Image:Example dft dct.svg

The plot shows the differences between a en:DFT and a en:DCT of a generic signal.

The first plot is a sampled ramp in the time domain. The second one represents the modulus of its DFT. The third one the plot of its DCT.

I obtained it in a two step process. First I ran the following en:Matlab code:

n = 0:10;
E = [ n; abs(fft(n)); dct(n)];
E = E';
save -ascii 'example_dft_dct.dat' E;

thus creating a file called example_dft_dct.dat. Then I ran the following en:Gnuplot code:

# set the output
set terminal svg
set output "example_dft_dct.svg"

# axis properties
set xlabel "n"
set xrange [-1:11]
set xzeroaxis linetype -1 linewidth 0.5
set yzeroaxis linetype -1 linewidth 0.5
set xtics axis
unset ytics
set key off

set pointsize 1.5

# Set up a four-pane multiplot
set size 1,1
set origin 0,0
set multiplot

set title "A generic sampled signal"
set size 1,0.35
set origin 0,0.69
plot "example_dft_dct.dat" using 1:1 with points 1
plot "example_dft_dct.dat" using 1:1 with impulses 1

set title "The modulus of its DFT"
set size 1,0.35
set origin 0,0.36
plot "example_dft_dct.dat" using 1:2 with points 2
plot "example_dft_dct.dat" using 1:2 with impulses 2

set title "Its DCT"
set size 1,0.35
set origin 0,0.03
plot "example_dft_dct.dat" using 1:3 with points 3
plot "example_dft_dct.dat" using 1:3 with impulses 3

November 2005

Alessio Damato

see below