Word Length Condition for DC Lossless DWT
Masahiro Iwahashi, Hitoshi Kiya · Institutional Repositories DataBase (IRDB) · 2009
Abstract — This report theoretically analyzes the condition on word length of coefficients and signals such that the discrete wavelet transform (DWT) becomes DC lossless. The DWT discussed here is irreversible for an arbitrary input signal. However, it becomes lossless for a constant valued (DC) input signal under the condition. In conventional approaches, error due to shortening of word length of signals (signal error) and that of coefficients (coefficient error) are treated as additive and multiplicative, respectively. In this report, we introduce a new model which shifts the coefficient error to the signal error in order to treat them as additive. Furthermore, utilizing the fact that the accumulated error inside the circuit is nullified by the rounding at its output, we derive the condition for the DC lossless DWT. Theoretical bound of the word length is derived and the minimum word length is found to be 14 [bit] for 8 [bit] input signals. I.