# Absolute Beginner - inverted signal?

Started by June 9, 2008
```Hi Guys,

First please excuse my ignorance, I am just starting in DSP as a bit of a
hobby.

I Have Richard Lyons "understanding dsp" here and am working my way
through the "Sampling Bandpass Signals" chapter. I understand the idea of
Aliases and aliasing in the sampled signal spectrum but in the diagrams for
the continuous signal spectrum there is always an inverse of the signal. So
say there is an amplitude of 1 and 2MHz then there is also have an
amplitude of 1 at -2MHz.

This doesn't seem to be explained, probably as it is something basic that

Could someone direct me to some information that would explain this to
me.

Thanks for any help.

Andy

```
```"BobTheDog" <andrew.capon@zen.co.uk> writes:

> Hi Guys,
>
> First please excuse my ignorance, I am just starting in DSP as a bit of a
> hobby.
>
> I Have Richard Lyons "understanding dsp" here and am working my way
> through the "Sampling Bandpass Signals" chapter. I understand the idea of
> Aliases and aliasing in the sampled signal spectrum but in the diagrams for
> the continuous signal spectrum there is always an inverse of the signal. So
> say there is an amplitude of 1 and 2MHz then there is also have an
> amplitude of 1 at -2MHz.
>
> This doesn't seem to be explained, probably as it is something basic that
>
> Could someone direct me to some information that would explain this to
> me.
>
> Thanks for any help.
>
> Andy

Hi Andy,

Yes, it is something basic. A real (as opposed to complex) signal will
always have a symmetric spectrum.

If you pick up a book on linear system theory (I like
you will find out why.

--Randy

@BOOK{signalsandsystems,
title = "{Signals and Systems}",
author = "{Alan~V.~Oppenheim, Alan~S.~Willsky, with Ian~T.~Young}",
publisher = "Prentice Hall",
year = "1983"}

--
%  Randy Yates                  % "My Shangri-la has gone away, fading like
%% Fuquay-Varina, NC            %  the Beatles on 'Hey Jude'"
%%% 919-577-9882                %
%%%% <yates@ieee.org>           % 'Shangri-La', *A New World Record*, ELO
http://www.digitalsignallabs.com
```
```Hi Randy,

Thanks very much for the information.

All the best

Andy
```
```Hi Andy,
This might help.
Steve

http://www.dspguide.com/ch10/3.htm

```
```SteveSmith wrote:

> http://www.dspguide.com/ch10/3.htm

Pretty good description.  It is sometimes described
as periodic boundary conditions, especially when used for
the solutions of differential equations.

Still, I find the part where modifications to the
spectrum (FFT of the time domain signal) to
"spill over from one period into the adjacent
period" to be a little strange.  It really can't
do that because there are no frequency components
in the transform that can do that.

The problem, as I see it, is in ones belief in the
modifications to the transform (most obvious in the
case of circular convolution).  That is, the modified
spectrum is not the desired spectrum.

But I can also see it in terms of spilling over.

Now, why does the audio spectrum in ch10/5.htm not have
a negative part?

-- glen

```
```>Now, why does the audio spectrum in ch10/5.htm not have
>a negative part?
>
>-- glen
>

Hi Glen,
It would certainly be useful to show the negative frequencies in this
figure.  Thanks for the suggestion-- I'll add it to my list for the next
edition.
Steve
```
```On Jun 10, 12:12&#2013266080;pm, "SteveSmith" <Steve.Smi...@SpectrumSDI.com>
wrote:
> >Now, why does the audio spectrum in ch10/5.htm not have
> >a negative part?
>
> >-- glen
>
> Hi Glen,
> It would certainly be useful to show the negative frequencies in this
> figure. &#2013266080;Thanks for the suggestion-- I'll add it to my list for the next
> edition.
> Steve

us old analog guys have learned that perspective using old fashioned
heterodyne spectrum analyzers.  If you tune below the zero, you can
actually see the negative frequencies, mirror images of the positive
ones...sure enough they are there...   :-)

Mark
```
```On Wed, 11 Jun 2008 08:58:47 -0700 (PDT), Mark <makolber@yahoo.com>
wrote:

>On Jun 10, 12:12&#2013266080;pm, "SteveSmith" <Steve.Smi...@SpectrumSDI.com>
>wrote:
>> >Now, why does the audio spectrum in ch10/5.htm not have
>> >a negative part?
>>
>> >-- glen
>>
>> Hi Glen,
>> It would certainly be useful to show the negative frequencies in this
>> figure. &#2013266080;Thanks for the suggestion-- I'll add it to my list for the next
>> edition.
>> Steve
>
>us old analog guys have learned that perspective using old fashioned
>heterodyne spectrum analyzers.  If you tune below the zero, you can
>actually see the negative frequencies, mirror images of the positive
>ones...sure enough they are there...   :-)
>
>Mark

Hi Mark,
Neat.  I think I tried that decades ago, but I forget
what it was that I saw on the old fashioned spectrum
analyzer.   It seems like you've verified that Steve Smith
was not just "making up" this whole notion of negative
frequencies.

[-Rick-]
```
```Rick Lyons wrote:
> On Wed, 11 Jun 2008 08:58:47 -0700 (PDT), Mark <makolber@yahoo.com>
> wrote:
>
>> On Jun 10, 12:12 pm, "SteveSmith" <Steve.Smi...@SpectrumSDI.com>
>> wrote:
>>>> Now, why does the audio spectrum in ch10/5.htm not have
>>>> a negative part?
>>>> -- glen
>>> Hi Glen,
>>> It would certainly be useful to show the negative frequencies in this
>>> figure.  Thanks for the suggestion-- I'll add it to my list for the next
>>> edition.
>>> Steve
>> us old analog guys have learned that perspective using old fashioned
>> heterodyne spectrum analyzers.  If you tune below the zero, you can
>> actually see the negative frequencies, mirror images of the positive
>> ones...sure enough they are there...   :-)
>>
>> Mark
>
> Hi Mark,
>   Neat.  I think I tried that decades ago, but I forget
> what it was that I saw on the old fashioned spectrum
> analyzer.   It seems like you've verified that Steve Smith
> was not just "making up" this whole notion of negative
> frequencies.

There's no need to assume negative frequencies for explaining what one
sees on the spectrum analyzer, but as with exponential forms for sine
and cosine, it is a convenient thing to do. Elevating a convenient
construct to an immutable reality can occasionally lead one far astray.

Jerry
--
Engineering is the art of making what you want from things you can get.
&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
```
```On 12 Jun, 14:28, Rick Lyons <R.Lyons@_BOGUS_ieee.org> wrote:
> On Wed, 11 Jun 2008 08:58:47 -0700 (PDT), Mark <makol...@yahoo.com>
> wrote:

> >us old analog guys have learned that perspective using old fashioned
> >heterodyne spectrum analyzers. &#2013266080;If you tune below the zero, you can
> >actually see the negative frequencies, mirror images of the positive
> >ones...sure enough they are there... &#2013266080; :-)
>
> >Mark
>
> Hi Mark,
> &#2013266080; Neat. &#2013266080;I think I tried that decades ago, but I forget
> what it was that I saw on the old fashioned spectrum
> analyzer. &#2013266080; It seems like you've verified that Steve Smith
> was not just "making up" this whole notion of negative
> frequencies.

What about AM? What's the point of SSB AM without
the concept of 'negative frequency'? No need to
play tricks with the novices minds by 'tuning the
spectrum analyzer to -5 Hz' when a trivial mixer
will show the effect. Once you see the output
of that analog mixer with an extra sideband below
the carrier, you understand that something 'weird'
is going on. Negative frequencies are there to help
you explain what is happening and you avoid the
hurdle of trying tho understand what it means to
'tune a reciever to negative frequency'.

Rune
```