A discussion on FFT complement 0 to improve frequency resolution

This is a question worth discussing, the author believes that the 0 FFT can improve the frequency resolution, and give the test results, it can be seen that the frequency of the details of the observation ability, I can be sure that this test is a real experiment. But all the digital-signal textbooks say that the 0 FFT does not improve the frequency resolution, is not a contradiction.

1 from the analysis angle, set FS as the sampling frequency, the FFT length is N, then the frequency resolution is fs/n, if N increases then the frequency resolution increases. This is the argument used in the following article.

2 from another angle, set FS as the sampling frequency, the FFT length is N, then the frequency resolution is fs/n, we introduce another concept: time-length dt (duration of times), you can see the DT = 1/frequency resolution. The frequency resolution is =1/DT. From this point of view, as long as the DT is constant, the frequency resolution will not change. Therefore, even if you fill 0 or interpolation, the resolution is not improved. This is the view of all current signal processing textbooks, but these textbooks do not give reasons, do not know why, I found that this problem has been found a lot of textbooks, no one to give reasons, ask the teacher also ambiguous. Later I thought it over and over again and felt that I should be able to explain it and welcome the discussion.

Why do two angles look contradictory. Why is there a different explanation for the same question?

From 1 We see that the added value is all zero, not the original signal content, which caused the particularity, our signal has changed not the original signal. It is a new periodic continuation of the 0 signal. However, it can be proved that the spectral values of the two signals are the same on the corresponding points (directly using the definition). It is the crux of the question whether the spectrum of the other multipoint at 0 is the content of the original signal.

In fact, the method used for practical use is not the method mentioned below, but rather the method of sampling data extraction and reducing sampling frequency. Because the length of the data is generally the maximum length of use, especially this application, it must have been the maximum data processing length, do not ask.

I have an experiment that was discussed with a classmate many years ago and was interested in trying to discuss this kind of problem. Percent of percent is used to test whether the 0 FFT improves resolution

Percent -percent conclusion: 1. 0 FFT Improving resolution is the resolution of the synthesized signal after the signal is added to the window.
In this case the FFT can help to distinguish the real peaks, but the resolution you can calculate should be changed to be unchanged.
% 2.   If the signal = Add a window after the synthesis signal to improve resolution, if the join point for the real data, of course, improve the resolution.

% 4. The essence of improving the resolution details is due to the widening of the window and the improvement of the window resolution detail rate. This is the process of observing small windows with large windows that contain small window signals. The frequency details seen in 0 are not the details of the signal itself, but the details of the window.

Clear
nfft=16;
SPAN=[0:NFFT-1];
OMGA=[1:3]*PI/8;
X=exp (J*OMGA (1) *span) +exp (J*OMGA (2) *span) +exp (J*OMGA (3) *span); Stem (pi/nfft*[0:nfft-1],abs (FFT (X,NFFT)), ' R '); figure (2);
Stem (pi/nfft/2*[0:nfft*2-1],abs (FFT (x,nfft*2)), ' B '); Figure (3);
Stem (pi/nfft/16*[0:nfft*16-1],abs (FFT (x,nfft*16)), ' G ');