N-point DFT of window function

Question

I am currently choosing a window function to analyze signals in frequency domain. While I understand the reasoning behind using a window function and what to look for concerning main lobe and side lobe forms, I have stumbled across the fact that the frequency domain representation of a window function that Matlab generates with the wvtool looks a lot different to what I can obtain from simply applying the fft command to my respective window function.

After some research, I now understand that the shape of the window function in frequency domain depends on how many points the fft command uses. E.g. when applying the fft command with 100 points to a window of length n=100, the result is a continuous curve. The more points I use for the fft, the more accurately the lobes start to form that are also visible in the wvtool.

I have also read in this Stack Exchange question that an fft with more points than the signal length n basically interpolates between the samples of the n-point fft and that every second point of a 2n-point fft coincides with the n-point fft.

So, can I assume that the 2n-point fft is more accurate than the n-point fft? And how would that be considering that the 2n-point fft is just created from adding n zeros to the original signal and therefore doesn't add meaningful information to the signal? And when applying ffts to signals that are not window functions: Am I generally better off just adding more points to the fft? Normally, to increase frequency resolution, I would perform an n-point fft over a larger sample size n. But no matter how large the sample size, I can never obtain the lobes of the window functions without performing an fft with more points than samples. So am I somehow missing information when performing only an n-point fft on a real-world signal?

Thanks for any help, the more I research this the more I am confused at the moment.

I have added a minimal code sample to better illustrate what I mean. ws is the window size and m is a factor to increase fft points. So e.g. use m=2 to perform a 2n-point fft.

ws = 1000;
m = 1;
hanning = abs(fft(hann(ws), m * ws)) / sum(hann(ws));
hanning = hanning / max(hanning);
hanning = hanning(1:ws/2+1);
f = (0:(1/m):(ws/(2*m)));
f = f';
figure;
plot(f, 20*log10(hanning));

Answer 1

So, can I assume that the 2n-point fft is more accurate than the n-point fft?

No. The N-point FFT contains all independent information that is required to completely represent the spectrum.

And how would that be considering that the 2n-point fft is just created from adding n zeros to the original signal and therefore doesn't add meaningful information to the signal?

Your reasoning is correct. Zero padding does not add information. It's just interpolation.

And when applying ffts to signals that are not window functions: Am I generally better off just adding more points to the fft?

Depends on the application. Sometimes yes, sometimes no, but that really depends on what you want to do with the data.

This is priamrily a function of "visual intepretation". Let's look at a simple sine wave at a normalized frequency of $\pi/2$

$$x[n] = \sin(\frac{\pi}{2}n+\pi/4)$$

Here is a graph using a standard plot() function

This looks like a trapezoid wave but it is a true sine wave. The misconception is created by the plot() function which simply connects the individual samples with straight lines. That assumption is wrong and creates a substantial visual error. The correct way to draw this would be sinc() interpolation.

So interpolation can be quite useful especially if you want to actually look (with your eyes) at the data. However, mathematically it's not required. All the information is there.