Fourier transform for 2 signals

1. Can two signals have the same Fourier transform?
2. What is 2D Fourier transform?
3. Does FFT have to be power of 2?
4. How do you find the Fourier transform of a given signal?

Can two signals have the same Fourier transform?

Of course they can. Simply imagine that a signal is composed by two sine waves with different frequencies. Then you create new signals by i) first let the lower frequency be present for a certain time interval with length t, and in a second identical time interval only the second, higher frequency is present.

What is 2D Fourier transform?

The (2D) Fourier transform is a very classical tool in image processing. It is the extension of the well known Fourier transform for signals which decomposes a signal into a sum of sinusoids. So, the Fourier transform gives information about the frequency content of the image.

Does FFT have to be power of 2?

It isn't actually true that FFT works only with powers of two. The original paper on the FFT is “An Algorithm for the Machine Calculation of Complex Fourier Series ” by Cooley and Tukey.

How do you find the Fourier transform of a given signal?

In signal processing, the Fourier transform can reveal important characteristics of a signal, namely, its frequency components. y k + 1 = ∑ j = 0 n - 1 ω j k x j + 1 . ω = e - 2 π i / n is one of the n complex roots of unity where i is the imaginary unit. For x and y , the indices j and k range from 0 to n - 1 .