• The integral of the magnitude squared will always be positive for an odd signal.
    4 KB (739 words) - 20:48, 30 July 2008
  • We start with part B by noticing that the integral of the delta function is a step function. So the energy over an infinite interval is just the integral of the step function <math>u(t + 2) - u(t - 2)</math>
    1 KB (210 words) - 19:53, 2 July 2008
  • ...</math> so <math>g(x) \in AC[0,1]</math> by the absolute continuity of the integral.
    905 B (182 words) - 11:43, 10 July 2008
  • ...|</math>, so two applications of MCT allow us to pass the limit inside the integral, yielding the result. <math>\square</math>.
    4 KB (748 words) - 11:54, 10 July 2008
  • The last but two inequality is due to the integral form of Jensen's inequality.
    872 B (174 words) - 11:15, 10 July 2008
  • .../math>, which we are afforded by the absolute continuity of the indefinite integral of <math>|g|^q</math>. By Egorov, we may select closed <math>F \subset X,
    1 KB (219 words) - 17:00, 10 July 2008
  • ...sect. 4, Corollary 15 gives f is absolutely continuous iff its the indef. integral of its derivative.
    463 B (68 words) - 10:54, 16 July 2008
  • *<span style="color:green"> Be careful! The stuff inside the integral should always be positive. You are integrating "t", which is sometimes posi
    6 KB (975 words) - 15:35, 25 February 2015
  • Computing the integral:
    803 B (142 words) - 07:55, 22 June 2009
  • ...c{\cos x}{\sqrt{\sin x}} \text{ is finite a.e. on a bounded domain, so the integral exists}</math>
    1 KB (201 words) - 18:10, 5 July 2009
  • Now, we need to pull the limit inside the integral, so we proceed as follows: ...w, by the Dominating Convergence Theorem, we can pull the limit inside the integral.
    2 KB (437 words) - 11:01, 6 July 2009
  • ...0}</math> is constant over <math>\tau</math> it can be factored out of the integral
    1 KB (240 words) - 16:58, 8 July 2009
  • Because the linearity of the integral.
    378 B (68 words) - 21:45, 8 July 2009
  • Letting <math>\tau</math>=t-<math>t_{0}</math> in the integral, and noticing that the new variable <math>\tau</math> will also range over<
    1 KB (200 words) - 03:44, 9 July 2009
  • Letting <math>\tau</math> = t - <math>t_0</math> in the new integral and noting that the new variable <math>\tau</math> will
    1 KB (266 words) - 03:10, 23 July 2009
  • Now, since f and g are both <math>L^{1}</math>, this integral exists, so by Fubini's Theorem, we may rewrite it as: ...again (since all of these are equalities, we don't need to check that the integral exists, since it's automatic), to get:
    1 KB (264 words) - 05:57, 11 June 2013
  • I forgot to justify why the integral exists in the first place. Well, since <math>f\in C_c^{\infty}(R^n)</math>
    2 KB (374 words) - 05:56, 11 June 2013
  • The integral is taken over the interval of T. The sum is taken from -infinity to infini
    137 B (25 words) - 16:54, 27 July 2009
  • The integral is taken over the interval T. The sum is taken from <math>-\inf to \inf</m
    138 B (27 words) - 16:58, 27 July 2009
  • We can pass this limit through the integral since <math>\hat{f}</math> is dominated by <math>f\in L^1</math>
    2 KB (315 words) - 05:55, 11 June 2013

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Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett