Say we have number of samples to be 128 and a signal sin(2*pi*1000*n*Ts)+sin(2*pi*2000*n*Ts) sampled at 8kHz.

Now say we have same signal but only N = 64 samples. But in order to create 128 samples, we pad the signal with 64 zeros.

Each of these scenarios the frequency resolution is 8000/128 = 62.5Hz, but the spectrum of the first one is much better, as in, you will have two clear peaks. Why is that?

Thanks in advance


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