# 2D IFFT implementation

I have a problem where I need to obtain 2D IFFT of a $$81\times64$$ signal. However, if we denote the reconstructed image $$I_{m,n}$$, its coordinates will be $$M\times N$$ but the k-space signal is sampled in a different fashion such as $$k_x\in[-200,200]$$ and $$k_y\in[-200,193.75]$$. How do i invert this sampled k-space signal? Thanks in advance.

• an IFFT (==IDFT) is a discrete transform that maps from discrete spaces to discrete spaces. If your k-space is continuous/compact, then the IFFT is not what you need. This sounds like you're a physicist. I think you will need to give us a lot more context on what you're doing for us to be able to help you. – Marcus Müller Nov 17 '19 at 15:41
• I see why the notation of k-space is ambigious in my question. I shall add that $k_x$ and $k_y$ are discrete in steps of 5 (i.e. $k_x$=[-200,-195, ... , 195, 200]). – strahd Nov 17 '19 at 17:04
• oh, then your notation is a bit unusual to me ($[a,b]$ to me is the compact interval between including $a$ and $b$). What are the "meanings" of these numbers? I'd generally understand transformed variables to be relative to the sampling rate, and thus inherently to something like $[0,1]$ or $[-\pi,\pi]$, depending on notation. – Marcus Müller Nov 17 '19 at 17:57
• again, I think this would really be easier for you if you actually described the context in which you're doing all this. "-200" doesn't tell us anything, because that's just relative to something in your system, which we don't know. That's like asking us which color of wire to cut: sorry, not our bomb. – Marcus Müller Nov 17 '19 at 20:57