What's difference between impulse and white noise signal?

Hello experts,
If impulse is one kind of white noise signal because of its flat power spectral density? If no, why?

Thanks in advance.

Best regards,
bittware

Re: What's difference between impulse and white noise signal

You are not comparing apples to apples. An impulse (delta function) is not a random process. When you say that it has a flat spectrum, you are referring to the Fourier Transform of a deterministic signal.

However, noise is a non-deterministic (or random) process, where the power is evenly distributed over all frequencies. For a random process, the power spectral density is defined to be the Fourier Transform of its autocorrelation, which you can see is a delta function. This means that a white noise signal only correlates with itself at t=0. In other words, a noise signal has no memory and a sample taken at any time has no correlation with any other sample taken at any other time (except when both times are equal, meaning the sample only correlates with itself).

Noise is a random process.Impulse does not fall under this category.But one similarity is that both impulse and white noise are ideal .

White noise is random process and it has flat spectrum. But the impulse doesnt.

But why you want to compare this two things, they are different right?

Re: What's difference between impulse and white noise signal

if you can a signal is impulse so it is not already random signal it is deterministic. but white noise signal is a random signal.

Hi

I see your point but comparing only the spectrum is not enough, in time domain noise exists all the time while an impulse is a single spike on a time To.

Sal

Re: What's difference between impulse and white noise signal

hi

White noise (Sample (help·info)) is a random signal (or process) with a flat power spectral density. In other words, the signal's power spectral density has equal power in any band, at any centre frequency, having a given bandwidth. White noise is so called as an analogy with white light which contains all frequencies.

An infinite-bandwidth white noise signal is purely a theoretical construct. By having power at all frequencies, the total power of such a signal is infinite. In practice, a signal can be "white" with a flat spectrum over a defined frequency band.


White random vector
A random vector is a white random vector if and only if its mean vector and autocorrelation matrix are the following:



I.e., it is a zero mean random vector, and its autocorrelation matrix is a multiple of the identity matrix. When the autocorrelation matrix is a multiple of the identity, we say that it has spherical correlation.

[edit]
White random process (white noise)
A continuous time random process w(t) where is a white noise process if and only if its mean function and autocorrelation function satisfy the following:



I.e., it is a zero mean process for all time and has infinite power at zero time shift since its autocorrelation function is the Dirac delta function.

The above autocorrelation function implies the following power spectral density.


since the Fourier transform of the delta function is equal to 1. Since this power spectral density is the same at all frequencies, we call it white as an analogy to the frequency spectrum of white light