Warning: Rank deficient, rank = 0... means what?

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Rick
Rick 2012-9-25
评论： Clara Casado-Coterillo 2024-12-10
Hi,
I am using the original signal FS and nbits. When i played the sound, it does have the speech, but its very noisy. I am currently doing this:
wavwrite(sig, Fs, nbits, 'Scrambled.wav');
i = 1;
k = 1;
siz = wavread('Scrambled.wav', 'size');
tot_samples = siz(1);
while(i<=tot_samples-15)
y = wavread('Scrambled.wav',[i i+15]);
ori_sig(:,k) = y\H;
if i == 1;
disp('Descrambling Speech in Progress...');
end
i = i+16;
k = k+1;
end
recon_sig = reshape(ori_sig,size(ori_sig,1)*size(ori_sig,2),1);
sound(recon_sig);
I have this warning: "Warning: Rank deficient, rank = 0, tol = 0.000000e+00."
What does it mean?
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John D'Errico
John D'Errico 2024-12-10
编辑：John D'Errico 2024-12-10
@Clara Casado-Coterillo
Please don't post new questions as an answer to an old question. Ask your question separately.
As far as how to solve it, you need to post sufficient code to know why it is happening. We cannot see inside your computer. If it is annoying, it is the result of a mistake you made in some way, so annoyance should not be a factor. Write better code. Or post enough code that someone can help you.
Clara Casado-Coterillo
Clara Casado-Coterillo 2024-12-10
I did not mean any disrespect by "annoying", and it was my first post, so I ask a little bit of patience. Sorry to have asked. Won't happen again.

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采纳的回答

Wayne King
Wayne King 2012-9-25
编辑：Wayne King 2012-9-25
The inverse of a NxN matrix only exists only if the matrix has rank N. In other words, the linear operator that the matrix represents is surjective.
Computing the inverse in a computer has numerical subtleties. That warning is telling you that the matrix is rank deficient.
The wavwrite warning indicates that your signal values exceed +/- 1 and are being clipped when the .wav file is written. I don't think you want that clipping, that distorts the signal. You can scale the vector in MATLAB to make sure that the values do not exceed +/- 1 for writing.
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Rick
Rick 2012-9-25
编辑：Rick 2012-9-25
i see, than what does rank deficient matrix affects?
Brandon Sackett
Brandon Sackett 2020-11-18
Isn't a surjective solution valid though? I guess bijections are the "best" but is there a reason a surjective solution gets that warning? Any relation to group theory would help my brain understand the problem.

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Walter Roberson
Walter Roberson 2012-9-25
I can't tell what your "H" is there, but your "y" is all zero (or close to it) for 16 consecutive samples at some point.
The "clipped" indicates that you are attempting to write samples outside the range -1 to +1.
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Rick
Rick 2012-9-25
编辑：Rick 2012-9-25
H is a hadamard matrix of order 16.
Because i scrambled the signal using frame of 16 samples using:
y(:,k) = H*x;
k = k + 1;
I am now trying to descrambled it using 16 samples too by doing:
ori_sig(:,k) = y\H;
k = k + 1;
I know that clipping introduces distortion. Is there anyway where i can change the range of "y" to –1.0 <= y < +1.0, because I'm using 8 bits.

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