Why convolution is multiplication in frequency domain?

We know that a convolution in the time domain equals a multiplication in the frequency domain. In order to multiply one frequency signal by another, (in polar form) the magnitude components are multiplied by one another and the phase components are added.

How do you divide a Fourier transform?

The Fourier transform is a sum-of-sines (and cosines), so to normalise the coefficients, divide by the integration time or length of the summation.

Is convolution the same as multiplication in frequency domain?

Convolution in time domain is equal to multiplication in frequency domain. Given any two signals (or signal and a filter), you need to find the Fourier Transform(DFT) of both of them and then do pointwise multiplication and then take the inverse DFT.

What does DFT stand for?

DFT

Which algorithm uses divide and conquer approach for computing DFT?

FFT algorithms
Divide-and-conquer approach is based on the decomposition of an N-point DFT into successively smaller DFTs. This basic approach leads to FFT algorithms.

What is the difference between convolution and multiplication of signals?

Convolution is a formal mathematical operation, just as multiplication, addition, and integration. Addition takes two numbers and produces a third number, while convolution takes two signals and produces a third signal. A star in a computer program means multiplication, while a star in an equation means convolution.

Are convolution and multiplication commutative?

but that follows from the fact that multiplication and convolution are separately commutative semigroup operations.