# What is x = I + jQ

Started by March 10, 2005
```This is regarding the DSP math/equations in general.  What is "x = I +
jQ"?  I know that j = 0 + 1i and i = sqrt(-1) and i^2 = -1.  But what
is x = I + jQ, where x represents a form of the input data signal.

I need this info to calc the atan(Q/I) for frequency demodulation
purposes.  Any help is appreciated.

```
```george_barr@yahoo.com schrieb:
> This is regarding the DSP math/equations in general.  What is "x = I +
> jQ"?  I know that j = 0 + 1i and i = sqrt(-1) and i^2 = -1.  But what
> is x = I + jQ, where x represents a form of the input data signal.
>
> I need this info to calc the atan(Q/I) for frequency demodulation
> purposes.  Any help is appreciated.
>

x is just a complex number. Since I and Q are real, you should have no

Thomas

```
```"Dr. Thomas Radtke" <thradtke@freenet.de> wrote in message
news:422FFB0A.90508@freenet.de...
> george_barr@yahoo.com schrieb:
>> This is regarding the DSP math/equations in general.  What is "x = I +
>> jQ"?  I know that j = 0 + 1i and i = sqrt(-1) and i^2 = -1.  But what
>> is x = I + jQ, where x represents a form of the input data signal.
>>
>> I need this info to calc the atan(Q/I) for frequency demodulation
>> purposes.  Any help is appreciated.
>>
>
> x is just a complex number. Since I and Q are real, you should have no
>
> Thomas
>
What Thomas said.  I is used for the In-phase component and Q for Quadrature
component.  People seem to use phase = atan2(imaginary part , real part) as
a convention , if this is what you are using then phase can be interpreted
as a clockwise rotation (looking into the paper) with respect to the
In-phase direction, when you draw your Q axis at 90 degrees clockwise to the
I.

Best of Luck - Mike

```
```"Dr. Thomas Radtke" <thradtke@freenet.de> writes:

> george_barr@yahoo.com schrieb:
>> This is regarding the DSP math/equations in general.  What is "x = I +
>> jQ"?  I know that j = 0 + 1i and i = sqrt(-1) and i^2 = -1.  But what
>> is x = I + jQ, where x represents a form of the input data signal.
>> I need this info to calc the atan(Q/I) for frequency demodulation
>> purposes.  Any help is appreciated.
>>
>
> x is just a complex number. Since I and Q are real, you should have no

Also note that a complex number can be expressed in rectangular form,

z = x + i*y

or polar form

z = r*e^{j*theta},

where

r = |z| = sqrt(x^2 + y^2}
theta = angle(z) = arctan(y/x),

the usual rectangular-to-polar conversion.
--
%  Randy Yates                  % "And all that I can do
%% Fuquay-Varina, NC            %  is say I'm sorry,
%%% 919-577-9882                %  that's the way it goes..."
%%%% <yates@ieee.org>           % Getting To The Point', *Balance of Power*, ELO
```
```I guess the missing part is that the math peoples i (imaginary element)
is called j in electrical engineering to avoid mixup with the current i.

Randy Yates wrote:

>
>
>>george_barr@yahoo.com schrieb:
>>
>>>This is regarding the DSP math/equations in general.  What is "x = I +
>>>jQ"?  I know that j = 0 + 1i and i = sqrt(-1) and i^2 = -1.  But what
>>>is x = I + jQ, where x represents a form of the input data signal.
>>>I need this info to calc the atan(Q/I) for frequency demodulation
>>>purposes.  Any help is appreciated.
>>>
>>
>>x is just a complex number. Since I and Q are real, you should have no
>
>
> Also note that a complex number can be expressed in rectangular form,
>
>   z = x + i*y
>
> or polar form
>
>   z = r*e^{j*theta},
>
> where
>
>   r = |z| = sqrt(x^2 + y^2}
>   theta = angle(z) = arctan(y/x),
>
> the usual rectangular-to-polar conversion.

--

```
```I is the inphase component and J is the quadratrature component.

```
```I is the inphase component and J is the quadratrature phase component.

```
```Andre wrote:
> I guess the missing part is that the math peoples i (imaginary element)
> is called j in electrical engineering to avoid mixup with the current i.

Mix-ups are so very easy! If I didn't know better, I could assume that
"current i" above refers to i as it is now, as opposed to what it might
become. (Anyone still confused should read "the current i" as "the
symbol 'i' that is used to represent electrical current.") Oh my!

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;
```
```Neo wrote:
> I is the inphase component and J is the quadratrature component.

Ignore that nonsense. (What is K?)

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;
```
```Neo wrote:
> I is the inphase component and J is the quadratrature phase component.

It doesn't matter that he repeated it. Ignore it anyway.

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;
```