One sided noise spectral density VS double sided noise spectral density

In summary, the one-sided noise spectral density (No) and the double-sided noise spectral density (N) have a relationship of 2N = No. This relationship is due to the difference in representation of complex and real signals, where a complex signal has a one-sided spectrum while a real signal has a two-sided spectrum. The power spectral density (PSD) of thermal noise also differs depending on the type of representation, with N0 being equal to 2N for white noise.
  • #1
unseensoul
47
0
No is the one sided noise spectral density in communication systems. N is the double sided noise spectral density.

The relationship between them is given by 2N = No but I don't understand why it is like that. Why isn't it N = 2No instead?!
 
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  • #2
A complex signal like [tex]\exp{i\omega_0 t}[/tex] has a one-sided spectrum, in this case [tex]\delta(\omega-\omega_0)[/tex]. Its real counterpart [tex]\cos{\omega_0 t}[/tex] has the two-sided spectrum

[tex]\frac{1}{2}[\delta(\omega-\omega_0)+\delta(\omega+\omega_0)][/tex]

The same power is spread in the real-signal case over positive and negative frequencies, each of which is half as large as the complex spectrum.

When you talk of the power spectral density (PSD) of thermal noise, it again matters whether you are using a real or a complex representation. Audio engineers often use the former, for instance, communications engineers generally the latter. For white noise where the PSD is a constant, and using your notation where N is two-sided and N0 is one-sided, they are related by N0 = 2N.
 

1. What is the difference between one sided noise spectral density and double sided noise spectral density?

One sided noise spectral density refers to the power spectrum of a signal that is only measured in the positive frequency domain, while double sided noise spectral density refers to the power spectrum of a signal that is measured in both positive and negative frequency domains.

2. Why is it important to differentiate between one sided and double sided noise spectral density?

It is important to differentiate between one sided and double sided noise spectral density because they represent different aspects of a signal's noise characteristics. One sided noise spectral density is typically used to analyze signals in the frequency domain, while double sided noise spectral density is used for noise calculations in the time domain.

3. Which type of noise spectral density is more commonly used in scientific research?

One sided noise spectral density is more commonly used in scientific research because it is easier to interpret and provides a more accurate representation of a signal's noise characteristics in the frequency domain. However, double sided noise spectral density is still important for certain applications, such as noise calculations in electronic circuits.

4. How are one sided and double sided noise spectral density related?

One sided noise spectral density is related to double sided noise spectral density through the Fourier transform. The one sided noise spectral density is equal to half of the double sided noise spectral density, as the negative frequency components are mirrored in the positive frequency domain.

5. Can one sided noise spectral density be converted to double sided noise spectral density?

Yes, one sided noise spectral density can be converted to double sided noise spectral density by multiplying it by 2. However, the reverse is not true as the negative frequency components cannot be accurately determined from the positive frequency components alone.

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