Optical Wavelet Signals Processing and Multiplexing

Abstract

We present compact integrable architectures to perform the discrete wavelet transform (DWT) and the wavelet packet (WP) decomposition of an optical digital signal, and we show that the combined use of planar lightwave circuits (PLC) technology and multiresolution analysis (MRA) can add flexibility to current multiple access optical networks. We furnish the design guidelines to synthesize wavelet filters as two-port lattice-form planar devices, and we give some examples of optical signal denoising and compression/decompression techniques in the wavelet domain. Finally, we present a fully optical wavelet packet division multiplexing (WPDM) scheme where data signals are waveform-coded onto wavelet atom functions for transmission, and numerically evaluate its performances

All-Optical Signal Processing for High Spectral Efficiency (SE) Optical Communication

“…In this section we briefly discuss the main features of WPT and its applications to CO-OFDM. The theory and applications of continuous wavelet transform (CWT) and discrete WT (DWT) can be found in a large number of books and articles (see, for example, [13], [14], [19]- [22] and references therein).…”

“…It is possible to localize the events described by f(t) in time and frequency domains simultaneously by means of WT choosing the appropriate values of the parameters a and  [19]. For this reason, wavelets are used in the multiresolution analysis (MRA) which decomposes a signal at different scales, or resolutions, using a basis whose elements are localized both in time and in frequency domains [14].…”

“…The orthogonal wavelet series expansions can be successfully used in DSP and multiplexing when the scaling and translation parameters are discrete [14]. In such a case, a signal s(t) ∈V can be represented by a smooth approximation at resolution (18) and Δτ is the inverse of their FSR.…”

“…The sinusoidal functions are infinitely long in the time domain while wavelets have finite length being localized in time and in frequency domains [13]. Wavelet signal analysis can be a base for an effective computational algorithm which is faster and simpler than FFT [14]. Wavelets have been used in optical communications for time-frequency multiplexing and ultrafast image transmission [14].…”

“…Wavelet signal analysis can be a base for an effective computational algorithm which is faster and simpler than FFT [14]. Wavelets have been used in optical communications for time-frequency multiplexing and ultrafast image transmission [14]. A signal may be expanded in an orthogonal set of wavelet packets (WPs) as the basis functions, each channel occupies a wavelet packet (WP), and IDWPT/ DWPT are used at the transmitter and receiver, respectively [13].…”