# RF complex mixing

Started by July 10, 2018
```On Thursday, July 12, 2018 at 9:00:59 AM UTC-7, Eric Jacobsen wrote:

> Think of the hands on a clock.   The second hand rotates around the
> clock face at 1/60 rotations per second, the minute hand at 1/360
> rotations/sec, and the hour hand at 1/4320 per second.    Since the
> clock hands rotate, you could imagine running the clock backwards so
> that the hand rotate counter-clockwise instead of clockwise.   In
> order to distinguish the backwards, ccw, rotations of the clock at the
> same frequencies from the forward, clock rotations, it's easy to put a
> negative sign in front of them.   This is consistent mathematically.

[Snipped by Lyons]

Hi Eric.
You made me think about my battery-powered electric drill.
(One of the all-time great applications of electric motors!)
It has a "Reverse" button that allows me to both "drive" screws in (clockwise rotation) and remove screws (counter-clockwise rotation). If we define positive rotations/minute (RPM) as clockwise rotation, then we could conceive of (define) "negative RPM" as being counter-clockwise rotation.

However, the notion of negative physical quantities is an interesting topic. For example, I cannot conceive of an old clock whose pendulum oscillates at a rate of negative one oscillations per second.
```
```"Richard (Rick) Lyons" <r.lyons@ieee.org> writes:

> On Thursday, July 12, 2018 at 9:00:59 AM UTC-7, Eric Jacobsen wrote:
>
>
>> Think of the hands on a clock.   The second hand rotates around the
>> clock face at 1/60 rotations per second, the minute hand at 1/360
>> rotations/sec, and the hour hand at 1/4320 per second.    Since the
>> clock hands rotate, you could imagine running the clock backwards so
>> that the hand rotate counter-clockwise instead of clockwise.   In
>> order to distinguish the backwards, ccw, rotations of the clock at the
>> same frequencies from the forward, clock rotations, it's easy to put a
>> negative sign in front of them.   This is consistent mathematically.
>
> [Snipped by Lyons]
>
> Hi Eric.
> You made me think about my battery-powered electric drill.
> (One of the all-time great applications of electric motors!)
> It has a "Reverse" button that allows me to both "drive" screws in
> (clockwise rotation) and remove screws (counter-clockwise rotation).
> If we define positive rotations/minute (RPM) as clockwise rotation,
> then we could conceive of (define) "negative RPM" as being
> counter-clockwise rotation.
>
> However, the notion of negative physical quantities is an interesting
> topic. For example, I cannot conceive of an old clock whose pendulum
> oscillates at a rate of negative one oscillations per second.

I was going to say, "Sure you can, if the pendulum traces out a 2D path and not a 1D path..."
but that's probably trying to be too smart.

It is also interesting (a consequence?) that the concept of complex
physical quantities is interesting. Complex mass?
--
Randy Yates, DSP/Embedded Firmware Developer
Digital Signal Labs
http://www.digitalsignallabs.com
```
```Randy Yates <yates@digitalsignallabs.com> writes:
> [...]
> It is also interesting (a consequence?) that the concept of complex
> physical quantities is interesting. Complex mass?

There ya' go. Reduced to babbling...
--
Randy Yates, DSP/Embedded Firmware Developer
Digital Signal Labs
http://www.digitalsignallabs.com
```
```On 7/13/2018 12:20 AM, Steve Pope wrote:
> RichD  <r_delaney2001@yahoo.com> wrote:
>
>> Watch a film of spoked wagon wheels.  At a certain speed,
>> the wheels appear to rotate backwards.  It's a consequence
>> of aliasing, due to the low sample rate of the human eye.
>>
>> That's a  negative frequency.
>
> I'm going to disagree with this analogy, as it is an aliasing
> effect and the original question applies to continuous time
> signals.
>
> Steve
>
The aliasing is due to the sampling of the visual signal by the camera
(whether film or video)

--
Best wishes,
--Phil
pomartel At Comcast(ignore_this) dot net
```
```Richard (Rick) Lyons wrote:
> On Thursday, July 12, 2018 at 9:00:59 AM UTC-7, Eric Jacobsen wrote:
>
>
>> Think of the hands on a clock.   The second hand rotates around the
>> clock face at 1/60 rotations per second, the minute hand at 1/360
>> rotations/sec, and the hour hand at 1/4320 per second.    Since the
>> clock hands rotate, you could imagine running the clock backwards so
>> that the hand rotate counter-clockwise instead of clockwise.   In
>> order to distinguish the backwards, ccw, rotations of the clock at the
>> same frequencies from the forward, clock rotations, it's easy to put a
>> negative sign in front of them.   This is consistent mathematically.
>
> [Snipped by Lyons]
>
> Hi Eric.
> You made me think about my battery-powered electric drill.
> (One of the all-time great applications of electric motors!)
> It has a "Reverse" button that allows me to both "drive" screws in (clockwise rotation) and remove screws (counter-clockwise rotation). If we define positive rotations/minute (RPM) as clockwise rotation, then we could conceive of (define) "negative RPM" as being counter-clockwise rotation.
>
> However, the notion of negative physical quantities is an interesting topic. For example, I cannot conceive of an old clock whose pendulum oscillates at a rate of negative one oscillations per second.
>

A pendulum only has "positive oscillations" and the time
base only goes one way. So it's a "real-only" oscillator. It's
insufficiently dimensional to account for negatives.

I have no idea of what use this is, but:

1) If we filmed the pendulum, then ran the film backwards, it
would be totally the same as if it ran forwards. Since the order of
events is reversed and the the timebase is reversed, the reverses cancel
each other out.

2) If there were a "complex pendulum", you might have enough dimensional
to get negative quantities. All I see of "complex pendulums" is double
pendulums. So perhaps a "complex pendulum" is a non-sequitur. But E/M
waves in space are not.

--
Les Cargill

```
```Randy Yates wrote:
> "Richard (Rick) Lyons" <r.lyons@ieee.org> writes:
>
>> On Thursday, July 12, 2018 at 9:00:59 AM UTC-7, Eric Jacobsen wrote:
>>
>>
>>> Think of the hands on a clock.   The second hand rotates around the
>>> clock face at 1/60 rotations per second, the minute hand at 1/360
>>> rotations/sec, and the hour hand at 1/4320 per second.    Since the
>>> clock hands rotate, you could imagine running the clock backwards so
>>> that the hand rotate counter-clockwise instead of clockwise.   In
>>> order to distinguish the backwards, ccw, rotations of the clock at the
>>> same frequencies from the forward, clock rotations, it's easy to put a
>>> negative sign in front of them.   This is consistent mathematically.
>>
>> [Snipped by Lyons]
>>
>> Hi Eric.
>> You made me think about my battery-powered electric drill.
>> (One of the all-time great applications of electric motors!)
>> It has a "Reverse" button that allows me to both "drive" screws in
>> (clockwise rotation) and remove screws (counter-clockwise rotation).
>> If we define positive rotations/minute (RPM) as clockwise rotation,
>> then we could conceive of (define) "negative RPM" as being
>> counter-clockwise rotation.
>>
>> However, the notion of negative physical quantities is an interesting
>> topic. For example, I cannot conceive of an old clock whose pendulum
>> oscillates at a rate of negative one oscillations per second.
>
> I was going to say, "Sure you can, if the pendulum traces out a 2D path and not a 1D path..."
> but that's probably trying to be too smart.
>
> It is also interesting (a consequence?) that the concept of complex
> physical quantities is interesting. Complex mass?
>

Mass is pretty single-ended.

--
Les Cargill
```
```Steve Pope wrote:
> RichD  <r_delaney2001@yahoo.com> wrote:
>
>> Watch a film of spoked wagon wheels.  At a certain speed,
>> the wheels appear to rotate backwards.  It's a consequence
>> of aliasing, due to the low sample rate of the human eye.
>>
>> That's a  negative frequency.
>
> I'm going to disagree with this analogy, as it is an aliasing
> effect and the original question applies to continuous time
> signals.
>
> Steve
>

So you ran out of Dirac deltas? :)

<enjoy the veal, I'll be here all week>

--
Les Cargill

```
```On 7/13/2018 7:44 PM, Les Cargill wrote:
> Richard (Rick) Lyons wrote:
>> On Thursday, July 12, 2018 at 9:00:59 AM UTC-7, Eric Jacobsen wrote:
>>
>>
>>> Think of the hands on a clock.&nbsp;&nbsp; The second hand rotates around the
>>> clock face at 1/60 rotations per second, the minute hand at 1/360
>>> rotations/sec, and the hour hand at 1/4320 per second.&nbsp;&nbsp;&nbsp; Since the
>>> clock hands rotate, you could imagine running the clock backwards so
>>> that the hand rotate counter-clockwise instead of clockwise.&nbsp;&nbsp; In
>>> order to distinguish the backwards, ccw, rotations of the clock at the
>>> same frequencies from the forward, clock rotations, it's easy to put a
>>> negative sign in front of them.&nbsp;&nbsp; This is consistent mathematically.
>>
>> [Snipped by Lyons]
>>
>> Hi Eric.
>> You made me think about my battery-powered electric drill.
>> (One of the all-time great applications of electric motors!)
>> It has a "Reverse" button that allows me to both "drive" screws in
>> (clockwise rotation) and remove screws (counter-clockwise rotation).
>> If we define positive rotations/minute (RPM) as clockwise rotation,
>> then we could conceive of (define) "negative RPM" as being
>> counter-clockwise rotation.
>>
>> However, the notion of negative physical quantities is an interesting
>> topic. For example, I cannot conceive of an old clock whose pendulum
>> oscillates at a rate of negative one oscillations per second.
>>
>
> A pendulum only has "positive oscillations" and the time
> base only goes one way. So it's a "real-only" oscillator. It's
> insufficiently dimensional to account for negatives.
>
> I have no idea of what use this is, but:
>
> 1) If we filmed the pendulum, then ran the film backwards, it
> would be totally the same as if it ran forwards. Since the order of
> events is reversed and the the timebase is reversed, the reverses cancel
> each other out.
>
> 2) If there were a "complex pendulum", you might have enough dimensional
> to get negative quantities. All I see of "complex pendulums" is double
> pendulums. So perhaps a "complex pendulum" is a non-sequitur. But E/M
> waves in space are not.
>

Foucaults's Pendulum?

https://www.fi.edu/exhibit/foucault%E2%80%99s-pendulum

It would definitely would be different if run backward - except if moved
to the southern hemisphere.

Rob.

```
```On 14.07.2018 6:39, Rob Doyle wrote:
> On 7/13/2018 7:44 PM, Les Cargill wrote:
>> Richard (Rick) Lyons wrote:
>>> On Thursday, July 12, 2018 at 9:00:59 AM UTC-7, Eric Jacobsen wrote:
>>>
>>>
>>>> Think of the hands on a clock.   The second hand rotates around the
>>>> clock face at 1/60 rotations per second, the minute hand at 1/360
>>>> rotations/sec, and the hour hand at 1/4320 per second.    Since the
>>>> clock hands rotate, you could imagine running the clock backwards so
>>>> that the hand rotate counter-clockwise instead of clockwise.   In
>>>> order to distinguish the backwards, ccw, rotations of the clock at the
>>>> same frequencies from the forward, clock rotations, it's easy to put a
>>>> negative sign in front of them.   This is consistent mathematically.
>>>
>>> [Snipped by Lyons]
>>>
>>> Hi Eric.
>>> You made me think about my battery-powered electric drill.
>>> (One of the all-time great applications of electric motors!)
>>> It has a "Reverse" button that allows me to both "drive" screws in
>>> (clockwise rotation) and remove screws (counter-clockwise rotation).
>>> If we define positive rotations/minute (RPM) as clockwise rotation,
>>> then we could conceive of (define) "negative RPM" as being
>>> counter-clockwise rotation.
>>>
>>> However, the notion of negative physical quantities is an interesting
>>> topic. For example, I cannot conceive of an old clock whose pendulum
>>> oscillates at a rate of negative one oscillations per second.
>>>
>>
>> A pendulum only has "positive oscillations" and the time
>> base only goes one way. So it's a "real-only" oscillator. It's
>> insufficiently dimensional to account for negatives.
>>
>> I have no idea of what use this is, but:
>>
>> 1) If we filmed the pendulum, then ran the film backwards, it
>> would be totally the same as if it ran forwards. Since the order of
>> events is reversed and the the timebase is reversed, the reverses cancel
>> each other out.
>>
>> 2) If there were a "complex pendulum", you might have enough
>> dimensional to get negative quantities. All I see of "complex
>> pendulums" is double
>> pendulums. So perhaps a "complex pendulum" is a non-sequitur. But E/M
>> waves in space are not.
>>
>
> Foucaults's Pendulum?
>
> https://www.fi.edu/exhibit/foucault%E2%80%99s-pendulum
>
> It would definitely would be different if run backward - except if moved
> to the southern hemisphere.
>
> Rob.
>

In physics, that's called CPT symmetry.

https://en.wikipedia.org/wiki/CPT_symmetry

Gene

```
```Les Cargill  <lcargill99@comcast.com> wrote:

>Steve Pope wrote:

>> RichD  <r_delaney2001@yahoo.com> wrote:

>>> Watch a film of spoked wagon wheels.  At a certain speed,
>>> the wheels appear to rotate backwards.  It's a consequence
>>> of aliasing, due to the low sample rate of the human eye.

>>> That's a  negative frequency.

>> I'm going to disagree with this analogy, as it is an aliasing
>> effect and the original question applies to continuous time
>> signals.

>So you ran out of Dirac deltas? :)
>
><enjoy the veal, I'll be here all week>

Relatedly, Dirac did indeed come up with the idea of imaginary mass,
in his Dirac Sea formulation.

So there.

Steve
```