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A lossless condition of lifting DWT for specific DC values

This report theoretically derives a condition on the word length of coefficients and signals such that the irreversible 9–7 discrete wavelet transform (DWT) in JPEG 2000 becomes lossless for a constant valued (DC) input signal. Under the condition, the output signal contains no error in spite of rounding of coefficients and signals inside the DWT circuit. We have previously analyzed the condition for any value of DC signals. However, it was too strict and the word length under the condition was redundant for a practical case. In this report, we derive a new condition for a specific DC value and show that the minimum word length is halved under the new condition.