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The Discrete Fourier Transform 163
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signal x(n), 0 Y1 = dft(y1,10); magY1 = abs(Y1(1:1:6));
>> k1 = 0:1:5 ;w1 = 2*pi/10*k1;
>> subplot(2,1,2);stem(w1/pi,magY1);title(’Samples of DTFT Magnitude’);
>> xlabel(’frequency in pi units’)
The plots in Figure 5.9 show there aren’t enough samples to draw any conclusions.
Therefore we will pad 90 zeros to obtain a dense spectrum. As explained
in Example 5.7, this spectrum is plotted using the plot command.
MATLAB Script:
>> n2 = [0:1:99]; y2 = [x(1:1:10) zeros(1,90)];
>> subplot(2,1,1) ;stem(n2,y2) ;title(’signal x(n), 0 xlabel(’n’)
>> Y2 =dft(y2,100); magY2 = abs(Y2(1:1:51));
>> k2 = 0:1:50; w2 = 2*pi/100*k2;
>> subplot(2,1,2); plot(w3/pi,magY3); title(’DTFT Magnitude’);
>> xlabel(’frequency in pi units’)
Now the plot in Figure 5.10 shows that the sequence has a dominant frequency
at ω =0.5π. This fact is not supported by the original sequence, which has two
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