# Which information do we get from magnitude and phase spectrum?

I am learning image processing. I want to ask very basic question related to FFT topic

Which information do we actually get from "phase spectrum" and "magnitude spectrum" about an image?

• Hi ! It is not really clear what is the question under #3, so, if you can, elaborate :) – Sektor Jun 9 '14 at 19:43
• It's best to only ask one question per post. #1 is likely a duplicate of this previous question. #2 is probably answered in many places (frequency-domain filtering can yield improved speed for large filters). I'm not sure what you're asking in #3. #4 is a very vague question, so you'd need to clarify. – Jason R Jun 9 '14 at 20:23
• ieeexplore.ieee.org/iel5/5/31301/01456290.pdf?arnumber=1456290 – geometrikal Jun 10 '14 at 6:53
• @Jason R sir i have edited my 3rd question – sagar Jun 10 '14 at 9:49

You get the exact same information you will receive if you analyse a 1-D signal using the Fourier analysis tools, for example. To illustrate this consider the following examples

We perform Fourier Transform on it and obtain the following spectrum

As you can see there are two symmetric dots representing the frequency that is present in the image and the central, DC, component.

Next up

Again the Fourier Transform

It is obvious that the higher frequencies are further away from the DC, central, component. To understand the logic behind this you shall remember that we are actually working with complex numbers and their properties kick in.

To answer your second question: You are usually working with sparse data structures (vectors, arrays, tensors, etc.) in the frequency domain. Now you tell me which is easier: Working on the original data set consisting of 500 different values or the transformed one with half of them 0s ?

Now, the importance of phase - drum rolls - it is the same, meaning HUGE

Again, a sample image

Fourier Magnitude Spectrum

Fourier Phase Spectrum

Now, we inverse the transformation by using just the amplitude and then just the phase information

Inverted amplitude spectrum

Inverted phase spectrum

I think you get the idea :D

Now, here are some sample images and their respective amplitude and phase spectra, so you can practice a wee bit

• May I ask why the downvote ? – Sektor Jun 9 '14 at 20:17
• @Sektir To elaborate on the meaning of the magnitude and phase. The magnitude corresponds to the (values) of the pixels in the time domain. While the phase, tells us how these values should be organized to get the full picture. Therefore; the phase is dominant to the magnitude. +1 for the effort! – Adel Bibi Jun 9 '14 at 20:37