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.
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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