A simple but important question on white/colored noise

Dear all,

what are the features of white noise in theory?

2nd-when using "randn" in MATLAB to create a white gaussian noise; what is meant by "white" ? I mean that this noise isn't infinite. I think it is called "white" because it contains most of the frequencies as the white noise in theory.

3rd- I have a question! assuming randn as white noise, does convolving this white noise by impulse resposes of environment (hrir-head related impulse response) make it colored? (I think that will be whitenoise again)

looking forward to hear from you.
Regards,

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White Noise means, it distords all the frequency components of the signal equally, its PSD (Power Sepctral Density) is Unity or Constant over all the frequency range.

Coloured noise dont do so, it distord different frequencies differently,

And Gaussian (or Normal) is actually the distridution in the sence of probablities, ie how ther are distributed with their probablities

A MatLab randn signal is a bandlimited sampled signal. All differences to ideal white noise are related to this property.

Convolving white noise with any fixed impulse response (even another pseudorandom signal) adds some autocorrelation to the output signal and makes it coloured. The convoluting signal could be restored by analyzing the output for a sufficient long time period.

>what are the features of white noise in theory?

It has the same power at all frequencies. In other words, its auto corrleation is an impulse.

>2nd-when using "randn" in MATLAB to create a white gaussian noise; what is meant by "white" ? I mean that this noise isn't infinite. I think it is called "white" because it contains most of the frequencies as the white noise in theory.

It cant be white. When you are producing samples of a signal, you are inherently assuming it is bandlimited. If you think about it, an infinite spectrum signal cannot be sampled without aliasing, at any sampling rate, however high.

>3rd- I have a question! assuming randn as white noise, does convolving this white noise by impulse resposes of environment (hrir-head related impulse response) make it colored? (I think that will be whitenoise again)

randn isnt white, but it is gaussian. Like FvM said, if you get hold of a white noise signal and filter it, you distort its "same power at every frequncy" nature, and thus bandlimit it. It wont be white any longer.
-b