resolution of the observation itself is higher, the noise will add together depending on the size of such an integration element. The depth of the filament within that element then sets the frequency range for the integration. In order to estimate the noise for each filament, we take every point of the spine given by the filament catalogue, then use its redshift to determine the angular size of the filament diameter and add together the trapezoid shaped patches set by two neighboring spine points. The parallel sides of the trapezoid are set by the angular size by going up and down 0.5  $h^{-1}$Mpc in declination, whereas the other two sides of the trapezoid are formed by connecting the tops and bottoms of the parallel sides. Fig. \[fig:filnoise\] gives a sketch of how a filament is divided up into the trapezoid patches along the sky for the integration.\

![Sketch of the filament noise integration scheme. The blue line shows the spine of the filament in the sky plane, where the yellow dots denote the filament points from the filament catalogue. The black lines denote the angular size of the 1 $h^{-1}$Mpc filament diameter at each point, $\Theta_i$. The cyan shaded trapezoid 