#### Kaushik Sv

##### Newbie level 3

- Joined
- Apr 18, 2014

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- Location
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Hi folk

During DFT of a input sequence of length N, we find X(k).

X(k) = <x[n], e[k, n]>

where e(k, n)=[e

For each value of k, I get a coefficient. Similarly I got coefficients for all basis in the vector space.

Now to reconstruct the original signal, isn't it enough to multiply the coefficients with appropriate basis vectors and add them? Why is each element N times the original value in x[n]? Why does it need a division by N at the end?

I can't understand this division part intuitively. Sorry if that was a dumb question. Please help me understand this.

Thanks.

Kaushik

SMK Fomra Inst of Tech, Chennai

India

During DFT of a input sequence of length N, we find X(k).

X(k) = <x[n], e[k, n]>

where e(k, n)=[e

^{-2kπ/N}e^{-2kπ*2/N}e^{-2kπ*3/N}... e^{-2kπ*(N-1)/N}].For each value of k, I get a coefficient. Similarly I got coefficients for all basis in the vector space.

Now to reconstruct the original signal, isn't it enough to multiply the coefficients with appropriate basis vectors and add them? Why is each element N times the original value in x[n]? Why does it need a division by N at the end?

I can't understand this division part intuitively. Sorry if that was a dumb question. Please help me understand this.

Code:

Thanks.

Kaushik

SMK Fomra Inst of Tech, Chennai

India

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