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Fundamentals of Digital Signal Processing

The Cyclic Prefix

Explore the role of the cyclic prefix in OFDM modulation to transform linear convolution from wireless channels into circular convolution. Understand how adding a cyclic prefix allows the received signal's discrete Fourier transform to equalize channel effects effectively, supporting efficient digital communication.

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Let’s discuss the DFT, before we attempt to equalize the impact of the wireless channel in this lesson.

Linear vs. circular convolution

In a continuous-time Fourier transform, the output of a system y(t)y(t) for a given input x(t)x(t) and impulse response h(t)h(t) is given by:

y(t)=x(t)∗h(t)y(t) = x(t) \ast h(t) ...