the output of a PCA process is a system of linear combinations of the data. so yes, you'd take the principal components of your future inputs, but the process would be super fast (it's a linear transformation with known parameters) since you don't need to rerun anything.

you can also do online PCA (updating the model as you get new data) but i'm not sure about runtime/computation requirements.

I think the paper disagrees w/ you: "Computing principal components can be an expensive task..."

The result of PCA is a linear projection matrix. Applying that projection is fast.

You learn the projection from an initial dataset. That is "slow". You apply the projection to new data. That is "fast".

thanks for explaining

I think you misunderstood the OP. Once you have the PCs (and loadings) for a dataset converting new data into the same axis system is just a linear conversion.