What is the effect of changing the order of a Butterworth filter from 3 to 5?

Changing the order of a Butterworth filter from 3 to 5 will result in the image appearing sharper. A Butterworth filter is designed to provide a smoother response in the passband, and increasing the filter order enhances its ability to attenuate frequencies in the transition band more steeply. This steeper roll-off allows the filter to preserve more high-frequency information, which contributes to sharpening the details in an image.

As the order increases, the filter becomes more selective, distinguishing between the low and high-frequency components more effectively. Therefore, while the image retains essential features, the details become clearer and more pronounced, leading to a sharper overall appearance. Higher-order filters can enhance edge definition, which is vital in imaging modalities where clarity is critical for diagnostic purposes.

Understanding the impact of filter order is essential in applications such as nuclear medicine imaging, where detail and contrast are crucial for accurate interpretation.