Appendix C. Time Reversal and the DFT

The notion of time reversal in discrete systems occasionally arises in the study of the discrete Fourier transform (DFT), the mathematical analysis of digital filters, and even in practice (straight time reversal is used in a digital filtering scheme described in Section 13.12). We give the topic of time reversal some deserved attention here because it illustrates one of the truly profound differences between the worlds of continuous and discrete systems. In addition, the spectral effects of reversing a time sequence are (in my opinion) not obvious and warrant investigation.

Actually, in discrete-time systems there are two forms of time reversal we need to think about. Consider the 6-point x(n) time-domain sequence