why the conv(u,v,'same') choose the a vector a little right deviated to center position

For example

>> a=[1:10];
>> b=[7:7:28];
>> conv(a,b)
ans =
     7    28    70   140   210   280   350   420   490   560   553   462   280
>>conv(a,b,'same')
ans =
    70   140   210   280   350   420   490   560   553   462

The same option give a vector vector from element 70. Why not from element 28? Are there any math/enginerr reasons?

Answer 1

[Greg Dionne]

If b is of odd length, you will obtain what you expect.

For even length it will move to the next available point having the gap at the beginning, not at the end. To get the other way, try:

>> fliplr(conv(fliplr(a),fliplr(b),'same'))
ans =
  28    70   140   210   280   350   420   490   560   553

[Tsung-Ju Yang]

Thank you very much! May I ask what is "the next available point having the gap at beginning"?

[Image Analyst]

Basically it's shifted a half element to the side if you're using an even number of elements in your scanning kernel window instead of an odd number.

[Tsung-Ju Yang]

Image Analyst, thank you!