An integer transform is an approximation of the mathematical DCT that uses only integer arithmetic — no floating-point numbers, no fractional rounding errors. Every modern codec from H.264 onwards uses integer transforms instead of the exact DCT for one critical reason: identical reconstruction across all implementations. If an encoder in California uses floating-point and a decoder in Tokyo uses slightly different floating-point hardware, the reconstructed frames will not be bit-for-bit identical, and that tiny difference would compound over GOPs into visible drift.
The clever part is keeping the compression benefit of the DCT while restricting to integer math. Codec designers pick integer matrices whose properties closely match the ideal DCT — energy concentrates in low-frequency coefficients, the transform is nearly orthogonal, errors are bounded. H.264 uses 4×4 and 8×8 integer transforms; HEVC adds 16×16 and 32×32; AV1 has a whole menu including DCT, ADST, flipped variants and identity transforms, all in integer form.
For a product team, integer transforms are pure invisible plumbing — you never configure them — but they explain why modern video plays back deterministically across every device on Earth. The same file looks identical on a phone in Berlin, a smart TV in Tokyo and a cloud transcoder in Virginia, because all of them run the same integer math. This determinism is also what lets hardware decoders be built cheaply: integer math is far easier to design in silicon than floating-point, and there's no need to worry about subtle implementation differences between vendors.
