180 deg phase shift

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6 total messages Started by Edwin Heredia Thu, 09 May 1991 16:01

#1767

Author: Edwin Heredia
Date: Thu, 09 May 1991 16:01

20 lines
1216 bytes

For those who can't believe that inverting the signal produces 
a 180 deg. phase shift and for those who think that this trick 
works only with "easy-to-work" signals as pure tones:

Given *ANY* signal  x(n)  with Fourier Transform  X(w)

Consider the transformation          y(n) = (-1) * x(n)

in the Fourier domain this gives     Y(w) = (-1) * X(w)

which is                         Y(w) = exp(j180) * X(w)

result: 180 deg. phase shift!

where *ANY* means really *any*, that is ECG's, speech, etc., and 
(-1)*x(n)  means really inverting the signal.

---------
If a 180 deg shift produced about 15 articles posted, how many 
would be produced by a 360 deg shift? Answer: 2*15 = 30

Re: 180 deg phase shift

#1769

Author: Michael Hui
Date: Thu, 09 May 1991 19:27

11 lines
856 bytes

In article <1991May9.160115.3494@cpsc.ucalgary.ca> heredia@enel.ucalgary.ca (Edwin Heredia) writes:
>For those who can't believe that inverting the signal produces 
>a 180 deg. phase shift and for those who think that this trick 
>works only with "easy-to-work" signals as pure tones:
>
>Given *ANY* signal  x(n)  with Fourier Transform  X(w)
        ^^^

Really? You surely mean _periodic_ signal.

      Michael MY Hui      Ottawa Canada      myhui@bnr.ca

Re: 180 deg phase shift

#1777

Author: Bruce Karsh
Date: Fri, 10 May 1991 12:55

13 lines
947 bytes

>>Given *ANY* signal  x(n)  with Fourier Transform  X(w)
>Really? You surely mean _periodic_ signal.

A signal doesn't have to be periodic to have a Fourier transform.  Any
sequence x(n) that is absolutely summable (i.e., the sum of the absolute
values is bounded) has a Fourier transform given by:

	       inf	
	X(w) = sum	  x(n)e^(-jwn)
	       n = -inf

			Bruce Karsh
			karsh@sgi.com

Re: 180 deg phase shift

#1775

Author: john f andrews ece
Date: Fri, 10 May 1991 15:37

15 lines
1283 bytes

In article <1991May09.192740.4165@bmerh2.bnr.ca> myhui@bnr.ca (Michael Hui) writes:
>In article <1991May9.160115.3494@cpsc.ucalgary.ca> heredia@enel.ucalgary.ca (Edwin Heredia) writes:
>>For those who can't believe that inverting the signal produces 
>>a 180 deg. phase shift and for those who think that this trick 
>>works only with "easy-to-work" signals as pure tones:
>>
>>Given *ANY* signal  x(n)  with Fourier Transform  X(w)
>        ^^^
>
>Really? You surely mean _periodic_ signal.
>
>      Michael MY Hui      Ottawa Canada      myhui@bnr.ca

Why do we keep tagging onto this thread? "any signal ..with a fourier
ransform" implies any periodic signal....so why the beef? Let it go!

Re: 180 deg phase shift

#1779

Author: Isaac K. Wong
Date: Fri, 10 May 1991 19:47

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1047 bytes

In article <1991May09.192740.4165@bmerh2.bnr.ca> myhui@bnr.ca (Michael Hui) writes:
=>In article <1991May9.160115.3494@cpsc.ucalgary.ca> heredia@enel.ucalgary.ca (Edwin Heredia) writes:
=>>
=>>Given *ANY* signal  x(n)  with Fourier Transform  X(w)
=>        ^^^
=>
=>Really? You surely mean _periodic_ signal.
=>

and a linear system too. and I am sure the ANY signal you mentioned doesn't
include DC. :)




-- 
Isaac Wong	     		||	There's no need to worry about death,
GenRad, Milpitas, CA		||	it will not happen in your lifetime.
wongi@topo.genrad.com 		||
wongi@topo.uucp 		||	-Raymond Smullyan

Re: 180 deg phase shift

#1778

Author: Bruce Karsh
Date: Fri, 10 May 1991 20:11

14 lines
1129 bytes

In article jfa0522@hertz.njit.edu (john f andrews ece) writes:

>Why do we keep tagging onto this thread? "any signal ..with a fourier
>ransform" implies any periodic signal....so why the beef? Let it go!

Because what you said is wrong.  It is simply not the case that the
existence of a Fourier transform of a function or a series implies periodicity.

The existence of a Fourier sequence implies periodicity, but that is another
matter.  The Fourier transform exists for non-periodic functions which are
absolutely summable.

			Bruce Karsh
			karsh@sgi.com

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