Sure. You can Fourier transform a vector, drop some number of the least contributing terms (frequencies) and store only the remaining coefficients. Which is ess

Sure. You can Fourier transform a vector, drop some number of the least contributing terms (frequencies) and store only the remaining coefficients. Which is essentially the basic idea behind MP3 and JPEG compression. You're trading space for time, of course, as now to get an approximation of the original vector you have to apply reverse Fourier transform first.