Hello all, I have got the system transfer function of a two port network in frequency domain,the frequency range is from 2Ghz to 12GHz.IFFT is used to get the time domain impulse response,but the result is complex ,not real.The impulse response of a system should be real.So,please give me some suggestions.thanks .

# How to use IFFT to get the system impulse response?

Started by ●January 11, 2008

Reply by ●January 11, 20082008-01-11

On Jan 11, 7:26�am, "antenna404" <wanfa...@163.com> wrote:> I have got the system transfer function of a two port network in frequency > domain,Do you mean that you have samples of the frequency response, either as real/imag or mag/phase pairs?> the frequency range is from 2Ghz to 12GHz.IFFT is used to get the > time domain impulse response,IFFT requires evenly-spaced frequency samples from 0 Hz to half the sampling frequency. How are you filling-in the missing measurements between 0 Hz and 2 GHz, and between 12GHz and Fs/2 (half the sampling frequency)? What are you assuming Fs to be?> but the result is complex ,not real.The > impulse response of a system should be real.So,please give me some > suggestions.thanks .For a real impulse response, the frequency domain data must be conjugate-symmetric about Fs/2 (or about 0 Hz). Are you satisfying this requirement? Or are you doing some sort of baseband processing? Greg

Reply by ●January 11, 20082008-01-11

> but the result is complex ,not real.The > impulse response of a system should be real.You can get a real sequence (after doing IFFT) only when the magnitude of frequency response is symmetric and phase response anti-symmetric. So make sure your data is in line with this. Kumar Vijay Mishra.

Reply by ●January 11, 20082008-01-11

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

Reply by ●January 13, 20082008-01-13

>> but the result is complex ,not real.The >> impulse response of a system should be real. > >You can get a real sequence (after doing IFFT) only when the magnitude >of frequency response is symmetric and phase response anti-symmetric. >So make sure your data is in line with this. > >Kumar Vijay Mishra. >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.

Reply by ●January 13, 20082008-01-13

>On Jan 11, 7:26=A0am, "antenna404" <wanfa...@163.com> wrote: > >> I have got the system transfer function of a two port network infrequency=> >> domain, > >Do you mean that you have samples of the frequency response, either as >real/imag or mag/phase pairs? > >> the frequency range is from 2Ghz to 12GHz.IFFT is used to get the >> time domain impulse response, > >IFFT requires evenly-spaced frequency samples from 0 Hz to half the >sampling frequency. How are you filling-in the missing measurements >between 0 Hz and 2 GHz, and between 12GHz and Fs/2 (half the sampling >frequency)? What are you assuming Fs to be? > >> but the result is complex ,not real.The >> impulse response of a system should be real.So,please give me some >> suggestions.thanks . > >For a real impulse response, the frequency domain data must be >conjugate-symmetric about Fs/2 (or about 0 Hz). Are you satisfying >this requirement? > >Or are you doing some sort of baseband processing? > >Greg >hi Greg 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. I have zero padding the missing measurement betweeen 0Hz and 2GHz.Then conjugate-transformation is done to form Hermitian symmetric about 0Hz before IFFT in matlab.No action is taken between 12GHz and Fs/2.The sampling frequency ,Fs,is 1/0.06GHz.should the missing measurement between 12GHz and Fs/2 be fill in to get the impulse response? thanks. Fajia

Reply by ●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

Reply by ●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 ●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 ●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 appearsas>>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 witha>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 theimaginary>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 sameamplitude as>the real parts, or are they like "1.000432e-015" (which you shouldinterpret>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, Ifound>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 thecausal>difference equation and use it to compute the impulse response. Matlabcode>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, "Tipsand>Tricks" article, Jan 2007 issue. If you don't have access to that, I canget>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