Non-phase shifting bidimensional filter
A band-pass filter with at least one passband, which is real, bidimensional, oriented along the phase axis and resulting from the product of two identical one-dimensional Hamming windows, the transfer function of each of these windows being: X i ( f ) = α i + ( 1 - α i ) cos π ( f - f q i ) f0 i , w h e r e f is a current frequency; αi is a real number, included between and excluding 0 and 1; fqi is a central frequency of the passband; and f 0 i defines half of the passband centered on fqi.
1. A band-pass filter in the frequency domain with at least one pass band, which is real, bidimensional, oriented along a phase axis and resulting from the product of two identical one-dimensional Hamming windows, a transfer function of each of these windows being:
X
i
(
f
)
=
α
i
+
(
1
-
α
i
)
cos
π
(
f
-
f
q
i
)
f0
i
,
where:
f is a current frequency;
α i is a real number, included between and excluding 0 and 1;
fq i is a central frequency of the passband; and
f0 i defines half of the passband centered on fq i .
2. The filter of claim 1 , wherein the windows are Hanning windows, for which a real number α i is 0.54.
3. The filter of claim 1 , wherein the filter has a passband having a width of one octave.
4. The filter of claim 3 , wherein the windows are Hanning windows and wherein the passband of each of the Hanning windows is defined by:
f0
i
=
π
3
arcos
(
1
2
-
α
i
1
-
α
i
)
f
q
i
,
where arcos designates the inverse cosine function.
5. A band-pass filter with several passbands, wherein each passband is defined by claim 1 .
6. The filter of claim 1 , wherein such a filter is applied to a detection of a texture of a ring-shaped element, the texture being a set of information varying according to an angular position in concentric circles.
7. The filter of claim 1 , wherein the filter is used to process a digital image.