FFT's and frequency

[RichardJ]

On 8/22/2009 8:24:28 AM, fkohlhepp wrote:

>I started out to see how rpm,
>Hz, and Hza were handled.
>That went as expected. Then I
>created a function with known
>amplitudes and frequencies.
>The plot of amplitudes vs
>frequencies has the correct
>amplitudes, but the frequency
>reports wrong between Hz and
>Hza.

I only looked at it briefly, but it seems to be right to me. Can you be more specific about what you think the problem is?

Richard

[PhilipOakley]

Units have never been 'right' with the various FFTs
because the 'horizontal' axis axis changes its
units.

There is also the impact of negative frequency
taking half the signal...

However it is a can of worms. Probably best not to
open it till work-surfaces are prepared.

Philip Oakley

[mzeftel]

Fred,

I can have a developer who works with signals look at the file, but I can't tell what's wrong with the plot. Can you write back with what you expected to see, to help us track down the problem.

Thanks,

Mona

[Fred_Kohlhepp]

On 8/22/2009 7:05:07 PM, MonaZ wrote:
>Fred,
>
>I can have a developer who
>works with signals look at the
>file, but I can't tell what's
>wrong with the plot. Can you
>write back with what you
>expected to see, to help us
>track down the problem.
>
>Thanks,
>
>Mona

From what I can see, if I define the frequencies in Hza, and label the graph in units Hz, the numbers come out the same. I would expect the graph to be right for units Hza.

Or have I messed it up again?

Fred Kohlhepp
fkohlhepp@sikorsky.com

[RichardJ]

The function needs to be v0*sin(2*pi*omega*t)

Richard

[Fred_Kohlhepp]

On 8/23/2009 5:14:36 PM, rijackson wrote:
>The function needs to be
>v0*sin(2*pi*omega*t)
>
>Richard

I agree that putting 2 pi in the function will make it come out right for frequencies in Hz; but the Hza already has the 2 pi in it (2 pi Hz = 1 Hza)

It's apparently my confusion, however! I did it this morning in version 11 and got the same result.

Fred Kohlhepp
fkohlhepp@sikorsky.com

[RichardJ]

On 8/24/2009 8:04:55 AM, fkohlhepp wrote:
> but the Hza already
>has the 2 pi in it (2 pi Hz = 1 Hza)

That's the point. If you use Hza you don't need the 2*pi in the function because it has the 2*pi already.

Richard

[Fred_Kohlhepp]

On 8/24/2009 10:42:13 AM, rijackson wrote:
>On 8/24/2009 8:04:55 AM, fkohlhepp
>wrote:
>> but the Hza already
>>has the 2 pi in it (2 pi Hz = 1 Hza)
>
>That's the point. If you use Hza you
>don't need the 2*pi in the function
>because it has the 2*pi already.
>
>Richard
>

What is confusing me is that when I define rpm in terms of Hza (which I must do for things like torque times speed = power to come out correctly, or centrifugal force to come put correctly), then the FFT resolves in plain Hz, not Hza.

Just one more piece of confusion we all deal with. At least Mathcad has units; I dispair of Matlab.

Fred Kohlhepp
fkohlhepp@sikorsky.com

[mzeftel]

The developer wrote back:

I looked at the thread and the attached 11 doc. I think it is just user confusion. Here is why

Mathcad is handling the units correctly



As expected. The quantities he is computing in the doc and passing to the fft are non dimensional (like you see above the units cancel out in the result)

so fft is returning a non dimensional vector.
When he plots the fft result, the plot is also responding correctly to the post scaling he is using whether Hz or Hza

Mona

[TomGutman]

Since Mathcad (still) doesn't have an angle dimension you will never get real consistency for quantities that depend on the angle dimension. The problem is that there are two common angular units used, the cycle and the radian, and it is up to the user to keep track of which is used in the representation of any particular quantity.

While the formal definition (according to standards) of the Hertz is just a reciprocal second, the side conditions in the standard, and the actual usage, make it clear that the Hertz is really what it always was, one cycle per second.

Angular velocities are commonly represented by one of two distinct units, the cycle per second and the radian per second. In common usage the symbol f is used for an angular velocity expressed in cycles per second, while ω is used for the exact same physical quantity expressed in radians per second. In Mathcad Hz is one cycle per second expressed in cycles per second. Hza is one cycle per second expressed in radians per second. rpm is one revolution per minute expressed, rather arbitrarily and without proper documentation, in radians per second. Thus rpm:=Hza/60 rather than the, perhaps expected, Hz/60.
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� � � � Tom Gutman