Windowing

[Alex S]

I am trying to understand why a larger window size of the signal will lead to a higher resolution of frequencies. Surely, as the sample duration of the window becomes smaller, the more defined / detailed the spectrum plot will be as it is not altered by other phones in the speech for example. (e.g. in the word ham, particular formants converge as the a approaches the bilabial consonant.)
Can someone explain why a larger window size of the signal will lead to a higher resolution of frequencies?

[Yusheng]

Below is my thought. It might be wrong.

When we transform ‘a window of’ signal into the frequency domain, we make an assumption that the signal is periodic with an interval of the window length T. We “give” a base frequency of 1/T to that piece of signal. Therefore 1/T is the frequency resolution, and the larger window size, the higher frequency resolution.

[Alex S]

That is starting to make sense. However, struggling to understand what you mean by a base frequency and why do we give this 1/T to the signal?

[Yusheng]

Sorry, I meant “fundamental frequency”.
Think about a square wave or a pulse wave which has a period of T. They contain a fundamental frequency 1/T, and many harmonics at the frequencies n*1/T.

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