
How do I create a white noise signal that has a sampling rate of 8 kHz and duration of 5 seconds?
The signal
should be zero-mean with variance equal to 1. Plot the magnitude and phase spectra of the signal at the
beginning, the middle and the end. The frequency resolution of the 1024-point spectra should at least be
1 Hz.
White noise has equal energy in all bands, and sounds like rushing air. you may obtain this by generating a list, v[*], which is a uniformly distributed pseudo-random sequence of samples;
Let N = | v[*] | = 8000 × 5 = 40000 samples, and given some amplitude, A, then
∀i: -A <= v[i] <= +A.
" variance of a random variable or distribution is the expected, or mean, value of the square of the deviation of that variable from its expected value or mean. " so, because mean=0, then variance = ( Σ v[i]² ) / N.
You will find that, to get a variance equal to 1,
A = √3
this should be enough info for you to generate all your samples with a little computer program.
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