Phase or Frequency Shifter Using a Hilbert Transformer
In this article, we'll describe how to use a Hilbert transformer to make a phase shifter or frequency shifter. In either case, the input is a real signal and the output is a real signal. We'll use some simple Matlab code to simulate these systems. After that, we'll go into a little more detail on Hilbert transformer theory and design.
Summary
This blog explains how to build a real-to-real phase shifter or frequency shifter using a Hilbert transformer, with practical Matlab simulations and code. It also reviews Hilbert-transform theory and FIR design considerations so readers can implement and evaluate these shifters for audio, communications, or radar signals.
Key Takeaways
- Implement a real-to-real phase shifter by generating the analytic signal with a Hilbert transformer and recombining quadrature components.
- Simulate frequency shifting by applying a complex exponential to the analytic signal and recover a real output using Matlab code examples.
- Design FIR Hilbert transformers using spectral design techniques and windowing, and evaluate trade-offs in passband/transition performance.
- Analyze phase and amplitude errors with FFT-based spectral tools and learn practical corrections to minimize distortion and aliasing.
- Apply the method to audio and communications use cases and recognize bandwidth and implementation limitations for real-time systems.
Who Should Read This
Intermediate DSP engineers, researchers, or students working on audio, speech, radar or communications who want to implement phase/frequency shifters and learn Hilbert-transform design and MATLAB simulation.
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