Chris' Page for HW 13 (Sampling at 3Hz): Difference between revisions
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'''Sample <math> sin( 2 \pi nt) </math> at |
'''Sample <math> sin( 2 \pi nt) </math> at 3 Hz; take the DFT, explain the results.''' |
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<pre> |
<pre> |
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</pre> |
</pre> |
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[[Image:3Hz&1kHz.jpg]] |
[[Image:3Hz&1kHz.jpg]] |
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<Pre> |
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figure(3) |
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plot(f1,2*abs(Y1(1:NFFT1/2))) |
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axis([0 2 0 1]) |
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title('3Hz Sampele Rate') |
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xlabel('Frequancy') |
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ylabel('Magnitude') |
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figure(4) |
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plot(f2,2*abs(Y2(1:NFFT2/2))) |
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axis([0 12000000 0 1]) |
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title('1Khz Sample Rate') |
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xlabel('Frequancy') |
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ylabel('Magnatude') |
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</pre> |
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[[Image:3HzSample.jpg]] |
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[[Image:1kHzSample.jpg]] |
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---- |
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With only 3 samples points per cycle the sinusoid looks like a triangle wave. Having too few sample points results in a DFT with edge effects that are large compared to the actual signal. As the number of sample points increases the accuracy of the digitized function increases and the DFT becomes a better representation of the true frequency components. |
Latest revision as of 15:47, 14 December 2007
Sample at 3 Hz; take the DFT, explain the results.
t1 = 0:1/3:3; t2 = 0:1/1000:3; y1 = sin(2*pi*t1); y2 = sin(2*pi*t2); NFFT1 = 2^nextpow2(length(y1)); NFFT2 = 2^nextpow2(length(y2)); Y1 = fft(y1,NFFT1)/length(y1); Y2 = fft(y2,NFFT2)/length(y2); f1 = 1/3./(2*linspace(0,1,NFFT1/2)); f2 = 10000./(2*linspace(0,1,NFFT2/2)); figure(2) hold on h = stem(t1(1:10),y1(1:10),'fill','--'); set(get(h,'BaseLine'),'LineStyle',':') set(h,'MarkerFaceColor','green') plot(t1(1:10),y1(1:10), t2(1:3000), y2(1:3000)) legend('3Hz Sample Points','Sine sampled at 3Hz','Sine sampled at 1kHz') xlabel('Time in seconds') ylabel('Magnitude') title('Sin(2\pi t) Sampled at 3 Hz') hold off
figure(3) plot(f1,2*abs(Y1(1:NFFT1/2))) axis([0 2 0 1]) title('3Hz Sampele Rate') xlabel('Frequancy') ylabel('Magnitude') figure(4) plot(f2,2*abs(Y2(1:NFFT2/2))) axis([0 12000000 0 1]) title('1Khz Sample Rate') xlabel('Frequancy') ylabel('Magnatude')
With only 3 samples points per cycle the sinusoid looks like a triangle wave. Having too few sample points results in a DFT with edge effects that are large compared to the actual signal. As the number of sample points increases the accuracy of the digitized function increases and the DFT becomes a better representation of the true frequency components.