Convolution Question?

[rock_win]

convolutional 2/4/8

If h1 and h2 are 2 signals such that their convolution and product are same, then how can i find those signals/What will be those signals?

Please suggest a solution.

 

[purnapragna]

i think it is posiible only when the two signals are discrete time impulses present at \[n=0\]

thnx

purna!

 

[haydaa]

yes i suppose so, it has to be impulse at n=0

 

[fiquran]

the answer might be hidden in the fourier domain analysis. we know that convolution operation corresponds to a multiplication in the fourier domain, and vice versa. Thus, an impluse at 0 cannot be a solution.

 

[purnapragna]

how can you conclude from the convolution properties that the answer is wrong? Please clarify me

thnx

purna!

 

[zorro]

In continuous time, gaussian-shaped waveforms can be considered a solution.
I say “can be” because convolving two gaussian-shaped waveforms the shape is gaussian, and also multiplying them the result is gaussian, but with a scale change in both axis.
Regards

Z

 

[ce_dps]

c thr is no way to find out whether the answer is correct in convolution method
but u can always verify your answer by another method

method
1> graphical ---- no way to find ans is correct or not
2> matrix--------usually correct way

h | 1 2 4
-------- |--------------------------
1 | 1 2 4
2 | 2 4 8


now move diagonally ie in the matrix region
1 then sum it = 1
2+2 = 4
4 +4 =8
8+0 =8

hence y={1,4,8,8}


hope this solves ur doubt else u can mail me

Added after 2 minutes:

c thr is no way to find out whether the answer is correct in convolution method
but u can always verify your answer by another method

method
1> graphical ---- no way to find ans is correct or not
2> matrix--------usually correct way

h | 1 2 4
-------- |--------------------------
1 | 1 2 4
2 | 2 4 8


now move diagonally ie in the matrix region
1 then sum it = 1
2+2 = 4
4 +4 =8
8+0 =8

hence y={1,4,8,8}


hope this solves ur doubt else u can mail me

Added after 3 minutes:

c thr is no way to find out whether the answer is correct in convolution method
but u can always verify your answer by another method

method
1> graphical ---- no way to find ans is correct or not
2> matrix--------usually correct way

h | 1 2 4
-------- |--------------------------
1 | 1 2 4
2 | 2 4 8


now move diagonally ie in the matrix region
1 then sum it = 1
2+2 = 4
4 +4 =8
8+0 =8

hence y={1,4,8,8}


hope this solves ur doubt else u can mail me

 

[smart_shaurya]

ce_dps is right...but u have another way for finding this...u can find the z transform of the 2 signals and then simply multiply them...and then take the inverse z-transform of the same which is ur answer...

dis method seems to b bit tedious but its d best way wen u know d z transform of the signals...

 

[tjr]

convolution in time domain is nothing but multiplication in frequency domain