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Convolution Question?

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rock_win

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convolutional 2/4/8

If h1(n) and h2(n) 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

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

thnx

purna!
 
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haydaa

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

fiquran

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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

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

thnx

purna!
 

zorro

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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

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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(n) | 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(n)={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(n) | 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(n)={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(n) | 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(n)={1,4,8,8}


hope this solves ur doubt else u can mail me
 

smart_shaurya

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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

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convolution in time domain is nothing but multiplication in frequency domain
 

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