Any kind of discrete Fourier transform, and also any device that generates the Fourier series of a periodic signal, even when done in an ideal way, must have outputs that are generated by a set of filters that have "a varying response to a range of frequencies".
Only a full Fourier transform, which has an infinity of outputs, could have (an infinite number of) filters with an infinitely narrow bandwidth, but which would also need an infinite time until producing their output.
So what you have said does not show that the eye cone cells do not perform a Fourier transform (more correctly a partial expansion in Fourier series of the light, which is periodic in time at the time scales comparable to its period).
The right explanation is that the sensitivity curves of the eye cone cells are a rather poor approximation of the optimal sensitivity curves of a set of filters for analyzing the spectral distribution of the incoming light (other animals except mammals have better sensitivity curves, but mammals have lost some of them and the ancestors of humans have re-developed 2 filters for red and green from a single inherited filter and there has not been enough time to do a job as good as in our distant ancestors).
Only a full Fourier transform, which has an infinity of outputs, could have (an infinite number of) filters with an infinitely narrow bandwidth, but which would also need an infinite time until producing their output.
So what you have said does not show that the eye cone cells do not perform a Fourier transform (more correctly a partial expansion in Fourier series of the light, which is periodic in time at the time scales comparable to its period).
The right explanation is that the sensitivity curves of the eye cone cells are a rather poor approximation of the optimal sensitivity curves of a set of filters for analyzing the spectral distribution of the incoming light (other animals except mammals have better sensitivity curves, but mammals have lost some of them and the ancestors of humans have re-developed 2 filters for red and green from a single inherited filter and there has not been enough time to do a job as good as in our distant ancestors).