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aad01e38-2ed2-4bf2-9bcc-1bfdeeb1c0a0 13 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

Fourier 2D Exercise

t0 1 time :

rgb

rgb 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mat :

Fourier

1. Define the functions

rgb cols rgb rows 12 mat 643312 mat

M cfft2d M mwfft2 :

M icfft2d M mwifft2 :

s mwfix s mwround ≡

M abs M mwabs eval :

A robust construct of the Matrix Scale function M Low High Scale min M Min : max M Max : maxmin max min - (1012 -^+ : HighLow High Low - (: i 1 M rows range j 1 M cols range N i j el M i j el min - maxmin / : for for HighLow N * Low + 61 line :

M nc nr Pad A M cfft2d : Fourier 2D cfft ≡ insert 'nc' cols in 'A' i 1 A rows range j 1 nc range vert i j el 0 : for for a A 1 A rows 1 A cols 2 / mwfloor submatrix : b A 1 A rows A cols 2 / mwfloor 1 + A cols submatrix : S a vert b augment transpose : insert 'nr' rows in the transpose 'S' i 1 S rows range j 1 nr range horiz i j el 0 : for for a S 1 S rows 1 S cols 2 / mwfloor submatrix : b S 1 S rows S cols 2 / mwfloor 1 + S cols submatrix : S a horiz b augment transpose : 111 line :

x lo hi f x lo ≤ 0 x hi ≥ 255 lo hi 21 mat 025521 mat x linterp if if :

f lo hi M Vectorise i 1 M rows range j 1 M cols range V i j el M i j el lo hi f eval : for for V 21 line :

2. Conclude the zoom demo

t0 1 time :

practical zoom limit 2 ≤

Group the recovered rgb S rgb 3216 Pad : iVrgb S icfft2d : RGB iVrgb mwabs eval : s RGB 0255 Scale : zoom s mwround : 51 line

Insert/center ncols/nrows inverse Fourier absolute of the inversed matrix scale to rgb grayscale round OFF the zoomed image 51 line

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Z f lo hi zoom Vectorise :

x 02551 range : i 1 x rows range reg i el x i el lo hi f eval : for Ω x reg augment : 31 line

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 Z

1 time t0 - 86 sec *

Typical RGB light intensifier

Ω region 2 1 sys