Samples, Not Local Area Averages
{"Image DocumentName": "Samples, Not Local Area Averages", "Image ImageDescription": "We represent the continuous wave with a series of samples, which is NOT a local average. This can be most easily shown by Fourier transforming a 2D grid of ones. The result is a single non-zero mesh point at the center of a mesh, but adding a guard-band shows that the single non-zero mesh point is really an under-sampled sine function. Matlab Script. x=1:1:128; x3=1:0.5:128.5; E = ones(1,128); E2 = fftshift(fft(fftshift(E))); E3 = fftshift(fft(fftshift(addGuardBand(E ,1)))); figure; plot(x,E./max(E), -o ); hold on; plot(x3,abs(E3)./max(abs(E3)), g - ); plot(x,E2./max(E2), rx- ); zoomOut(0.1);", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}