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E.g. the constant Q-transform is built by adding so called "Fourier filters".

What's a "Fourier filter"?

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People (usually from fields outside signal processing) sometimes use the term Fourier filter for a filtering operation in the FFT domain, which simply works by multiplying the FFT bins of a signal with a given filter function (often just ones and zeros, corresponding to pass bands and stop bands, respectively). Why this is generally not such a good idea is explained here.

Also in Computer Vision, the term Fourier filter is used as explained above.

In the document you linked to in a comment, the term is used to describe the computation of the Discrete-Time Fourier Transform (DTFT) at a given frequency from a finite length portion of a signal. This computation can be interpreted as a filtering operation, because it is a sum of products. The corresponding filter is a band pass filter with center frequency equal to the given DTFT frequency. More more information on the filter interpretation of the D(T)FT have a look at this page.

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  • $\begingroup$ See my comment on the question. $\endgroup$ – mavavilj Dec 7 '15 at 12:04
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Each bin of a DFT or FFT result can be considered to be the result of a filter operation. Each filter's frequency response is either Sinc shaped, or if a non-rectangular window is applied before the FFT, the response will be shaped like the transform of that window, with a passband width roughly proportional to from Fs/N to twice that.

Computing a single unwindowed DFT bin is nearly identical to a Goertzel filter. So that's yet another potential synonym for the same thing.

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