Ghassanalregib ece6258 fall2012 9 questions f m n f

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Unformatted text preview: u, v) Over the entire plane u X , v Y Over an area (tile) in the plane Can we simplify this further? What if the signal is bandlimited? Ghassan AlRegib ECE 6258 Fall 2012 9 Questions? f [m, n] f a ( x, y ) • When can we reconstruct from ? Fa ( , w) F (u , v) • What is the relation between and ? Ghassan AlRegib ECE 6258 Fall 2012 10 f a ( x, y ) Reconstruct from f [m, n] Fa ( , w) • Fact: of a bandlimited signal is zero outside a region of finite extent • Thus, let us assume that X and Y are chosen to be small enough such that Then, becomes when Ghassan AlRegib 11 Ghassan AlRegib 12 3 9/3/2012 ECE 6258 Fall 2012 ECE 6258 Fall 2012 f a ( x, y ) Reconstruct from f [m, n] f a ( x, y ) Reconstruct from f [m, n] • So far, we showed that for a bandlimited Fa ( , w) signal, we can recover from Exactly Recovered F (X , Y ) f f a ( x, y ) • Now, let us derive from [m, n] Ghassan AlRegib ECE 6258 Fall 2012 13 ECE 6258 Fall 2012 f a ( x, y ) Reconstruct from f [m, n] Ghassan AlRegib Ghassan AlRegib 15 14 f a ( x, y ) Reconstruct from f [m, n] Ghassan AlRegib 16 4 9/3/2012 ECE 6258 Fall 2012 2‐D Sampling Theorem • A bandlimited continuous image m...
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