# Shouldn't the spectrum of a sine tone be an impulse, rather

Hi, I am sort of a newbie to the signal world. I studied the fourier transform or amplitude spectrum of a sine wave is an impulse in the frequency domain.
So, when I generated a tone of 440 Hz sine wave in audacity, according to the theory I learnt, The spectrum of the tone should have been a single impulse at 440 Hz , right?
But when I clicked on the “Plot Spectrum” option in the “Analyze” section, Audacity gave me this…

Where it’s not an impulse in frequency domain. It’s more like a band.
I knew the plot spectrum option gives the FFT of the given signal.

What is going on here then ? Is my conception about fourier series wrong?
Or is it due to something of FFT? I don’t know much about FFT, but it’s basically fourier transform ,right?

I didn’t know where to post. I saw signal processing written on the section in the forum, so…

Increase the “Size” value. At small Size values, the analysis is sloppy and you get a broad messy display. If you pick a value too high, the tiny, thin purple needles are impossible to see (but probably what you’re actually looking for).

You might also want to pick “Log” frequencies. That gives you Orchestra Oboe “A” 440 Hz roughly in the middle. If you don’t do that, the middle is 10,000 Hz which, while technically correct, some older people can’t even hear that high.

You can drag the analysis bigger and get greatly improved viewings (but analysis still doesn’t have a magnifier).

Koz

Sorry, not got a lot of time to reply right now, but this article should shed some light: https://en.wikipedia.org/wiki/Window_function

tiny, thin purple needles

And thinking about this a little more, technically, what you’re looking for can’t be seen. Don’t confuse printed artist interpretations in a book with an actual analyzer. A pure, correct analysis of an undistorted sine wave might be less than one computer screen pixel wide.
Koz