If you want to achieve this effect, you'll need to get creative with CSS and JavaScript. While CSS doesn't have native support for blur, you can simulate it using text-shadow as explained here. It's also possible to blur images with a combination of jQuery, CSS, and JavaScript, although dealing with partial image blurring presents its own challenges.
Should you choose to tackle this task, you'll likely need to use JavaScript to detect which parts of the page pass under the banner and apply the appropriate styles. The complexity of this task will depend on your page layout, but in an ideal scenario where both the banner and content container match the body width, implementing the necessary scanning functionality shouldn't be too difficult. However, real-world scenarios are rarely that simple, and if the effort outweighs the benefits, it might be wise to consider alternative strategies with better returns.