FFT INVERSE ANALYSIS

[ilver belletti]

If you have a real number series, if you perform a FFT analysis you get a
series of complex numbers that are the components in the frequency domain of
the function. If you perform an inverse FFT analysis from a complex number
series why do you get again a complex number series ?
Are the real parts the function from which you get the initial harmonic
components ?
What is the meaning of the imaginary parts ?
Best Regards
Ilver Belletti

 

[Dana DeLouis]

If you perform an inverse FFT analysis from a complex number

series why do you get again a complex number series ?

Hi. A fft program works with both a real & imaginary array of data.
If you take the FFT of Real data, and then take the Inverse, you should end
up with the original array of Real data.
Is this not happening for you?
The inverse of a random array of complex numbers would most likely return
complex numbers.
An array of Real data such as {1,2,3,4}, is really {1+0 i, 2+0 i, 3+0 i, 4+0
i} to a FFT Program.
In Excel you can take the FFT of an array or Real Data {1,2,3,4}.
However, like most FFT programs, Excel can take the FFT of an array of
string data in the following format {1i, 2i, 3i, 4i}
(You can use the letter "j" as well)
The only difference here is that the output will be phased 90 Degrees.

What is the meaning of the imaginary parts ?

It's a shorthand notation for Euler's equation to represent Cos(x)+i Sin(x).
Together, it's just a single Sin (or Cos) function whose phase is shifted.
See the equations (1) and (2) for some discussion on this.
Note the phase shift from (3) which is usually the hard part to see.
http://mathworld.wolfram.com/ComplexNumber.html

By some "Standard", the position of the complex number in the output of the
FFT determines it's frequency.
The first output has 0 frequency (DC component, Average value, etc). The
second ouput is the main Harmonic, etc.

 

[ilver belletti]

If I have a series of 400 complex numbers, that is not a power of 2 (512), is
there a way to calculate the real number sequence of wich the complex number
series is the FFT ?
With the inverse FFT function I get again a complex number series because I
have to use only 256 numbers, can I add 112 complex numbers with zero real
and imaginary parts ?
Best Regards
Ilver Belletti

 

[Dana DeLouis]

How did you get the 400 complex numbers?
Did you do a FFT on 400 real data using a different program, and then
looking to do an inverse using Excel?

 

[ilver belletti]

I get the complex numbers from an analyzer during a gearbox no load test and
now I would like to get the real signal.
Best Regards
Ing. Ilver Belletti

 

[Dana DeLouis]

I get the complex numbers from an analyzer during a gearbox no load test..

Hi. Very interesting. :>)
The reason I asked is that I was curious on your first value.
The first value is usually a Real value (Not complex) that is the average,
or sum, of all your real values. If it was from Excel, it would be the sum.
I'd be curious to learn if there are any Real data in your list??
If you have all complex numbers, then I'm not sure if you will be able to
inverse your data to get all real data.

In general, no. That technique usually won't work (afaik).
There is a "zero-packing" technique where you can insert the same amount of
0's between each complex value.
(One can also 'Fold' the data as well.) However, I don't see a way to bring
this to a 2^x value.
What this means is that complex data {A,0,B,0,C,0,D,0} has an inverse of
{a,b,c,d,a,b,c,d}.
Again, trailing 0's usually doesn't work (afaik)

Some analyzer's rotate the fft data to display the zero frequency in the
middle of the display. We will have to watch for that.
The best thing I think is to use is a FFt that can operate on non-radix 2
size data.

Feel free to send me your data, and I'll take a look at it via another
program. I may be able to check it against a few different equations.
There are a few standard equations for a FFt. I'm not sure which one your
analyzer uses.