2*pi frequency term

Can anyone let me know how to interpret frequency term 2*pi*n used in
discrete frequency domain transform. Does it refer to any specific
frequency?

On Sep 13, 8:35&#4294967295;am, "manishp" <manishp.p18@n_o_s_p_a_m.gmail.com>
wrote:
> Can anyone let me know how to interpret frequency term 2*pi*n used in
> discrete frequency domain transform. Does it refer to any specific
> frequency?

2*pi*n is the power to which we must raise exp(j) or e^j to get 1,
that is, (e^j)^{2*pi*n} = 1, or equivalently, e^j is a (2*pi*n)-th
root of unity.

WHERE do you see 2*pi*n in a discrete frequency domain transform?

Sheeeesh!

>Can anyone let me know how to interpret frequency term 2*pi*n used in
>discrete frequency domain transform. Does it refer to any specific
>frequency?
>

It is a normalized frequency, normalized with respect to the sampling
frequency in Hz. To get the 'specific' frequency (in rad/s)
2*pi*n*Fs/N , where N is the length of the DFT/FFT and Fs is sampling
frequency in Hz.

>>Can anyone let me know how to interpret frequency term 2*pi*n used in
>>discrete frequency domain transform. Does it refer to any specific
>>frequency?
>>
>
>It is a normalized frequency, normalized with respect to the sampling
>frequency in Hz. To get the 'specific' frequency (in rad/s)
>2*pi*n*Fs/N , where N is the length of the DFT/FFT and Fs is sampling
>frequency in Hz.
>

thank you ...

On Tue, 13 Sep 2011 21:54:54 -0500, manishp wrote:

>>>Can anyone let me know how to interpret frequency term 2*pi*n used in
>>>discrete frequency domain transform. Does it refer to any specific
>>>frequency?
>>>
>>>
>>It is a normalized frequency, normalized with respect to the sampling
>>frequency in Hz. To get the 'specific' frequency (in rad/s) 2*pi*n*Fs/N
>>, where N is the length of the DFT/FFT and Fs is sampling frequency in
>>Hz.
>>
>>
> thank you ...

I would advise you to learn a bit more about SHM (simple harmonic motion) 
and this will force you to learn/revise cosine and sine (i.e. 
trigonometry). The 2*pi term comes from SHM or the fact that the path (in 
radians) of a complex number around a unit circle is 2*pi rad.

Simeon

Simeon wrote:
> 
> On Tue, 13 Sep 2011 21:54:54 -0500, manishp wrote:
> 
> >>>Can anyone let me know how to interpret frequency term 2*pi*n used in
> >>>discrete frequency domain transform. Does it refer to any specific
> >>>frequency?
> >>>
> >>>
> >>It is a normalized frequency, normalized with respect to the sampling
> >>frequency in Hz. To get the 'specific' frequency (in rad/s) 2*pi*n*Fs/N
> >>, where N is the length of the DFT/FFT and Fs is sampling frequency in
> >>Hz.
> >>
> >>
> > thank you ...
> 
> I would advise you to learn a bit more about SHM (simple harmonic motion)
> and this will force you to learn/revise cosine and sine (i.e.
> trigonometry). The 2*pi term comes from SHM or the fact that the path (in
> radians) of a complex number around a unit circle is 2*pi rad.

The "path" will be the same whether you include "2*pi" or not.
Using "pi" allows you to periodically repeat the same steps along that
path.

-jim


> 
> Simeon

Simeon <kotapaka@yahoo.com> wrote:

(snip)
> I would advise you to learn a bit more about SHM (simple harmonic motion) 
> and this will force you to learn/revise cosine and sine (i.e. 
> trigonometry). The 2*pi term comes from SHM or the fact that the path (in 
> radians) of a complex number around a unit circle is 2*pi rad.

If you use angular frequency (radians/sec) instead of cycles/sec
then many of the 2*pi go away.  If more frequency counters were
calibrated in radians/second that would be easier.

Mostly physics uses angular frequency and EE uses cycle frequency.
Also, physics uses wavenumber and wavevector (2*pi/wavelength).

-- glen

On 9/19/11 3:09 PM, glen herrmannsfeldt wrote:
> Simeon<kotapaka@yahoo.com>  wrote:
>
> (snip)
>> I would advise you to learn a bit more about SHM (simple harmonic motion)
>> and this will force you to learn/revise cosine and sine (i.e.
>> trigonometry). The 2*pi term comes from SHM or the fact that the path (in
>> radians) of a complex number around a unit circle is 2*pi rad.
>
> If you use angular frequency (radians/sec) instead of cycles/sec
> then many of the 2*pi go away.  If more frequency counters were
> calibrated in radians/second that would be easier.
>
> Mostly physics uses angular frequency and EE uses cycle frequency.
> Also, physics uses wavenumber and wavevector (2*pi/wavelength).
>

besides being an EE, one reason i like cycle frequency better than 
angular frequency is the simplicity offered in the forward and inverse 
(continuous) Fourier transform.

Fourier transform:

                  +inf
     X(f)  =  integral{ x(t) * e^(-j*2*pi*f*t) dt}
                  -inf


inverse Fourier transform:

                  +inf
     x(t)  =  integral{ X(f) * e^(+j*2*pi*f*t) df}
                  -inf


the symmetry between inverse and forward F.T. is obvious, which lends 
itself nicely to the duality property (which makes my life easier when i 
have to think about the F.T. of sinc() and rect() and the convolution 
theorem and Parseval's theorem).  but you have to remember the 2*pi in 
the exponent.  but nowhere else (unless you are representing capacitors 
or inductors in the frequency domain).

all other representations of the F.T. are scaled versions of the above 
and have either or both asymmetry in the forward and inverse transform 
and/or require weird scaling factors of 1/(2*pi) or 1/(sqrt(2*pi) 
somewhere else, where it is harder to remember.  convolution and 
Parseval's theorem always kill me using the angular frequency 
representation as well as remembering simple transforms like the rect() 
or sinc() functions.


-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

On Sep 19, 3:09=A0pm, glen herrmannsfeldt <g...@ugcs.caltech.edu> wrote:
> Simeon <kotap...@yahoo.com> wrote:
>
> (snip)
>
> > I would advise you to learn a bit more about SHM (simple harmonic motio=
n)
> > and this will force you to learn/revise cosine and sine (i.e.
> > trigonometry). The 2*pi term comes from SHM or the fact that the path (=
in
> > radians) of a complex number around a unit circle is 2*pi rad.
>
> If you use angular frequency (radians/sec) instead of cycles/sec
> then many of the 2*pi go away. =A0If more frequency counters were
> calibrated in radians/second that would be easier.
>
> Mostly physics uses angular frequency and EE uses cycle frequency.
> Also, physics uses wavenumber and wavevector (2*pi/wavelength).
>
> -- glen

Depends on what you are measuring. In Astronomy, we tend to use
minutes and seconds or arc for common angular measures. I haven't
found a protractor ruled in radians yet ;-) But I haven't really
looked too hard either. I just use what is convenient. Sometimes I use
the 2pi and sometimes I don't.

It is sort of like what Lord Rutherford had to say about statisitics
and the social sciences. "Some people do and some people don't!"

Clay

Clay <clay@claysturner.com> wrote:

(snip, I wrote)
>> If you use angular frequency (radians/sec) instead of cycles/sec
>> then many of the 2*pi go away. &#4294967295;If more frequency counters were
>> calibrated in radians/second that would be easier.

>> Mostly physics uses angular frequency and EE uses cycle frequency.
>> Also, physics uses wavenumber and wavevector (2*pi/wavelength).

> Depends on what you are measuring. In Astronomy, we tend to use
> minutes and seconds or arc for common angular measures. 

I was thinking of it in terms of wave propagation, but also
for simple harmonic motion in general.  Maybe not for Keplerian
motion, though.

Did you ever read the book "Feynman's Lost Lecture" by David Goodstein?

It seems that Feynman once gave a lecture on Newton's derivation of
Kepler's laws without Calculus, which is the way Newton would have
done it.  There was no transcript of the lecture, only a few notes
about how it would go.  While on vacation, Goodstein rederived 
the equations that Newton and then Feynman might have used.

> I haven't found a protractor ruled in radians yet ;-) 

I think they are in the same drawer with the natural log graph paper.

> But I haven't really looked too hard either. I just use what 
> is convenient. Sometimes I use the 2pi and sometimes I don't.

-- glen