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From: hyeewang on 18 Jan 2010 02:26 1.If signal in time domain is infinite ,it must be finite in frequency domain, vice versa. 2.If signal in time domain is infinite, it must be infinite in frequency domain,vice versa. How to prove them? Which articles/textbooks implemented that? Do not just give a example to deduct them,I require a proof of theory. cheers
From: hyeewang on 18 Jan 2010 02:34 >1.If signal in time domain is infinite ,it must be finite in frequency >domain, vice versa. > >2.If signal in time domain is infinite, it must be infinite in frequency >domain,vice versa. > >How to prove them? Which articles/textbooks implemented that? >Do not just give a example to deduct them,I require a proof of theory. > >cheers > 1.If signal in time domain is infinite ,it must be finite in frequency domain, vice versa. 2.If signal in time domain is infinite, it must be finite in frequency domain,vice versa. How to prove them? Which articles/textbooks implemented that? Do not just give a example to deduct them,I require a proof of theory. cheers
From: hyeewang on 18 Jan 2010 02:36 1.If signal in time domain is infinite ,it must be finite in frequency domain, vice versa. 2.If signal in time domain is finite, it must be infinite in frequency domain,vice versa. How to prove them? Which articles/textbooks implemented that? Do not just give a example to deduct them,I require a proof of theory. thank you in advance. cheers
From: Andor on 18 Jan 2010 05:08 "hyeewang wrote: > 1.If signal in time domain is infinite ,it must be finite in frequency > domain, vice versa. As Greg already pointed out, this statement (assuming by "is (in) finite" you mean "has (in)finite extent") is not correct. > 2.If signal in time domain is finite, it must be infinite in frequency > domain,vice versa. > > How to prove them? Which articles/textbooks implemented that? There is a nice discussion for continuous-time signals by Slepian on this topic: http://www.sm.luth.se/csee/courses/sms/022/2001/artiklar/Sle76e.pdf For discrete-time signals you can apply an argument very similar to what Robert Adams described in his interpolation article [1]. Regards, Andor [1] R. W. Adams: Nonuniform Sampling of Audio Signals, J. Audio Eng. Soc., Vol. 40,No. 11, p. 886-894, November 1992.
From: Tim Wescott on 18 Jan 2010 10:26
On Mon, 18 Jan 2010 01:34:13 -0600, hyeewang wrote: >>1.If signal in time domain is infinite ,it must be finite in frequency >>domain, vice versa. >> >>2.If signal in time domain is infinite, it must be infinite in frequency >>domain,vice versa. >> >>How to prove them? Which articles/textbooks implemented that? Do not >>just give a example to deduct them,I require a proof of theory. >> >>cheers >> >> > 1.If signal in time domain is infinite ,it must be finite in frequency > domain, vice versa. > 2.If signal in time domain is infinite, it must be finite in frequency > domain,vice versa. > > How to prove them? Which articles/textbooks implemented that? Do not > just give a example to deduct them,I require a proof of theory. cheers Easy. Take the Fourier transform of x(t) = e^(-at), which is infinite in time. Note that it is (give or take a few sign changes) 1/(jw + a), which is infinite in frequency. Oops. -- www.wescottdesign.com |