Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!sdd.hp.com!hplabs!hpl-opus!hpcc05!hpsciz!hpdtczb!horner
From: horner@hpdtczb.HP.COM (James G Horner)
Newsgroups: sci.electronics
Subject: Re: 180 deg phase shift
Message-ID: <1310042@hpdtczb.HP.COM>
Date: 15 May 91 18:01:29 GMT
References: <1991May5.233533.18783@ux1.cso.uiuc.edu>
Organization: HP Design Tech Center - Santa Clara, CA
Lines: 80

Alex McPhail writes:

>>> Inverting is NOT the same as 180 deg phase shift. For a symetric waveform
>>>(eg a sine wave) it looks the same, but with something assymetric what you
>>>will see is the waveform upside-down, which is not the same as shifted 180
>>>deg. Phase shifting moves a waveform along the time axis: it stays the same
>>>way up. Try it on an oscilloscope.
>
>In article <1991May10.003817.5593@milton.u.washington.edu> whit@milton.u.washington.edu (John Whitmore) writes:
>
>>	That's wrong.  The inverter is a perfectly good 180 degree
>>phase shifter, and if you test it at ANY frequency you will see
>>180 degrees of phase shift; the phase shift versus frequency is
>>EXACTLY what was asked for.
>>	Your 'assymmetric waveform' has a lot of Fourier components,
>>and time-shifting it as you seem to be describing is NOT a
>>well-defined operation.  You have to find some particular frequency,
>>derive a time delay from THAT ONE FREQUENCY COMPONENT, and apply
>>that time delay to get the time-shift, and that is NOT the correct
>>phase shift for any frequency component except the one you
>>chose as 'most significant'.
>>
>	John Whitmore
>
>
>Sorry, John.  I usually don't butt into other people's business here, but
>you really are dead wrong.  The phase shift described above is indeed 
>correct.  Since any periodic function is always measured against time, 
>shifting the function's phase is also a time-related operation.  
>
>In specific response to your article, frequency and Fourier components
>have nothing to do with phase shifting.  The shift of a phase, in degrees,
>can be expressed by:
>

Sorry, Alex, but you are incorrect.  John is dead on in his explanation.

Fourier theory says that any time function can be resolved into the sum
of an infinate number of complex exponentials of the form:

	   exp(j*w*t)

	   where w is the radian frequency,
	   and j is the square root of -1.

If your not comfortable with the above expression, remember that
Euler's identity says that:

	   exp(j*w*t) == cos(w*t) + j*sin(w*t)

Mathematically, a 180 degree (pi radians) phase shift of the above equation 
is written as:

	   exp[j*(w*t+pi)] == cos(w*t + pi) + j*sin(w*t + pi)

	   or

	   exp(j*w*t)*exp(j*pi)

In effect, to achieve the phase shift of any function, we multiply
the infinite sum of complex exponentials by:
   
           exp(j*pi)

now, let's us Euler's identity on the above:

	   exp(j*pi) == cos(pi) + j*sin(pi)
	    
	    or if you prefer degrees:

           exp(j*pi) == cos(180) + j*sin(180)

Simple trig says that the above equation is identical to -1.

Therefore, a 180 degree phase shift is THE EXACT SAME as  inverting the
function.  This is true even if the signal is DC because a DC signal
is really a sinusoid of 0 radian frequency.  


Jim Horner