Time-domain and frequency-domain transformation-meaning of Fourier Transformation

I am so ashamed to learn "digital signal processing" for a long time. I also remembered the Fourier transformation formula and made the FFT program, but I don't know what the significance of Fourier transformation is! That's it !!

Fortunately, I understand it. Aside from the mathematical meaning, let alone some practical meanings. Fourier transform is used to convert signals from the time domain to the frequency domain. In this way, the characteristics of signals that are overlapped and invisible in the time domain can be clearly seen in the frequency domain. For example:

Figure1 is a graph of a = 0.4 * sin (4 * w * (x). figure2 is a graph of B = 1.6 * Cos (12 * w * (x. These two figures are easy to see on the timeline. But some information in the two sums, namely a + B, is invisible, as shown in figure3. However, it is obvious to do a Fourier transformation and convert it to the frequency domain, as shown in figure4. The abscissa of figure4 is frequency, and the ordinate is amplitude. It can be seen that figure3 consists of two signals, and the amplitude of the signal with a large frequency is relatively large (that is, B, because fftshift is used here, so exactly the opposite), the meaning is more obvious.

Alas, it's really hard to say. At that time, I read a lot of books related to digital signals, but I didn't understand what was going on. Why? Poor self-learning ability! In this example, we should take the precaution.

Appendix: MATLAB program

W = 2 * PI;
X =-1:0. 01:1;
A = 0.4 * sin (4 * w * (x ));
B = 1.6 * Cos (12 * w * (x ));

Subplot (2, 2, 1 );

Plot (w * X, A), title ('figure 1: A = 0.4 * sin (4 * w * (x ))');
Subplot (2, 2 );
Plot (w * X, B), title ('figure 2: B = 1.6 * Cos (12 * w * (x ))');
Subplot (2, 2, 3 );
Plot (w * X, A + B), title ('figure 3: A + B ');
C = FFT (A + B );
Subplot (2, 2, 4 );
Plot (x, fftshift (ABS (c), title ('figure 4: FFT ');

Http://www.360doc.com/content/11/0530/20/4539198_120561433.shtml