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How many real multiplications are required to find DFT of 32 point signal using DFT

Question

How many real multiplications are required to find DFT of 32 point signal using DFT

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Solution

The Discrete Fourier Transform (DFT) of an N-point sequence involves N^2 complex multiplications. However, each complex multiplication involves 4 real multiplications. Therefore, the total number of real multiplications required to compute the DFT of an N-point sequence is 4N^2.

For a 32-point sequence, the number of real multiplications required would be 4 * (32^2) = 4 * 1024 = 4096.

So, 4096 real multiplications are required to find the DFT of a 32-point signal using DFT.

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Using exponential notation, we can write 32 as

1/1

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