Fourier Transform of a Sinc Function

[nickc75]

Hello,

I am trying to demonstrate the Fourier Transform property between the Sinc fuction and the Rect (rectangle) function.  In my case, the Sinc function is in the time domain.  When I put this through the FFT block (using Hanning window), I don't get the Rect function, in fact I don't get anything like it, and I am trying to figure out why.  I found a similar posting here, but I don't fully understand why it is necessary to do what the response given there indicates.  Ultimately I want to compute the convolution of the sinc function with blocks of my continuously acquired time domain signal, essentially low pass filtering the input signal.  Since my signals are not periodic, I am using the windowed FFT.  I have studied digital signal processing (e.g. Oppenheim and Schafer, 1975), but this seems like it should be very simple to show the relationship between the Sinc and Rect pair in LabVIEW.   My code is attached.  Any advice would be greatly appreciated.

N.

[natasftw]

You're trying to merge theory with a practical usage.  The theoretical response is something you're calculating by hand. 

The FFT is a special case of the discrete fourier transform.  When you start entering the discrete world, you're not longer working with a continuous signal.  If you've studied DSP, you should be aware the sinc is an infinite signal.  You mentioned it's not periodic, which is correct.  There's a reason the sinc cannot truly be captured in a practical environment.  It's the same reason the dirac delta is a theoretical signal. 

You want to compute the convolution of an infinite signal.  How?  Are you going to flip and slide your convolution forever?  If not, you're never going to encapsulate the sinc.

[altenbach]

It makes no sense whatsoever to apply a window here. All your interesting data is early in the trace.

Use the plain transform and adjust dt and df of the graph directly.

Works just fine here, Try it!