Defective recording element detecting apparatus, defective recording element detecting method, and image forming apparatus

A defective recording element detecting apparatus comprising:

• an image signal acquiring device which acquires read image signals obtained by reading, at a read pitch WS in a first direction, a linear test pattern recorded by an image recording apparatus having:
• a recording head in which a plurality of recording elements are aligned so that, when the plurality of recording elements are projected on a straight line that is parallel to the first direction, an interval of projected recording elements is equal to a recording pitch WP;
• and a medium conveying device which causes relative movement between a recording medium and the recording head in a direction perpendicular to the first direction, the test pattern being recorded by operating recording elements corresponding to projected recording elements per every detection pitch unit PP among the projected recording elements;
• a signal decomposing device which sequentially assigns reading pixel numbers 0 to n (where n is a natural number) to the acquired read image signals starting from an end in the first direction, divides the reading pixel numbers by an analysis pitch unit PS to obtain remainders, and decomposes the read image signals into an image signal of each of the obtained remainders;
• a fluctuation signal calculating device which calculates a fluctuation signal of each of the remainders based on a predicted signal that is predicted for each of the remainders and on the image signal of each of the remainders;
• and
• an identifying device which identifies a defective recording element among the plurality of recording elements based on the fluctuation signal of each of the remainders,
• wherein a value of the analysis pitch unit PS is set in such a manner that a period T obtained by
• T=WP×PP/|WS×PS−WP×PP|
• is equal to or exceeds an analysis minimum period set in advance.