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A chroma interpolation filter combines retained colour-difference samples to estimate values at the output locations required by chroma upsampling. It acts on the components of YCbCr separately from full-resolution luma. The filter coefficients and the assumed chroma sample location jointly determine the reconstruction. Microsoft's primary conversion guide gives a four-sample interpolation example and states its progressive-scan and edge-handling assumptions.^[ref]

For an original one-dimensional linear interpolation rule, let retained samples $c_k$ lie at positions $x=2k$. Define output samples byThe two coefficient sets, one for each output parity, both sum to one. A constant input is therefore reproduced at every output position. With $c_0=40$, $c_1=120$ and $c_2=80$, the outputs through $x=4$ are $40,80,120,100,80$. The values at odd-integer positions are estimates, while the retained even-integer positions are unchanged.

Higher-order interpolation need not remain between neighbouring input values. As an original exact-arithmetic illustration, take a half-position rule with coefficients $(-1,9,9,-1)/16$ applied to four consecutive samples. Their sum is one, so constants are preserved. But the sample sequence $0,200,200,0$ yields $225$ between the two central samples; $200,0,0,200$ yields $-25$. Negative coefficients permit overshoot. Quantization and clipping then change the result further. The primary Microsoft example uses these interpolation coefficients with integer rounding and clipping.^[ref]

The same numerical coefficients can produce spatially misplaced colour if their assumed input grid is wrong. Centered chroma and co-sited chroma require their actual coordinates to be respected. At image boundaries, missing neighbours require an explicit extension rule. No choice of chroma interpolation filter can uniquely recover arbitrary colour variation discarded by chroma subsampling.

Chroma upsampling increases the spatial sample count of the colour-difference components after chroma subsampling. For example, converting 4:2:0 chroma subsampling to 4:2:2 chroma subsampling doubles the vertical colour sample count, while conversion to 4:4:4 chroma sampling also doubles it horizontally.^[ref] The added values are estimates, not newly measured image detail.

An original one-dimensional derivation separates increasing the grid density from interpolation. Start with samples $c_k$ and insert zero-valued placeholders:Apply the chroma interpolation filterIt follows that $y_{2k}=c_k$ and $y_{2k+1}=(c_k+c_{k+1})/2$. Thus this stipulated filter preserves the original positions and fills the intervening positions by linear interpolation.

The scaling is essential. For a constant input $c_k=128$, the correctly scaled result is128 at every output position. Using the ordinary three-tap averaging coefficients $(1/4,1/2,1/4)$ on the zero-inserted sequence would instead give64 everywhere. Those coefficients are suitable for a different operation; their unit sum alone does not preserve a constant after zero insertion.

The derivation assumes the retained samples occupy the even positions of the output grid and ignores image boundaries. Centered chroma can require a different alignment, and finite images require an edge rule. The Microsoft example specifies progressive scanning, interpolation and edge handling explicitly.^[ref] Upsampling quality therefore depends on chroma sample location, filter choice and boundary treatment, rather than only on output dimensions.