wfbm function wierdly crashes for a range of hurst exponent

The function wfbm(H,L) used to generate a fractional brownian signal returns an error for H .

H = 0.49;
L=200;
Brownian_signal = wfbm(H,L);

Returns an error inside wfbm itself.

Error using idwt

Lowpass (scaling) and highpass (wavelet) filters must be the same length and

must have an even number of samples.

Error in wfbm (line 145)

CA = idwt(CA,CD,fs1,gs1,len);

However it works fine for H={0.01 0.02 .... 0.48} soo any idea?

Answer 1

[Walter Roberson]

H-(1/2) is passed to an internal function named alphacfs .

In that function

I   = 1:1000;
cka = gamma(alpha+1)./(gamma(I).*gamma(alpha+2-I));

is calculated, and then find() is done to locate positions where abs(cka) <= 1e-4 . The beginning part of cka up to there is extracted and returned.

When H is in the range you indicate, it happens that the matching first location is at index 107, which is odd. When H is smaller then the first matching location is even. (The sign of the cka entries alternate.)

The returned coefficients are then conv() with something of length 20. When the coefficient length is 107 that gives a result of length 126. But the result of that is conv() again with something of length 2, which gives an final length of 127.

Then later the code checks to see whether the number of coefficients is odd or even, and finds that 127 is odd, and gives the error message.

The internal documentation implies that the code expects to work with H up to 1-eps but clearly it is not doing so.

I would say this is an internal bug that you should report.