Not sure about duty cycle of a waveform. The frrequency is the inverse of the period and the period is the inverse of the frequency. Frequency (it pains me to tell you) is measured in Hertz, cycles per second. Period is the time for one cycle or seconds per cycle. If we let f be frequency and T be period, then f=1/T and T= 1/f
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Time period = 1 / frequency. Frequency = 1 / time period.
the relation between frequency and time period is ''t=1/f''
Period = 1 / frequency
The period of 1GHz is 1 ns. The waveform is irrelevant.
A Fourier series is a set of harmonics at frequencies f, 2f, 3f etc. that represents a repetitive function of time that has a period of 1/f. A Fourier transform is a continuous linear function. The spectrum of a signal is the Fourier transform of its waveform. The waveform and spectrum are a Fourier transform pair.