Continue to Site

Welcome to

Welcome to our site! is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

Why the PSDF of white noise is N/2 ?

Not open for further replies.


Full Member level 5
Apr 21, 2005
Reaction score
Trophy points
27.45N, 85.20E KTM, NP
Activity points
White Noise

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?


White Noise

Only positive frequency has real meanings in real world. For example, you can only see spectrum for positive frequency in a spectrum analyzer.

White Noise

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.

Not open for further replies.

Similar threads

Part and Inventory Search

Welcome to