On 10/7/15 3:02 PM, Theo Verelst wrote:
Stijn Frishert wrote:
Hey all,
In trying to get to grips with the discrete Fourier transform,
Depending on how deep you want to study/understand the subject, get a
good textbook on the subject, like "The Fourier Transform and its
Applications" from th
I think it's all starting to sink in.
(This may seem obvious to some, but as a way to chronicle this and for people
reading along and struggling with this as well.)
I've always seen the correlation as the original signal doing something to/with
the sinusoid (like scaling or projecting on it). I
Stijn Frishert wrote:
Hey all,
In trying to get to grips with the discrete Fourier transform,
Depending on how deep you want to study/understand the subject, get a good textbook on the
subject, like "The Fourier Transform and its Applications" from the Stanford "see"
courses, or this one whi
Ethan Duni wrote:
> Also there are different conventions about where to put the normalization
> constants (on the analysis side, or on the synthesis side, or take the
> square root and include it on both).
I remember it blew my mind when I first learned there was a symmetric form of
the Fourier
>the reason why it's merely convention is that if the minus sign was
swapped
>between the forward and inverse Fourier transform in all of the literature
and
>practice, all of the theorems would work the same as they do now.
Note that in some other areas they do actually use other conventions. It's
On 10/5/15 5:40 PM, robert bristow-johnson wrote:
about an hour ago i posted to this list and it hasn't shown up on my end.
okay, something got lost in the aether. i am reposting this:
On 10/5/15 9:28 AM, Stijn Frishert wrote:
In trying to get to grips with the discrete Fourier transform, I
On 10/5/15 9:28 AM, Stijn Frishert wrote:
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 searc
"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
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, S
Think of the Fast Fourier Transform as computing the inner product of a piece of signal
(the length of the transform) with all kinds of basis functions: the various frequencies
that can "fit" in the interval. Without going into engineering basics, you can take a sine
and a cosine as a basis func
Hi again,
You can see the Fourier Transform as a projection. Finding projections
can be seen as computing inner products. Inner products of complex
numbers (or functions) involve complex-conjugating one of the numbers
(functions).
Here's an alternative read:
https://sites.google.com/site/bu
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 conju
Since e^(-jw) equals 1/(e^(jw)), the same sinusoids are used, just
reverting what the other transformation did. No phase shift involved.
Sebastian
Stijn Frishert wrote:
Hey all,
In trying to get to grips with the discrete Fourier transform, I have a
question about the minus sign in the expo
On 10/5/2015 6:15 PM, Esteban Maestre wrote:
the complex sinusoid you are "testing", and its complex-conjugate
Sorry:
I mean "your signal and the complex sinusoid your are testing".
Esteban
--
Esteban Maestre
CIRMMT/CAML - McGill Univ
MTG - Univ Pompeu Fabra
http://ccrma.stanford.edu/~este
HI Stijn,
That "minus" comes from complex-conjugate (of Euler's formula). To find
the projection coefficients (Fourier Transform), in each of the terms in
the summation one computes the inner product of two complex vectors: the
complex sinusoid you are "testing", and its complex-conjugate. The
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
multiplic
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 Fourie
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