# Pulse compression implemented by the convolution vs. by fft

Started by 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 :)

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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 :)

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 :)

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 :)
>
>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 :)
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```
```>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 :)
>
>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?
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```
```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 :)
>>
>>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 :)
>>>
>>>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!
---------------------------------------
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```
```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 :)
>>>>
>>>>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 :)
>>>>>
>>>>>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. :-)
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```