negative freqs

Hi there, 

Iam trying to understand what is meant by negative and positive frequencies. 

If anyone can explain in a simple terms....would appreciate it. 

Regards

Sundar

sundar wrote:

> Hi there, 
> 
> Iam trying to understand what is meant by negative and positive frequencies. 
> 
> If anyone can explain in a simple terms....would appreciate it. 
> 
> Regards
> 
> Sundar

The mathematically easy way to do a Fourier transform is to do it 
against exp(i * 2*pi*f), which makes a rotating vector on the complex 
plane.  So a positive frequency corresponds to this vector rotating 
counterclockwise and a negative frequency corresponds to this vector 
rotating clockwise.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

I think of the negative frequencies as just a side
effect of the use of complex exponentials to get a single 
transform rather than using a cosine transform for the even
part of the signal and a sine transform for the odd part.  

As I recall Lathi lays this out nicely in his signals & systems 
books.   

In article <2b5e8f90.0407280709.4eefe60f@posting.google.com>,
sundar <snsundar@olemiss.edu> wrote:
>Hi there, 
>
>Iam trying to understand what is meant by negative and positive frequencies. 
>
>If anyone can explain in a simple terms....would appreciate it. 
>
>Regards
>
>Sundar

sundar wrote:
> Hi there, 
> 
> Iam trying to understand what is meant by negative and positive frequencies. 
> 
> If anyone can explain in a simple terms....would appreciate it. 
> 
> Regards
> 
> Sundar

Some people give off positive vibes, others give off negative vibes.

Stan Pawlukiewicz wrote:

> sundar wrote:
> 
>> Hi there,
>> Iam trying to understand what is meant by negative and positive 
>> frequencies.
>> If anyone can explain in a simple terms....would appreciate it.
>> Regards
>>
>> Sundar
> 
> 
> Some people give off positive vibes, others give off negative vibes.

Well, there are even people with negative personalities. When such a
person enters a room, you get the impression that someone just left.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Jerry Avins wrote:
> Stan Pawlukiewicz wrote:
> 
>> sundar wrote:
>>
>>> Hi there,
>>> Iam trying to understand what is meant by negative and positive 
>>> frequencies.
>>> If anyone can explain in a simple terms....would appreciate it.
>>> Regards
>>>
>>> Sundar
>>
>>
>>
>> Some people give off positive vibes, others give off negative vibes.
> 
> 
> Well, there are even people with negative personalities. When such a
> person enters a room, you get the impression that someone just left.
> 
> Jerry
Instead of empathy, its more like entropy.

If your sampling at Nyquist or better you really don't have to worry about
negative frequencies too much. However, if you are radically subsampling,
negative frequencies can be your life.

I first got a grasp on negative frequencies when I read an article in RF
Design magazine called "Understanding digital signal processing's frequency
domain" by Richard Lyons it has a small section in it called "Don't negate
negative frequencies". The issue is Nov 1, 2001. The magazine has nice
diagrams that makes understanding of negative frequencies easy. However, it
doesn't have the diagrams when you read it online and makes it hard to
follow.

Mathematically, I use the formula f(K) = RF + K*FS. Where RF is your input
frequency, FS is your sampling frequency and K is an integer (positive or
negative image).

For my current project I'm using the -642 image to lock on to. The trick is
keeping the negative images away from the positive ones.

Thomas

"sundar" <snsundar@olemiss.edu> wrote in message
news:2b5e8f90.0407280709.4eefe60f@posting.google.com...
> Hi there,
>
> Iam trying to understand what is meant by negative and positive
frequencies.
>
> If anyone can explain in a simple terms....would appreciate it.
>
> Regards
>
> Sundar

Stan Pawlukiewicz <spam@spam.mitre.org> wrote in message news:<ceb1p4$ah1$1@newslocal.mitre.org>...
> sundar wrote:
> > Hi there, 
> > 
> > Iam trying to understand what is meant by negative and positive frequencies. 
> > 
> > If anyone can explain in a simple terms....would appreciate it. 
> > 
> > Regards
> > 
> > Sundar
> 
> Some people give off positive vibes, others give off negative vibes.

Mix'em and you get a real mess.

Rune

The way that I find easiest to picture the difference between positive and
negative frequencies is to consider a cosine function.

cos(x) = 1/2 * (exp(jx)+exp(-jx))

When you plot this on the complex plain and vary x, you can clearly see that
one rotor circles clockwise and the other circles counter-clockwise.  These
are the positive and negative frequency components that you learn to expect
from a real signal such as a cos function.  The imaginary parts cancel each
other leaving you with the real component.

"sundar" <snsundar@olemiss.edu> wrote in message
news:2b5e8f90.0407280709.4eefe60f@posting.google.com...
> Hi there,
>
> Iam trying to understand what is meant by negative and positive
frequencies.
>
> If anyone can explain in a simple terms....would appreciate it.
>
> Regards
>
> Sundar

On Thu, 29 Jul 2004 18:02:36 GMT, "Thomas Magma"
<somewhere@overtherainbow.com> wrote:

>If your sampling at Nyquist or better you really don't have to worry about
>negative frequencies too much. However, if you are radically subsampling,
>negative frequencies can be your life.
>
>I first got a grasp on negative frequencies when I read an article in RF
>Design magazine called "Understanding digital signal processing's frequency
>domain" by Richard Lyons it has a small section in it called "Don't negate
>negative frequencies". The issue is Nov 1, 2001. The magazine has nice
>diagrams that makes understanding of negative frequencies easy. However, it
>doesn't have the diagrams when you read it online and makes it hard to
>follow.
>
>Mathematically, I use the formula f(K) = RF + K*FS. Where RF is your input
>frequency, FS is your sampling frequency and K is an integer (positive or
>negative image).
>
>For my current project I'm using the -642 image to lock on to. The trick is
>keeping the negative images away from the positive ones.
>
>Thomas
>

Hi Thomas,

    the RF Design magazine folk induced 
several errors in that article (like incorrectlty 
changing variable names in the text & deleting my 
original Equation 2, and replacing it with Equation 3.
So Equation 3 appears twice!)

I can send you a corrected version of that article if you wish.

Regards,
[-Rick-]