Publisher Summary This chapter discusses wavelet bases for IR library compression, searching, and reconstruction. Most of the commercial databases to date use Fast Fourier Transform (FFT) for spectra compression. The IR spectra show many absorption bands of local character, which makes wavelets well suited for their decomposition. Also, Wavelet Transform is quite faster than FFT. During successful library construction three important factors must be considered— namely, efficient compression algorithm and ratio, fast search speed method, and good spectra reconstruction quality. Fulfillment of all these demands requires some kind of compromise and there are different possible approaches to this problem. Wavelets, well localized in both time and frequency (scale) domains are basis functions ideally suited for description of the unstationary instrumental signals, such as IR or NMR spectra. In addition, signals, such as IR spectra, have in a wavelet domain sparse representation. It means that in wavelet domain there are many wavelet coefficients with small amplitude (absolute value), which can be discarded without loss of essential information carried by a signal. Elimination of small coefficients is equivalent to spectra compression.