Question: Explain various frequency domain in low pass filter in detail
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Mumbai University > Computer Engineering > Sem 7 > Image Processing

Marks: 10 Marks

Year: May 2016

 modified 2.9 years ago  • written 2.9 years ago by Sayali Bagwe • 2.2k
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Low Pass Filters pass low frequency components up to cutoff frequency and attenuate or eliminate high frequency components present in the image.

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

1. 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.

1. 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.