Hilbert Transform, Analytic Signal, and SSB Modulation

This chapter reviews generation of analytic signals and single-side band (SSB) modulation signals using the Hilbert transform. The Hilbert transform is a linear operator. The system that performs the Hilbert transform (called a Hilbert transformer) is a linear system with a frequency transfer function. The analytic signal is a conceptual complex signal, but it is widely used in signal analysis. The chapter examines the spectral characteristics of the analytic signal. The impulse response of the Hilbert transformer can be calculated by taking the inverse Fourier transform of frequency transfer function. The sampled vector of the Hilbert transform is generated from the sampled vector of an audio signal. The chapter describes the implementation of an SSB modulation and demodulation system using a band pass filter (BPF). It is designed to help teach and understand communication systems using a classroom-tested, active learning approach.