"does not mean" > "does mean"
Esteban
On 10/5/2015 8:47 PM, Esteban Maestre wrote:
By the way: complex-conjugate does not mean it rotates in opposite
direction; check out this picture:
http://www.eetasia.com/STATIC/ARTICLE_IMAGES/200902/EEOL_2009FEB04_DSP_RFD_NT_01c.gif
Rotation in opposite direction happens with negative frequencies.
Cheers,
Esteban
On 10/5/2015 8:06 PM, Stijn Frishert wrote:
Thanks Allen, Esteban and Sebastian.
My main thought error was thinking that negating the exponent was the
complex equivalent of flipping the sign of a non-complex sinusoid
(sin and -sin). Of course it isn’t. e^-a isn’t the same as -e^a. The
real part of a complex sinusoid and its complex conjugate are the
same, they only rotate in different directions.
And so the minus is to negate that rotation in the complex plane.
Correct me if I’m wrong, of course.
Stijn
On 5 Oct 2015, at 15:51, Allen Downey <dow...@allendowney.com> wrote:
In Chapter 7 of Think DSP, I develop the DFT in a way that might
help with this:
http://greenteapress.com/thinkdsp/html/thinkdsp008.html
If you think of the inverse DFT as matrix multiplication where the
matrix, M, contains complex exponentials as basis vectors, the
(forward) DFT is the multiplication by the inverse of M. Since M is
unitary, its inverse is its conjugate transpose. The conjugation is
the source of the negative sign, when you write the DFT in summation
form.
Allen
On Mon, Oct 5, 2015 at 9:28 AM, Stijn Frishert
<stijnfrish...@gmail.com> wrote:
Hey all,
In trying to get to grips with the discrete Fourier transform, I
have a question about the minus sign in the exponent of the
complex sinusoids you correlate with doing the transform.
The inverse transform doesn’t contain this negation and a quick
search on the internet tells me Fourier analysis and synthesis
work as long as one of the formulas contains that minus and the
other one doesn’t.
So: why? If the bins in the resulting spectrum represent how
much of a sinusoid was present in the original signal
(cross-correlation), I would expect synthesis to use these exact
same sinusoids to get back to the original signal. Instead it
uses their inverse! How can the resulting signal not be 180
phase shifted?
This may be text-book dsp theory, but I’ve looked and searched
and everywhere seems to skip over it as if it’s self-evident.
Stijn Frishert
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--
Esteban Maestre
CIRMMT/CAML - McGill Univ
MTG - Univ Pompeu Fabra
http://ccrma.stanford.edu/~esteban
--
Esteban Maestre
CIRMMT/CAML - McGill Univ
MTG - Univ Pompeu Fabra
http://ccrma.stanford.edu/~esteban
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