why we need scale in implementations of FFT?

Hi, Actually, i'm a civil engineering. I'm trying to understand on FFT because i need calculate response of structure under moving load in frequency domain after i calculated it (response) in time domain. And when i study on implementations of FFT in Matlab some problem that i don't understand. I found a document that provide to me a guide. I don't understand this sentence: "Since the FFT only does the summation of terms, the values returned by FFT must be scaled by dividing them by the number of points, k" with k is the number of points. i.e. 5th step in above figure. Why we need scale?

Answer 1

[Santhana Raj]

This is because the FFT equation implmented by Matlab is little different from your textbook equation.

Usually in a engineering textbook, you will see a (1/N) factor at the start of a DTFT/FFT equation. If you type "help fft" in your command window, you will be able to see that the forward fft formula is missing the (1/N) factor.