http://imagej.273.s1.nabble.com/Frequency-Filtering-in-Time-Dimension-tp5021367p5021385.html
plots of various filters, and it seems Gaussian is pretty non-brick wall. I
> Hi Jacob,
>
> when you are doing a Gaussian Blur, in the Fourier domain it corresponds
> to multiplying the amplitudes with a Gaussian as well.
>
> A Gaussian
> exp(-pi * x²/a²)
> in real space corresponds to
> exp(-pi * f² * a²)
> in Fourier space
>
> If you want to attenuate a frequency component f1 by a factor 1/e =
> 0.37, you thus need a² = 1/(pi f1²), i.e. exp (pi² * f1² * x²)
>
> In terms of sigma, a Gaussian is given by
> exp(-x²/(2*sigma²))
>
> Thus, attenuation by a factor of 1/e at f1 corresponds to
> sigma = 1/(pi * f1 * sqrt(2))
>
>
> You can easily check it with the following macro:
>
> period = 16; // between about 10 and 100
> // best accuracy with powers of 2
> f=1/period; // spatial frequency
> newImage("Untitled", "32-bit white", 256, 256, 1);
> run("Macro...", "code=v=sin(2*PI*x*"+f+")"); //create sine wave
> sigma = 1/(PI*f*sqrt(2));
> run("Gaussian Blur...", "sigma="+sigma);
> run("Set Measurements...", "min display redirect=None decimal=4");
> makeRectangle(25, 0, 200, 256);
> run("Measure");
>
>
> You will see that the maxima and minima of the sine wave (which has had
> an original amplitude of 1) gets attenuated to an amplitude of about 0.37.
>
> If you take sigma = 1/(pi * f1) you will get an attenuation factor of
> 1/e² = 0.13 at the frequency f1.
>
> So far an excursion into the math of Gaussians and their Fourier
> transform...
>
>
> Michael
> ________________________________________________________________
> On 30.10.18 16:23, Jacob Keller wrote:
> >>
> >> do you have simply a 1D data set or an image stack, with slices for
> >> different times?
> >>
> >
> > The latter--image stack, one plane over time.
> >
> > - In the second case, you can use Process>Filters>Gaussian Blur 3D and
> >> specify the x and y sigma as zero.
> >> For high-pass filtering, you would have to duplicate the stack first
> and
> >> then subtract the filtered image.
> >>
> >
> > Ah, this is a great idea--I will try it out. How can I figure out the
> > relationship between sigma and the desired frequency cutoff? For
> example,
> > let's say the stack has 120 frames per period--what sigma value should
> be
> > input?
> >
> > Thanks very much for these suggestions--I think they are going to be
> > very helpful,
> >
> > Jacob
> >
> > If you rather want moving averages or a median, you can reslice the
> >> stack (Image>Stacks>Reslice) to have the time direction in x or y and
> >> apply the 'Fast Filters' plugin, which can do 1D filtering. Then
> Reslice
> >> to make time the z axis again.
> >> The 'Fast Filters' plugin also has an option to subtract the filtered
> >> image (i.e., highpass operation)
> >>
> >>
> >> Michael
> >> ________________________________________________________________
> >> On 29.10.18 20:51, Jacob Keller wrote:
> >>> Hi All,
> >>>
> >>> is there a way to do high-pass/low-pass filtering in the time
> dimension?
> >> Or
> >>> a suggestion for a workaround?
> >>>
> >>> All the best,
> >>>
> >>> Jacob Keller
> >>
> >> --
> >> ImageJ mailing list:
http://imagej.nih.gov/ij/list.html> >>
> >
> > --
> > ImageJ mailing list:
http://imagej.nih.gov/ij/list.html> >
>
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