A Spectrum of a pure sine wave

[Siyu D]

When I did this week’s lab and analysed the spectrum of a pure sine wave at 100Hz, I found that its spectrum is a contious line with a broad peak at 100Hz. But actually, there shoud just be a verticle straight line at 100Hz because the wave is only composed of one pure sine wave.So why do computers treat a pure wave just as it does when treating complex aperiodic waves?

[Simon]

Two things are going on here

1. What you see in the FFT spectrum is plotted on a logarithmic vertical scale, so that emphasises the very low energy parts. You can ignore these and just focus on the peaks.

2. We see a peak with some width, not a perfect vertical line. The width of that peak depends on

a) the analysis window size (number of FFT points): longer window = higher frequency resolution = narrower peak

b) the use of a tapered window, which introduces this as an artefact (but without tapered window we would have worse artefacts due to discontinuities in the time-domain signal)

A technical aside (not relevant for this course): different tapered window shapes – Hamming, Hanning, Blackman,… – lead to slightly different widths and shapes of this peak.

[Author]

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