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Pulse compression implemented by the convolution vs. by fft

Started by tsuyahog January 13, 2016
Hi there! I'm working on Pulse compression for radar signal using FFT, the
echo is N points, and the length of match filter is also N points, then I
use N points FFT to calculate the pulse compression result, it seems that
I can indeed get the right result. I  just get a little confused, since
two N-points signals for linear convolution needs L(L>=2N-1) points FFT to
get the right thing. Is there anything wrong with my realization? Could
someone kindly help me out :)
Thanks in advance!


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On Wednesday, January 13, 2016 at 7:17:09 AM UTC-8, tsuyahog wrote:
> Hi there! I'm working on Pulse compression for radar signal using FFT, the > echo is N points, and the length of match filter is also N points, then I > use N points FFT to calculate the pulse compression result, it seems that > I can indeed get the right result. I just get a little confused, since > two N-points signals for linear convolution needs L(L>=2N-1) points FFT to > get the right thing. Is there anything wrong with my realization? Could > someone kindly help me out :) > Thanks in advance!
What does "it seems that I can indeed get the right result" really mean and how would you tell the difference between "the right result" and "the right result with some aliasing"? Dale B. Dalrymple
On Wed, 13 Jan 2016 09:17:03 -0600, "tsuyahog" <111318@DSPRelated>
wrote:

>Hi there! I'm working on Pulse compression for radar signal using FFT, the >echo is N points, and the length of match filter is also N points, then I >use N points FFT to calculate the pulse compression result, it seems that >I can indeed get the right result. I just get a little confused, since >two N-points signals for linear convolution needs L(L>=2N-1) points FFT to >get the right thing. Is there anything wrong with my realization? Could >someone kindly help me out :) >Thanks in advance!
Convolution with the FFT is inherently circular. Research the differences between linear and circular convolution. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
>On Wednesday, January 13, 2016 at 7:17:09 AM UTC-8, tsuyahog wrote: >> Hi there! I'm working on Pulse compression for radar signal using FFT, >the >> echo is N points, and the length of match filter is also N points, then
I
>> use N points FFT to calculate the pulse compression result, it seems
that
>> I can indeed get the right result. I just get a little confused,
since
>> two N-points signals for linear convolution needs L(L>=2N-1) points
FFT
>to >> get the right thing. Is there anything wrong with my realization?
Could
>> someone kindly help me out :) >> Thanks in advance! > >What does "it seems that I can indeed get the right result" really mean
and
>how would you tell the difference between "the right result" and "the
right
>result with some aliasing"? > >Dale B. Dalrymple
Thank you for your reply. I mean I can get the right range of the target after implementing the pulse compression. Actually it should be an aliased version of the linear convolution(N points circular convolution for L points linear convolution), I can still get the right range even if it's aliased, could you give me some suggestion? Thanks :) --------------------------------------- Posted through http://www.DSPRelated.com
>On Wed, 13 Jan 2016 09:17:03 -0600, "tsuyahog" <111318@DSPRelated> >wrote: > >>Hi there! I'm working on Pulse compression for radar signal using FFT,
the
>>echo is N points, and the length of match filter is also N points, then
I
>>use N points FFT to calculate the pulse compression result, it seems
that
>>I can indeed get the right result. I just get a little confused, since >>two N-points signals for linear convolution needs L(L>=2N-1) points FFT
to
>>get the right thing. Is there anything wrong with my realization? Could >>someone kindly help me out :) >>Thanks in advance! > >Convolution with the FFT is inherently circular. Research the >differences between linear and circular convolution. > > >Eric Jacobsen >Anchor Hill Communications >http://www.anchorhill.com
Thank you,Eric. I don't get it. Could you give me more details about it? --------------------------------------- Posted through http://www.DSPRelated.com
On Wed, 13 Jan 2016 23:05:04 -0600, "tsuyahog" <111318@DSPRelated>
wrote:

>>On Wed, 13 Jan 2016 09:17:03 -0600, "tsuyahog" <111318@DSPRelated> >>wrote: >> >>>Hi there! I'm working on Pulse compression for radar signal using FFT, >the >>>echo is N points, and the length of match filter is also N points, then >I >>>use N points FFT to calculate the pulse compression result, it seems >that >>>I can indeed get the right result. I just get a little confused, since >>>two N-points signals for linear convolution needs L(L>=2N-1) points FFT >to >>>get the right thing. Is there anything wrong with my realization? Could >>>someone kindly help me out :) >>>Thanks in advance! >> >>Convolution with the FFT is inherently circular. Research the >>differences between linear and circular convolution. >> >> >>Eric Jacobsen >>Anchor Hill Communications >>http://www.anchorhill.com > >Thank you,Eric. >I don't get it. Could you give me more details about it?
Perhaps you should clarify what exactly is causing you difficulty. I don't want to try to guess which part you don't understand. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
>On Wed, 13 Jan 2016 23:05:04 -0600, "tsuyahog" <111318@DSPRelated> >wrote: > >>>On Wed, 13 Jan 2016 09:17:03 -0600, "tsuyahog" <111318@DSPRelated> >>>wrote: >>> >>>>Hi there! I'm working on Pulse compression for radar signal using
FFT,
>>the >>>>echo is N points, and the length of match filter is also N points,
then
>>I >>>>use N points FFT to calculate the pulse compression result, it seems >>that >>>>I can indeed get the right result. I just get a little confused,
since
>>>>two N-points signals for linear convolution needs L(L>=2N-1) points
FFT
>>to >>>>get the right thing. Is there anything wrong with my realization?
Could
>>>>someone kindly help me out :) >>>>Thanks in advance! >>> >>>Convolution with the FFT is inherently circular. Research the >>>differences between linear and circular convolution. >>> >>> >>>Eric Jacobsen >>>Anchor Hill Communications >>>http://www.anchorhill.com >> >>Thank you,Eric. >>I don't get it. Could you give me more details about it? > >Perhaps you should clarify what exactly is causing you difficulty. I >don't want to try to guess which part you don't understand. > > >Eric Jacobsen >Anchor Hill Communications >http://www.anchorhill.com
Sorry for my vague reply. My question here is, I&rsquo;m wondering whether it is possible to use fft(for circular convolution) to replace the linear convolution when doing match filtering(Just use N points fft to substitute for 2N-1 points linear convolution). I think there may be something like transient response so that the total 2N-1 points linear convolution are not all useful, so I can just pick N points of it to get the filtering result. Is there anything wrong? Thanks again! --------------------------------------- Posted through http://www.DSPRelated.com
On Thu, 14 Jan 2016 03:28:37 -0600, "tsuyahog" <111318@DSPRelated>
wrote:

>>On Wed, 13 Jan 2016 23:05:04 -0600, "tsuyahog" <111318@DSPRelated> >>wrote: >> >>>>On Wed, 13 Jan 2016 09:17:03 -0600, "tsuyahog" <111318@DSPRelated> >>>>wrote: >>>> >>>>>Hi there! I'm working on Pulse compression for radar signal using >FFT, >>>the >>>>>echo is N points, and the length of match filter is also N points, >then >>>I >>>>>use N points FFT to calculate the pulse compression result, it seems >>>that >>>>>I can indeed get the right result. I just get a little confused, >since >>>>>two N-points signals for linear convolution needs L(L>=2N-1) points >FFT >>>to >>>>>get the right thing. Is there anything wrong with my realization? >Could >>>>>someone kindly help me out :) >>>>>Thanks in advance! >>>> >>>>Convolution with the FFT is inherently circular. Research the >>>>differences between linear and circular convolution. >>>> >>>> >>>>Eric Jacobsen >>>>Anchor Hill Communications >>>>http://www.anchorhill.com >>> >>>Thank you,Eric. >>>I don't get it. Could you give me more details about it? >> >>Perhaps you should clarify what exactly is causing you difficulty. I >>don't want to try to guess which part you don't understand. >> >> >>Eric Jacobsen >>Anchor Hill Communications >>http://www.anchorhill.com >Sorry for my vague reply. My question here is, I&rsquo;m wondering whether it >is possible to use fft(for circular convolution) to replace the linear >convolution when doing match filtering(Just use N points fft to substitute >for 2N-1 points linear convolution). I think there may be something like >transient response so that the total 2N-1 points linear convolution are >not all useful, so I can just pick N points of it to get the filtering >result. Is there anything wrong? Thanks again!
I think it really depends on your system parameters and requirements. It is clearly possible to do it with an FFT, as many radar systems have operated this way for many decades. My first engineering job out of school in the 1980s was working on a radar processor, and the pulse compression and range processing was done with an FFT even back then. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
>On Thu, 14 Jan 2016 03:28:37 -0600, "tsuyahog" <111318@DSPRelated> >wrote: > >>>On Wed, 13 Jan 2016 23:05:04 -0600, "tsuyahog" <111318@DSPRelated> >>>wrote: >>> >>>>>On Wed, 13 Jan 2016 09:17:03 -0600, "tsuyahog" <111318@DSPRelated> >>>>>wrote: >>>>> >>>>>>Hi there! I'm working on Pulse compression for radar signal using >>FFT, >>>>the >>>>>>echo is N points, and the length of match filter is also N points, >>then >>>>I >>>>>>use N points FFT to calculate the pulse compression result, it
seems
>>>>that >>>>>>I can indeed get the right result. I just get a little confused, >>since >>>>>>two N-points signals for linear convolution needs L(L>=2N-1) points >>FFT >>>>to >>>>>>get the right thing. Is there anything wrong with my realization? >>Could >>>>>>someone kindly help me out :) >>>>>>Thanks in advance! >>>>> >>>>>Convolution with the FFT is inherently circular. Research the >>>>>differences between linear and circular convolution. >>>>> >>>>> >>>>>Eric Jacobsen >>>>>Anchor Hill Communications >>>>>http://www.anchorhill.com >>>> >>>>Thank you,Eric. >>>>I don't get it. Could you give me more details about it? >>> >>>Perhaps you should clarify what exactly is causing you difficulty. I >>>don't want to try to guess which part you don't understand. >>> >>> >>>Eric Jacobsen >>>Anchor Hill Communications >>>http://www.anchorhill.com >>Sorry for my vague reply. My question here is, I&acirc;&#128;&#153;m wondering
whether it
>>is possible to use fft(for circular convolution) to replace the linear >>convolution when doing match filtering(Just use N points fft to
substitute
>>for 2N-1 points linear convolution). I think there may be something
like
>>transient response so that the total 2N-1 points linear convolution are >>not all useful, so I can just pick N points of it to get the filtering >>result. Is there anything wrong? Thanks again! > >I think it really depends on your system parameters and requirements. >It is clearly possible to do it with an FFT, as many radar systems >have operated this way for many decades. My first engineering job >out of school in the 1980s was working on a radar processor, and the >pulse compression and range processing was done with an FFT even back >then. > > >Eric Jacobsen >Anchor Hill Communications >http://www.anchorhill.com
Thanks for your reply! I think I should go through the related theory seriously. :-) --------------------------------------- Posted through http://www.DSPRelated.com