9-1 一維內??

ҿסu@v]1-D Interpolation^ANOھڤ@դwI]]tJοXA䤤JO@ơAX]O@ơ^Aӫإߤ@ӳs򪺨ơAHKpNJIҹXȡC@kܦhAMATLAB ѤFذ򥻤kG

`NoؤkӶi满C

MATLAB ̱`Ϊ@OO interp1AzOQΦhӶi椺BCinterp1 ϥλyk

yi = interp1(x, y, xi, method)

䤤Vq x OI x yС]Jȡ^AVq y OI y yС]Xȡ^AVq xi OI]JȡAXȡ^Ar method hwϥΪkA@ءG

bUCdҤAڭ̨ϥΤWzke|بӹ@ƶi椺G

Example 1: 09-k/interp101.mx = 0:1:4*pi; y = sin(x).*exp(-x/5); xi = 0:0.1:4*pi; y1 = interp1(x, y, xi, 'nearest'); y2 = interp1(x, y, xi, 'linear'); y3 = interp1(x, y, xi, 'pchip'); y4 = interp1(x, y, xi, 'spline'); plot(x, y, 'o', xi, y1, xi, y2, xi, y3, xi, y4); legend('Original', 'Nearest', 'Linear', 'Pchip', 'Spline');

ѤWϥiݥXASpline M Cubic ҲͪuơA̩һݪpɶ][CHWo|ؤkpUG

  Nearest Linear Cubic Cubic Spline
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1]t^ 2 3 4]n^
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bϥ interp1 ɡAVq x OY滼WλAOjC~Axi d]b x d򤧤A~i椺BC

Hint
pG xi db x d򤧥~Aڭ̥iHϥ yi = interp1(x, y, xi, method, extrap) 覡Ӷi~]Extrapolation^AHDobd~ xi ҹ yi ȡC

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ϥΪ̥iHbWzϧεAC@ӨIANiHߨݨ줺uܤơA]PɥiHDUؤkSʡC

F interp1 ~At@Ӹ֥Ϊ MATLAB O interpft ii FFT]Fast Fourier TransformAֳtť߸ഫ^kCkpIť߸ഫAAΧKIӶiϳť߸ഫCinterft ϥλyk

y = interpft(yi, n)

䤤Vq yi O@ӸgѵZIƭȡAn hOZIIơCҦpG

Example 2: 09-k/interpft01.mn = 11; % Number of the original data points factor = 4; % Increase the data by this factor x = linspace(0, 2*pi, n); y = sin(x).*exp(-x/5); xi = (0:factor*n-1)*(x(2)-x(1))/factor; yi = interpft(y, factor*n); plot(x, y, 'ro', xi, yi, '.-'); legend('Original', 'Curve by interpft');

Hint
@ӨAuqLC@ӤwIAӰjkuhݭnqLIC]AkAΩTܤ֪˸ơC]uXΰjkRAаѾ\ѡuuXPjkRv`C^

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bUCdҤAڭ̦@CӸIAGbGתŶAڭ̥iHϥ interp1 spline kAӵeXs򥭷ƪϧΡApUG

Example 3: 09-k/interp102.mx = [0 2 4 3 1 2 1]; y = [4 1 2 4 5 2 0]; index = 1:length(x); index2 = linspace(1, length(x), 101); x2 = interp1(index, x, index2, 'spline'); y2 = interp1(index, y, index2, 'spline'); plot(x, y, 'o', x2, y2, '-'); legend('Origianl data', 'Interpolated data');

bWzdҤA즳ƥuCIAOϥΤ@Aڭ̴NiHͥƳs򪺹ϧΡAo]ObqϾǡ]Computer Graphics^̱`kA]NOHּƱI]Control Points^ӥN@ӪAMAϥΤӲ;Ӫ󪺲ӽoϧΡC

MApGڭ̿ΤPkAo쪺ƮĪG]|PAUCdҨϥ interp1 |ؤkAӹW@ӽdҪIi椺ApUG

Example 4: 09-k/interp103.mx = [0 2 4 3 1 2 1]; y = [4 1 2 4 5 2 0]; index = 1:length(x); index2 = linspace(1, length(x), 101); x2 = interp1(index, x, index2, 'nearest'); y2 = interp1(index, y, index2, 'nearest'); x3 = interp1(index, x, index2, 'linear'); y3 = interp1(index, y, index2, 'linear'); x4 = interp1(index, x, index2, 'pchip'); y4 = interp1(index, y, index2, 'pchip'); x5 = interp1(index, x, index2, 'spline'); y5 = interp1(index, y, index2, 'spline'); plot(x, y, 'o', x2, y2, '-'); plot(x, y , 'o', x2 ,y2, x3 ,y3 ,x4 ,y4, x5, y5); legend('Original', 'Nearest', 'Linear', 'Pchip', 'Spline');

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