File:DFT zero-padding technique example (2N) - DFT.pdf

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English: Example of zero-padding technique for the Discrete Fourier Transform (DFT): DFT of the gate sequence with .
Italiano: Esempio di tecnica di aggiunta degli zeri per la trasformata di Fourier discreta (DFT): DFT della sequenza porta con .
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Source Own work
Author Luca Ghio
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Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
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N=10;
n=[0:N-1]
x=[ones(1,N)];
y=fft(x,length(x));
figure
set (gca,'FontSize',14)
stem(n,x)
xlabel('n')
ylabel('x(n)')
axis([0 N-1 -0.5 1.5])
grid on

figure
set (gca,'FontSize',14)
stem(n,abs(y),'o')
xlabel('n')
ylabel('|X(k)|')
axis([0 N-1 -1 11])
grid on

N=10;
N1=2*N;
x=[ones(1,N) zeros(1,N1-N)];
n=[0:N1-1];
y=fft(x,length(x));
figure
set (gca,'FontSize',14)
stem(n,x)
xlabel('n')
ylabel('x(n)')
axis([0 N1-1 -0.5 1.5])
grid on

figure
set (gca,'FontSize',14)
stem(n,abs(y),'o')
xlabel('k')
ylabel('|X_z(k)|')
axis([0 N1-1 -1 11])
grid on

N=10;
N1=4*N;
x=[ones(1,N) zeros(1,N1-N)];
n=[0:N1-1];
y=fft(x,length(x));
figure
set (gca,'FontSize',14)
stem(n,x)
xlabel('n')
ylabel('x(n)')
axis([0 N1-1 -0.5 1.5])
grid on

figure
set (gca,'FontSize',14)
stem(n,abs(y),'o')
xlabel('k')
ylabel('|X_z(k)|')
axis([0 N1-1 -1 11])
grid on

N=10;
N1=1000;
x=[ones(1,N) zeros(1,N1-N)];
n=[0:N1-1];
y=fft(x,length(x));
f=n/N1;

figure
set (gca,'FontSize',14)
plot(f,abs(y))
xlabel('f')
ylabel('|X(e^{j2\pi f})|')
axis([0 1 -1 11])
grid on

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Date/TimeThumbnailDimensionsUserComment
current20:52, 22 January 2017Thumbnail for version as of 20:52, 22 January 20171,162 × 870 (5 KB)Luca Ghio (talk | contribs){{Information |Description= {{en|Example of zero-padding technique for the Discrete Fourier Transform (DFT): DFT <math>X(k)</math> of the gate sequence <math>x \left( n \right) = \begin{cases} 1 & 0 \leq n \leq N - 1 \\ 0 & n \geq N \end{cases}</math>...

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