# FWHM Equations

If it is desired to reduce high frequency 2D spatial noise, a LPF (Low Passs Filter) can be used by selecting a LPF choice. Then prior to the FFT, the fid image is multiplied by the specified 2D filter.

The K-space gaussian filter has a HWHM (Half Width - Half Maximum) equal to the radius specified in Radius field. The FWHM (Full Width - Half Maximum) is simply equal to twice the radius. The values, g(r), of the gaussian filter are given for one dimension in Equation 1 for a radius = h and an image width of N pixels. The for the HWHM radius, h, is given in Equation 2. Multiplication in K-space is equivalent to convolution in Image-space. Thus the relationship between gaussian filter FWHM in K-space to the FWHM in Image-space can be determined by taking the Fourier Transform (FT) of the K-space gaussian. But a gaussian with in the numerator is just another gaussian with in the denominator. By equating the exponents and replacing , the Image-space can be determined. From equation 2 the Image-space HWHM, , is Substituting for and noting that FWHM = 2h John Paul Strupp
Wed Jan 29 11:44:13 CST 1997