you are now clear that both are producing different results. 

the question now is which is best. 

the answer could be it depends on the number of computations each takes to perform.

you use tic and toc functions in your program. at least you come to know how much time each one is consuming. and accordingly you come to conclusion.

thanking you 

I suppose that the difference between the calculation of convolution by means of FFT and the function convolveolve ( conv in MatLab) takes place. The point is that the conv function in Matlfb carries out the usual convolution of the sliding average type (similar to polynomial multiplication), but the Fourier-based convolution is cyclical (with the moving last elements of the sliding vector to its beginning). In order for the cyclic convolution to coincide with the usual one, it is necessary to padding the vectors vx  and vy with zeros by the length of the vectors themselves (length of the t).

From a theoretical point of view, convolving vx (10 samples length) and vy (also 10 samples length) should provide an output signal of length length(vx) + length(vy) -1 = 19 samples.

Using matlab functions, you can do

1- conv(vx,vz) that performs the complete convolution. The length of the result is length(vx)+ length(vy)-1=19 samples

2- filter(vx,[1],vy) that gives an output of the same length than vy (i.e. 10 samples)

Pascal Scalart

the following is the description of the inbuilt convolve function (conv):

c = conv(a,b) outputs the convolution of input vectors a and b, at least one of which must be a fi object.

c = conv(a,b,'shape') returns a subsection of the convolution, as specified by the shape parameter:

full — Returns the full convolution. This option is the default shape.

same — Returns the central part of the convolution that is the same size as input vector a.

valid — Returns only those parts of the convolution that the function computes without zero-padded edges. In this case, the length of output vector c is max(length(a)-max(0,length(b)-1),

0).

kindly look in to the description before using the inbuilt function.

it is better to write our own program if the task is simple as here

when we convolve two sequence with L and M as the lengths, the convoluted sequence is having the length of L+M-1.

when you use the inbuilt function you are not getting the above mentioned length. it means both are not correct.

perhaps the inbuilt function is performing the circular convolution.

you can as well use the inbuilt function for sure. but you have to perform zero padding before using the function.

thanking you

Thank you all for your answers. It seems that convolve in R uses FFT for efficiency and if set to default arguments, it performs a circular convolution (i.e. concolve(vx,vy)).  But I am still confused which is the best convolution way to use, regular convolution using the Matlab function 'conv' that produces 19 samples (length(vx)+ length(vy)-1) or convolve function to get the same length of x(t) and y(t) i.e 10? Thank you

you are now clear that both are producing different results. 

the question now is which is best. 

the answer could be it depends on the number of computations each takes to perform.

you use tic and toc functions in your program. at least you come to know how much time each one is consuming. and accordingly you come to conclusion.

thanking you 

Back to you guys, I am still confused about which function (technique) to use regardless of the computation time. I attached a plot that shows the results of convolving two vectors V1 and V2  from a response function.  Both vectors have a length of 150.

- The black curve shows the plot of the first vector V1 

- The blue shows the plot of the vector V2 

- Red curve indicate the output of the convolution using matlab 'conv' function with (the length of the vector here is 150+150-1

- Green is the result using 'convolve' function from R which as understand performs a circular convolution the length of the vector here is 150

- Brown color using convolve from R but specifying the type argument to "open" the length is 150+150-1. 

My question is how can I 'choose' between these different results? I want my result to have the same length as my input vectors so I think to select the green one, but I am not sure. 

I also included a link to the R function I used i.e convolve() 

Thank you!

https://stat.ethz.ch/R-manual/R-devel/library/stats/html/convolve.html