Summary

This paper reviews the mathematical definition of the Hilbert transform and discusses several numerical methods to compute it. It then surveys applications in signal processing and system identification, and closes with historical remarks on its development.

Key Takeaways

• Explain the mathematical definition and fundamental properties of the Hilbert transform.
• Compute the Hilbert transform using time-domain FIR Hilbert filters and frequency-domain (FFT) methods.
• Apply the Hilbert transform to form analytic signals, extract envelopes and instantaneous frequency for audio and communications tasks.
• Use Hilbert-based quadrature techniques in system identification to estimate phase, impulse responses, and complex-valued system models.
• Evaluate practical trade-offs and historical context when selecting numerical implementations.

Who Should Read This

Intermediate DSP engineers, researchers, or graduate students who design or analyze algorithms in audio, communications, radar, or system identification and want practical theory and computation methods for the Hilbert transform.

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