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From: myhui@bnr.ca (Michael Hui)
Subject: Re: 180 deg phase shift
Message-ID: <1991May15.031706.15559@bmerh2.bnr.ca>
Sender: news@bmerh2.bnr.ca (Usenet News Admin)
Organization: Bell Northern Research, Ottawa, Ontario Canada
References: <1991May8.222501.19572@syd.dms.CSIRO.AU> <1991May10.003817.5593@milton.u.washington.edu> <625@fudd.dataco.UUCP>
Date: Wed, 15 May 91 03:17:06 GMT

In article <625@fudd.dataco.UUCP> mcphail@taarna.UUCP (Alex McPhail,DC ) writes:
>      .      .      .      .
>     /|     /|     /|     /|
>    / |    / |    / |    / |
>   /  |   /  |   /  |   /  |
>  /   |  /   |  /   |  /   |
> /    | /    | /    | /    |
>/     |/     |/     |/     |          Normal sawtooth wave
>
>         .      .      .      .
>        /|     /|     /|     /|
>       / |    / |    / |    / |
>      /  |   /  |   /  |   /  |
>     /   |  /   |  /   |  /   |
>    /    | /    | /    | /    |
>   /     |/     |/     |/     |       Shifted sawtooth wave
>
>\     |\     |\     |\     |
> \    | \    | \    | \    |
>  \   |  \   |  \   |  \   |
>   \  |   \  |   \  |   \  |
>    \ |    \ |    \ |    \ |
>     \|     \|     \|     \|
>      `      `      `      `         Inverted sawtooth wave
>============================================================================
>________
>|\     /  Alex McPhail
>| \   /
>|  \ /    mail to mcphail@dataco              
>|---X     (uunet!mitel!melair!dataco!mcphail)

Brilliant. Absolutely brilliant (!).

Now for my comments, IMHO: inverting shifts all frequency components by pi
degrees. That means, taken time-wise, high frequencies are shifted less in time
than low frequencies. That's how you get the inverted sawtooth above. Imagine
how the fundamental would look in the original wave. Invert it. Lo and behold,
it does fit the inverted sawtooth!!!

But the original question was to shift the phase of a signal by 180 degrees,
which implicitly means to delay the signal by pi degrees as referred to its
fundamental frequency.

      Michael MY Hui      Ottawa Canada      myhui@bnr.ca