🚀 go-pugleaf

In article <1991May8.222501.19572@syd.dms.CSIRO.AU> steveq@syd.dms.CSIRO.AU (Stephen Quigg) writes:
>In article <5781@media-lab.media.mit.edu.MEDIA.MIT.EDU> cas@media-lab.media.mit.edu (Scud) writes:
>>In article <1991May5.233533.18783@ux1.cso.uiuc.edu> frerichs@adsl.ece.uiuc.edu (dfRERICHS) writes:
>>>Does anyone know the algorithm that would take a stream of sampled sound
>>>,shift it 180 deg in phase and spit it back out again?
>>
>>Use an op-amp as as inverter (ie with a gain of -1). One chip, one resistor,
>>one pot.
>>
>>cas
> 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.



Are we talking about phase shifts or time shifts?  
Phase Shift:  Since the signal can be represented as a sum (or integral) of
complex exponetials, phase shifting can be done by simply multiplying the whole
sum (integral) by exp(  i*p ), where p is the value of the phase shift. This
can be visualized by rotating a vector (our signal) by 180 degrees in the 
complex plane. Since a phase shift of pi (180 degrees) for each component of 
the Fourier series gives that same component multiplied by -1 (e(i*180) = -1), 
the sum of the phase shifted (180 degrees) components gives the original signal
multiplied by -1.  So phase shifting by 180 degrees IS inverting.  This is
why signals that are 180 degrees out of phase are said to cancel eachother out

Time Shift:  A time shift is equivalent to phase shifting each component of
the signal by its frequency times the value of the time shift, not simply 
phase shifting each frequency component by the same phase. This is NOT 
the same thing as performing a simple phase shift on the entire signal.  (It
just happens that for a signal composed of a single frequency (a sine wave), 
a time shift of half the period is equivalent to a phase shift of 180 degrees)

As I understand it, a phase shift by 180 degrees IS inversion.
If I am not using the conventional definitions of the terms "phase shift" and 
"time shift", please let me know.
 






















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