Can we see the Fourier transform as a filtering operation? Is the Fourier Transform (FT) a filtering operation?
Is it possible to graphically represent this transform?
I know that a signal can be represented in the frequency domain, but I want to know if the FT operation can be "drawn" as a coefficient series.

The FT matrix is composed by $N\times N$ elements, and I can apply it to the input sequence of length $N$ in order to obtain an output sequence of length $N$. But I want to understand if there is another way to see the FT matrix in one dimension.
Hint:

The DFT matrix only contains powers of a complex root of unit. Every row or column holds increasing powers of a common power ($\omega^{mn}=(\omega^m)^n$); hence the real and imaginary parts follow (co)sinusoids of increasing frequencies.

https://www.dsprelated.com/freebooks/mdft/DFT_Sinusoids.html

Every component of the DFT of a signal is a convolution of the signal with those sinusoids.