# SVD vs Fourier analysis for data.

Fourier analysis is useful for analysis in the frequency domain. SVD on the other hand is useful for analysis of data, and expressing noise in the data. I have a problem that needs extensive data analysis, it is in the area medicine. This could be generalized to other problems.

The problem is that of gene expression, in case of long term gene mutation. Using Fourier analysis we can get a time series analysis of the genes(and thereby get noisy gene expression), and as time progresses, the changes in a particular organ. On the other hand, we could use Singular Value Decomposition, and the noisy gene expresses itself. This, is just an outline of the problem. Both SVD, and Fourier lend themselves to solve the problem that of expressing noisy genes. Is there any comparison of the two techniques, why one would be preferred over another qualitatively, or references that one can use for the problem of gene expression, thanks in anticipation.

• Fourier analysis approximates a continuous function using trigonometric polynomials; SVD approximates a matrix using eigenvectors of its left (or right) singular matrix. These are a priori completely different problems, and your question doesn't make much sense unless you can indicate why you think these two problems are related. – Paul Siegel Sep 23 '15 at 2:35
• You might get more feedback on sites like scicomp.stackexchange.com, stats.stackexchange.com, or dsp.stackexchange.com. But if you ask your question in its current form, they might also close it, because it is not really clear what you want to do exactly. For my answer, I just guessed that stochastic processes might be your context, because both Fourier analysis and "optimal" decompositions make sense in that context. – Thomas Klimpel Sep 23 '15 at 20:00
• @PaulSiegel I guess the OP has in mind that the discrete Fourier transform transforms discrete "spatial" data to discrete "frequency" data. I would say that the SVD decomposes every matrix $A$ as $U^TDV$ with a diagonal $D$ and orthonormal $U$ and $V$ while the diagonal Fourier transform $F$ is also orthonormal and gives $C = F^HDF$ with diagonal $D$ for circulant matrices $C$. – Dirk Sep 24 '15 at 7:12