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Spectrogram contains magnitude values only, that explains why the values start at 0 instead of some negative value. And scipy seems to calculate it with 24bit accuracy, where $2^{24}\approx 16.7\cdot10^6$.

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I see how you added the carrier by multipying by $1 + 0.5cos(2\pi f t)$ (or you used sine, wouldn't change it), and that approach seems fine to me. It looks like you do actually see the carrier in your plot! What I see from your plot does appear to be a signal at +/-25 Hz which is what we would expect to see for $cos(2\pi 25 t)$ (or sine if you used that) ...

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I'm not sure but there's something called the time-frequency resolution limit, basically the shorter your windowing interval the broader your spectrum is going to be. The frequency resolution in the low frequency area may be poor because of this. Things like wavlets attempt to resolve this problem but i dont know anything about them.

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dB is a power ratio, so when we see units in dB we are seeing units on a relative scale. The reason that a 0 dB reference is so common is because this is simply normalizing the number scale to 1. $10Log(1) = 0$ dB This is similar to using 100% (1) instead of absolute numbers.

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This is not generally true. As mentioned in the comments, it may be a preference to take the maximum of the signal as 0 dB. But a counter example is the power measurements in wireless systems. We define dBm as: $P [dBm] = 10log(P / 1 (mW))$ We may have actual powers as high as 30 dBm. The voice ratings are other counter examples. There is no single ...

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I dont know if this is what you are looking for but the formula to calculate time array in spectrogram for MATLAB is : t = $((colindex-1)+((nwind)/2)') /Fs$; where colindex is the starting index of columns along which time increases and nwind is the length of the window. The elements in t are centered in the segment. colindex is calculated by \$colindex= 1 ...

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From the power spectrums you have plotted, it seems like there are a lot more deviations with the data. Perhaps when the song was recorded or encoded, the sampling rate (number of samples in each second) was less than the original one.

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