A Fourier transform is just a change of coordinates. It has nothing to do with the signal per se. If you have a signal which was measured or recorded with finite precision (as any signal must be) then the fourier transform (as a pure mathematical object) simply preserves the same amount of loss that the original signal had. But, in fact, to do that, we would need to do the transform on hardware that could represent real numbers. This hardware does not exist in computers or in your brain, and so a fourier transform is lossy in that case. Still, the idea that your brain encodes all information in oscillations is not accurate - your temporary electrical activity can be substantially disrupted without you losing your memories, suggesting very strongly (to put it mildly) that some of your memories are encoded chemically and physically in changes to the connectivity between neurons that do not depend on persistent electrical activity. That encoding scheme must be lossy.

Fourier transforms are simply ways of interpreting. The senses restrict, the existing memory/engram/affinity of those senses: we don't yet know how much is lost, whether any of it is lost. In the schema, we must assume their inputs are preserved in some way, (study those with photographic memory, or the eidetic as example) and it is assumed preservation is chemical in nature that represents or co-represents the oscillations, yet we're not sure what exactly this is as of 2024 (I haven't finished reading this year's). Of course there are disruptions, and sleep - you do not remember the sounds around us when asleep. But if you recorded an event, it is still there. By lossless, I am referring to the idea there is no true separation between the world and the brain. While the senses mitigate, the fields interact. Would the toroidal manifold of the entorhinal cortex exist without a Copernican-Mach universe? Of course not. In essence, as Northoff illustrates on his last book's cover, the universe is within us. He is neither being poetic nor ironic. Rather paradoxical. Brain's are oscillatory Copernican bulbs, the design elements of the brain reflect the Machian idea that everything affects.

Without direct perception, and using such poor tools as symbols and narratives to externalize memory, we're deeply impoverished as to the nature of memory and our ability to access it. But once we have a better grasp of the neuronal units, spatial-syntax, we will unlock every memory.

https://pmc.ncbi.nlm.nih.gov/articles/PMC10500127/

Also to consider are the shapes and phases between oscillation. "It’s high dimensional complexity; the mind is an attractor in high dimensional phase space formed between neural oscillators." Emergent properties are not reducible to their constituent parts.