Keywords: Fourier transform, Fourier series, DTFT, DFT.gif sampling at interval T and/or periodic summation at interval P of the underlying time-domain function 2014-08-02 09 21 16 own Bob K https //commons wikimedia org/wiki/File Variations_of_the_Fourier_transform tif Matlab commands <source lang Matlab > N 1024; x -N/2 N/2-1; 1xN y exp -0 1 x 2 ; 1xN z exp -0 8 x 2 ; 1xN Y fftshift abs fft y zeros 1 7 N ; W exp j 2 pi/ 3 N x' -4 N 4 N-1 ; Nx1 1x8N Z abs z W ; 1xN Nx8N figure subplot 2 2 1 area -4 N 4 N-1 Y 'FaceColor' 0 4 6 xlim -4 N 4 N-1 ; set gca 'XTick' 0 set gca 'YTick' ylabel 'amplitude' xlabel 'frequency' subplot 2 2 3 area -4 N 4 N-1 Z 'FaceColor' 0 4 6 xlim -4 N 4 N-1 ; set gca 'XTick' 0 set gca 'YTick' ylabel 'amplitude' xlabel 'frequency' Y1 zeros 1 8 N ; Y1 1 128 end Y 1 128 end ; subplot 2 2 2 stem -4 N 4 N-1 Y1 '-' 'Color' 0 4 6 ; set findobj 'Type' 'line' 'Marker' 'none' xlim -4 N 4 N-1 ; set gca 'XTick' 0 set gca 'YTick' ylabel 'amplitude' xlabel 'frequency' Z1 zeros 1 8 N ; Z1 1 128 end Z 1 128 end ; subplot 2 2 4 stem -4 N 4 N-1 Z1 '-' 'Color' 0 4 6 ; set findobj 'Type' 'line' 'Marker' 'none' xlim -4 N 4 N-1 ; set gca 'XTick' 0 set gca 'YTick' ylabel 'amplitude' xlabel 'frequency' </source> cc-zero math Uploaded with UploadWizard Fourier analysis Digital signal processing |