# Can gaussian low pass filter remove ringing effect from the image?

An image is convolved with an ideal low pass filter. The resultant image is convolved with a Gaussian low pass filter to obtain a final image. Will you observe ringing effect in the final image. WPlease give reason.

The ringing from convolving with an ideal low pass filter is Gibbs oscillations. If you convolve with a smooth function, you won't get ringing, but of course you will get some smoothing and attenuation. You could try multiplying by a function like $\exp(-x^4)$ in the Fourier domain or its ilk. These functions are flat around $0$, unlike the Gaussian, so they are more ideal low pass filter-like.