This invention solves problems due to employing error degraded data in digital processing. It particularly solves the multi-generation problem wherein transform data degrade during each inverse transform and forward transform cycle even without any processing due to the rounding and clipping errors. It provides methods, systems and apparatus for transform-domain correction of real-domain errors in the processing of transform, transform-coded, and coded data. After inverse transformation of transform data the high-precision numbers are converted to integers and clipped to an allowed range forming converted data. High-precision differences are obtained by subtracting converted data from the high-precision output of the inverse transform. The differences are re-transformed back to the transform domain and saved. In an alternate embodiment the differences are quantized, thus, only significant errors are saved. In still another embodiment the quantized differences are entropy encoded. Then after re-transforming the processed converted data, the decoded differences, the dequantized differences, or the transformed differences can be used in the transform domain to remove the real-domain errors introduced by the original conversion to integers and clipping to the allowed range.