MF, are you *completely sure* that the H'(w) is intended to be a
derivative of H (with respect to what variable)? The "H prime" notation
tends to be used a lot to mean "complex conjugate" rather than
"derivative." That sort of interpretation seems more consistent with the
statement that "only one of the two spectral motifs must be
synthesized". That would make sense when one 'motif' is the complex
conjugate of the other -- synthesize one, and you know them both.
I don't know what that paper is referring to when it says "the inverse
FFT algorithm only uses the positive frequency half spectrum." Strictly
speaking that might be true. But beware, that half-spectrum typically
needs to be used in "complex conjugate mirror image" form to set up the
second half of your FFT inverse-transform, so that you get a real-valued
sequence out.
On 04/01/2015 01:07 PM, MF wrote:
Hi Forum,
I am trying to implement a formula from a paper:
Y(w) = e^(i*phase) * (H(w) + H’(w))
Where H is the fourier transform of a window function h (a blackman window
in my case), H’ is the derivative of H (in the paper, H and H' are called
spectrum motifs). A signal will then be generated from ifft(Y).
In the paper it says:
In practice, the signals to be synthesized are real, and the inverse FFT
algorithm only uses the positive frequency half spectrum, *so only one of
the two spectral motifs must be synthesized*.
I don’t understand what it means by “only one of the two spectral motifs
must be synthesized”. How do I decide which spectral motive to use?
ps. I simplified the formula for simplicity. But in case you want to see
the complete formula:
Y(wk) = e^(i*phase) * (0.5 * A * H(wk - wf) + 0.5* B *H’(wk - wf))
for |wk - wf| <= K * 2pi / N
ps2. sorry I just by accident posted the same question without a subject an
hour ago, is there a way to delete it from the archive?
Thanks in advance!!!
MF
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