Show Equivalence Between Multiplication in Time Domain to Convolution in Frequency Domain

1. Why multiplication in time domain is convolution in frequency domain?
2. What is the relation between convolution in time domain and frequency domain?
3. Which property of Fourier transform states that convolution in frequency domain is multiplication in time domain?
4. How do you convert time domain to frequency domain in FFT?

Why multiplication in time domain is convolution 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.

What is the relation between convolution in time domain and frequency domain?

Convolution is cyclic in the time domain for the DFT and FS cases (i.e., whenever the time domain has a finite length), and acyclic for the DTFT and FT cases. That is, convolution in the time domain corresponds to pointwise multiplication in the frequency domain.

Which property of Fourier transform states that convolution in frequency domain is multiplication in time domain?

In this lesson, we will cover additional properties of the Fourier Transform. The most useful one is the Convolution Property. It tells us that convolution in time corresponds to multiplication in the frequency domain.

How do you convert time domain to frequency domain in FFT?

Simply stated, the Fourier transform converts waveform data in the time domain into the frequency domain. The Fourier transform accomplishes this by breaking down the original time-based waveform into a series of sinusoidal terms, each with a unique magnitude, frequency, and phase.