> On Tuesday, January 22, 2019 at 11:28:16 PM UTC-6, won...@gmail.com wrote:
>
> > Could u explain why u add 0 and 4 to the complex hermitian conjugate when a number is even.
>
> The reason to put *values* at DC and Fs/2 is because the DFT of a real sequence with an even number of elements is conjugate-symmetric about DC and Fs/2 -- they serve as "pivot points" for the symmetry. The reason that the values at DC and Fs/2 are *real* is that the only way a number can be its own complex conjugate is if it's real. The reason that the values are "0" and "4" has been lost to history -- this is, after all, an eleven year old thread.
>
> - Greg
Thanks Greg for your explanation.
Reply by ●January 23, 20192019-01-23
On Wednesday, January 23, 2019 at 8:01:23 AM UTC-5, Greg Berchin wrote:
> On Tuesday, January 22, 2019 at 11:28:16 PM UTC-6, won...@gmail.com wrote:
>
> > Could u explain why u add 0 and 4 to the complex hermitian conjugate when a number is even.
>
> The reason to put *values* at DC and Fs/2 is because the DFT of a real sequence with an even number of elements is conjugate-symmetric about DC and Fs/2 -- they serve as "pivot points" for the symmetry. The reason that the values at DC and Fs/2 are *real* is that the only way a number can be its own complex conjugate is if it's real. The reason that the values are "0" and "4" has been lost to history -- this is, after all, an eleven year old thread.
>
> - Greg
wow an 11 year gap and the conversation picks right up where it left off
:-)
mark
Reply by Greg Berchin●January 23, 20192019-01-23
On Tuesday, January 22, 2019 at 11:28:16 PM UTC-6, won...@gmail.com wrote:
> Could u explain why u add 0 and 4 to the complex hermitian conjugate when a number is even.
The reason to put *values* at DC and Fs/2 is because the DFT of a real sequence with an even number of elements is conjugate-symmetric about DC and Fs/2 -- they serve as "pivot points" for the symmetry. The reason that the values at DC and Fs/2 are *real* is that the only way a number can be its own complex conjugate is if it's real. The reason that the values are "0" and "4" has been lost to history -- this is, after all, an eleven year old thread.
- Greg
Reply by ●January 23, 20192019-01-23
Hi Greg,
Could u explain why u add 0 and 4 to the complex hermitian conjugate when a number is even.
THanks.
> On Jan 13, 5:52 am, "antenna404" <wanfa...@163.com> wrote:
>
> > I am sure that I have made my data Hermitian symmetric.
> > just like this:
> > 1-j*1,2-j*2,3-j*3,0,3+j*3,2+j*2,1+j*1.
> > but after doing IFFT,the output is still a complex sequence.
>
> Just as an experiment, try structuring your data set like
>
> "0, 3+j*3, 2+j*2, 1+j*1, 1-j*1, 2-j*2, 3-j*3",
>
> if your FFT size is odd, or
>
> "0, 3+j*3, 2+j*2, 1+j*1, 4, 1-j*1, 2-j*2, 3-j*3",
>
> if it is even, and run that through Matlab's IFFT.
>
> Greg
Reply by vizziee●January 15, 20082008-01-15
On Jan 13, 3:52 am, "antenna404" <wanfa...@163.com> wrote:
> hi Kumar Vijay Mishra
> I am sure that I have made my data Hermitian symmetric.
> just like this:
> 1-j*1,2-j*2,3-j*3,0,3+j*3,2+j*2,1+j*1.
> but after doing IFFT,the output is still a complex sequence.
But your data is, in fact, not complex conjugate symmetric! The
correct sequence will be: [0, 1-1i, 2-2i, 3-3i, 3+3i, 2+2i, 1+1i].
This is because the dc component is NOT included while considering the
above-said symmetry of the sequence.
Kumar Vijay Mishra.
Reply by Fajia Wang●January 15, 20082008-01-15
>On Sun, 13 Jan 2008 05:35:01 -0600, "antenna404" <wanfajia@163.com>
wrote:
>
>> In fact,I am dealing with a transmit-receiveing UWB antenna system
>>operating between 3.1GHz and 10.6GHz.
>> The frequency response is obtained from a VNA measurement,it appears
as
>>mag/phase pairs.I want to get the impulse response of the system.
>
>Wow. Deja vu all over again. That's exactly the problem I faced in my
>thesis research. In 1985.
>
>> I have zero padding the missing measurement betweeen 0Hz and 2GHz.
>
>That results in a convolution of your derived time domain waveform with
a
>sinc function. That method really doesn't work well, even with
>non-rectangular windows.
>
>>Then
>>conjugate-transformation is done to form Hermitian symmetric about 0Hz
>>before IFFT in matlab.
>
>I'm not certain whether Matlab needs [-Fs/2 ... Fs/2) or [0 ... Fs)
data.
>However, even if you got that wrong it still wouldn't explain the
imaginary
>parts in your IFFT outputs. It would just modulate by exp(jPI)
(alternate
>multiplying the time waveform by +1, -1.
>
>Are the imaginary parts in the IFFT waveform of roughly the same
amplitude as
>the real parts, or are they like "1.000432e-015" (which you should
interpret
>as zero)?
>
>>No action is taken between 12GHz and Fs/2.The
>>sampling frequency ,Fs,is 1/0.06GHz.
>
>I'm hoping that "1/0.06GHz" is greater than 2*12GHz.
>
>>should the missing measurement between
>>12GHz and Fs/2 be fill in to get the impulse response?
>
>Again, though this does not explain your complex time domain results, I
found
>it better to have as much of the spectrum as possible.
>
>Oh ... how did I solve the problem? Frequency Domain Least Squares, of
>course. Once I had the discrete transfer function, I could derive the
causal
>difference equation and use it to compute the impulse response. Matlab
>Tricks" article, Jan 2007 issue. If you don't have access to that, I can
get
>a copy to you.
>
>Greg
>
Hi,Greg.Thanks a lot for your help.
I am trying to use FDLS.But I know nothing about it yet.Please give one
copy of the magazine article in IEEE Signal Processing Magazine,Jan 2007
issue.It is not available to me on line.
My email:antenna404@163.com
Thanks again.
Fajia Wang
Reply by Greg Berchin●January 14, 20082008-01-14
On Jan 13, 5:52�am, "antenna404" <wanfa...@163.com> wrote:
> �I am sure that I have made my data Hermitian symmetric.
> just like this:
> 1-j*1,2-j*2,3-j*3,0,3+j*3,2+j*2,1+j*1.
> but after doing IFFT,the output is still a complex sequence.
Just as an experiment, try structuring your data set like
"0, 3+j*3, 2+j*2, 1+j*1, 1-j*1, 2-j*2, 3-j*3",
if your FFT size is odd, or
"0, 3+j*3, 2+j*2, 1+j*1, 4, 1-j*1, 2-j*2, 3-j*3",
if it is even, and run that through Matlab's IFFT.
Greg
Reply by Greg Berchin●January 13, 20082008-01-13
On Sun, 13 Jan 2008 05:35:01 -0600, "antenna404" <wanfajia@163.com> wrote:
> In fact,I am dealing with a transmit-receiveing UWB antenna system
>operating between 3.1GHz and 10.6GHz.
> The frequency response is obtained from a VNA measurement,it appears as
>mag/phase pairs.I want to get the impulse response of the system.
Wow. Deja vu all over again. That's exactly the problem I faced in my
thesis research. In 1985.
> I have zero padding the missing measurement betweeen 0Hz and 2GHz.
That results in a convolution of your derived time domain waveform with a
sinc function. That method really doesn't work well, even with
non-rectangular windows.
>Then
>conjugate-transformation is done to form Hermitian symmetric about 0Hz
>before IFFT in matlab.
I'm not certain whether Matlab needs [-Fs/2 ... Fs/2) or [0 ... Fs) data.
However, even if you got that wrong it still wouldn't explain the imaginary
parts in your IFFT outputs. It would just modulate by exp(jPI) (alternate
multiplying the time waveform by +1, -1.
Are the imaginary parts in the IFFT waveform of roughly the same amplitude as
the real parts, or are they like "1.000432e-015" (which you should interpret
as zero)?
>No action is taken between 12GHz and Fs/2.The
>sampling frequency ,Fs,is 1/0.06GHz.
I'm hoping that "1/0.06GHz" is greater than 2*12GHz.
>should the missing measurement between
>12GHz and Fs/2 be fill in to get the impulse response?
Again, though this does not explain your complex time domain results, I found
it better to have as much of the spectrum as possible.
Oh ... how did I solve the problem? Frequency Domain Least Squares, of
course. Once I had the discrete transfer function, I could derive the causal
difference equation and use it to compute the impulse response. Matlab code
for FDLS is available at
"http://apollo.ee.columbia.edu/spm/external/tipsandtricks/files/TandT_Jan2007.zip".
Explanation of the technique is in IEEE Signal Processing Magazine, "Tips and
Tricks" article, Jan 2007 issue. If you don't have access to that, I can get
a copy to you.
Greg
Reply by antenna404●January 13, 20082008-01-13
>You need to modify your frequency response to include "negative
>frequencies" before taking the IFFT. Here is how its done:
>
>http://www.dspguide.com/ch12/1.htm
>
Thanks a lot,Steven W. Smith.The book is very helpful!
Fajia