Low Pass Filters pass low frequency components up to cutoff frequency and attenuate or eliminate high frequency components present in the image.

**Ideal LPF**Transfer function of Ideal LPF is given by,

H(u,v)= $1 \ \ \ \ if D(u,v)≤ D0 \\ 0 \ \ \ \ D(u,v)› D0$

Where,

D0: is a non-negative quantity (cut-off frequency)

D(u,v): is the distance from point (u,v) to the origin of the frequency plane and D(u,v) and $D(u,v)=\sqrt{(u^2+v^2 )}$

**Butterworth LPF**Transfer function of Butterwoth LPF is given by, $H(u,v)=\dfrac{1}{(1+[D(u,v)/D0]2N)}$

Where

D0 is the cutoff frequency

$D(u,v)= \sqrt{(u^2+v^2 )}$

N is the order of the filter

Butterworth LPF produces smooth transition in blurring as a function of increases cutoff frequency.

A Butterworth Filter of order 1 has no ringing. Ringing is imperceptive in filters of order 2 but can become a significant factor in filters of higher order.

**Gaussian Low-Pass Filter**Transfer function of Gaussian LPF is given by, $H(u,v) = \dfrac{e(-D(u,v))}{2σ2}$

Where

D(u,v): is the distance from the origin of the Fourier Transform

σ : is a measure of the spread of the Guassian Curve

Let σ = D0, then $H(u,v)=e\dfrac{(-D(u,v))}{2σ2}$ where D0 is cutoff frequency.

GLPF produces smooth transition I blurring as a function of increasing cutoff frequency. GLPF does not produce ringing effect. This is an important characteristic in practice.