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magnetra
Joined: 21 Apr 2005
Posts: 260
Helped: 3
Location: 27.45N, 85.20E KTM, NP
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 02 Mar 2006 13:59 White Noise |
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The psdf of white noise is N/2 when defined for both ±freq where as N when defined for positive freq. Why is it so? once defined for ±freq, why define again for only pos freq?
Magnetra
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carpa
Joined: 12 Nov 2004
Posts: 78
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| 02 Mar 2006 14:06 White Noise |
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| Only positive frequency has real meanings in real world. For example, you can only see spectrum for positive frequency in a spectrum analyzer.
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claudiocamera
Joined: 19 Aug 2005
Posts: 249
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Location: Salvador-BA-Brazil
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| 02 Mar 2006 17:51 White Noise |
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The PSD is an even function, thus Sn(-w) = Sn(w).
For the white noise the PSD is a constant "C" in practical values of frequency. For instance we can call "C" of N/2 , thus we can say that the PSD of the white noise is constant with the value of N/2.
The power over a range of frequency is the integral of the PSD in the specified range. As the PSD of white noise is constant we can say that P = (N/2)* 2* (Delta F), where delta F is the range of frequency ( positive values) . The question raised here is why multiplying by 2 ? The answer is simple for each positive interval of frequency we have a correspondent negative interval of frequency so that we need to consider both areas in the integration: areas due to positive and negative frequency intervals.
Now imagine if you have the frequency interval from 0 to wo , we have P = (N/2)*2*( wo-0) = N*wo, now consider wo goint to infinite. It is just your question... the positive range of frequency . Thus P = N*(positive range of frequency), now can you realize the answer of you question? I hope so.
By the way, there is nothing to do with what you can see in a spectrum analyzer. Negative frequency is a mathematical tool very useful in solving problems in real world.
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