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Clipping Raster to Polygon

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I have a raster with 30m resolution, and I want to clip it using much smaller polygons. In the attached image, the pink and grey pixels are my original raster, and the blue pixel is what was returned using the clipping tool.

When I use the raster clipping tool with the option "use input features for clipping geometry", it looks like whats returned is a raster where pixels whose centroid are contained in the clipping geometry are returned. I want to keep all the pixels that intersect any part of my polygons.

Is there another tool I should be using or some other approach that would work?
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