### Example: Synthesis of 1/F Noise (Pink Noise)

Pink noise^{7.10}or ``1/f noise'' is an interesting case because it occurs often in nature [294],

^{7.11}is often preferred by composers of computer music, and there is no exact (rational, finite-order) filter which can produce it from white noise. This is because the ideal amplitude response of the filter must be proportional to the irrational function , where denotes frequency in Hz. However, it is easy enough to generate pink noise to any desired degree of approximation, including perceptually exact.

The following Matlab/Octave code generates pretty good

*pink noise*:

Nx = 2^16; % number of samples to synthesize B = [0.049922035 -0.095993537 0.050612699 -0.004408786]; A = [1 -2.494956002 2.017265875 -0.522189400]; nT60 = round(log(1000)/(1-max(abs(roots(A))))); % T60 est. v = randn(1,Nx+nT60); % Gaussian white noise: N(0,1) x = filter(B,A,v); % Apply 1/F roll-off to PSD x = x(nT60+1:end); % Skip transient responseIn the next section, we will analyze the noise produced by the above matlab and verify that its power spectrum rolls off at approximately 3 dB per octave.

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Example: Pink Noise Analysis

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Example: FIR-Filtered White Noise