(a) A motion for new trial is not necessary to authorize an appeal.
(b) If a motion for new trial is made, it must be filed not later than the 10th day after the date of the rendition of the judgment of conviction.
(c) One or more amended motions for new trial may be filed without leave of court before any preceding motion for new trial filed by the movant is overruled if the motion is filed not later than 15 days after the date of the rendition of the judgment of conviction.
(d) If an original or amended motion for new trial is not determined by written order signed not later than 30 days after the date of the rendition of the judgment of conviction, the motion is overruled by operation of law.