let-x-1-a-2-x-2-if-x-lt-a-and-x-0-if-x-a-find-the-fourier-transform-of- Tinku Tara June 4, 2023 Integration 0 Comments FacebookTweetPin Question Number 35632 by abdo mathsup 649 cc last updated on 21/May/18 letφ(x)=1a2−x2if∣x∣<aandφ(x)=0if∣x∣⩾afindthefouriertransformofφ. Commented by abdo mathsup 649 cc last updated on 21/May/18 F(f(x))=12π∫−∞+∞f(t)e−ixtdt. Commented by abdo mathsup 649 cc last updated on 24/May/18 wehaveF(φ(x))=12π∫−∞+∞φ(t)e−ixtdtandφisevenF(φ(x))o=12π∫−∞+∞φ(t)e−ixtdt=12π∫−aae−ixta2−t2dt=2π∫0acos(xt)a2−t2dtletfindw(x)=∫0acos(xt)a2−t2dtwehsvew′(x)=∫0a−tsin(xt)a2−t2andbypartsw′(x)=[a2−t2sin(xt)]0a−∫0aa2−t2xcos(xt)dt=−x∫0aa2−t2cos(xt)dtchsngementt=asinαgivew′(x)=∫0π2acos(α)cos(axsinα)acosαdα=a2∫0π2cos2(α)cos(axsinα)dα=a2∫0π2cos(α)(cos(α)cos(axsinα))dα=a2{1axsin(axsin(α))cos(α)]0π2−∫0π2−sin(α)sin(axsinα)dα}=∫0π2sin(α)sin(axsinα)dα….becontinued… Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Question-166701Next Next post: Question-35635 Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.