algorithmic structure, multirate/polyphase realizations, and practical implementation trade-offs for efficient real-time DSP.

Key Takeaways

• Implement a combined FIR structure that performs differentiation, Hilbert transformation, and half-band filtering using shared polyphase components.
• Exploit multirate techniques (decimation/interpolation and half-band symmetry) to cut computation and memory costs.
• Design FIR differentiators and Hilbert transformers to meet amplitude, phase, and group-delay specifications using windowed or equiripple methods.
• Analyze frequency response and group delay with FFT-based spectral tools to verify analytic-signal formation and differentiator accuracy.
• Optimize fixed-point and resource usage for real-time DSP targets to balance precision, latency, and computational load.

Who Should Read This

Advanced DSP engineers or graduate students focused on filter design and multirate/real-time implementations who need efficient methods for analytic-signal generation and differentiators.

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