A spectrum analyzer is connected to an unknown signal. The spectrum analyzer displays the power level of signals in dBm vertically and frequency horizontally. The spectrum of the unknown signal creates the following display:
A continuous spectrum that is completely filled so no lines are visible.
The spectrum has a sin X / X shape. The spectrum has maximum power spectral density at 0 Hz and falls to zero at 2 kHz, 4 kHz, 6 kHz and other even kHz frequencies.
a. What sort of waveform does the input signal have?
b. Is the input signal periodic or non-periodic?
c. If the input waveform is non-periodic, what is its pulse width?
d. If the spectrum suddenly changes to have zeroes at 5 kHz, 10 kHz, 15 kHz, etc, what is the new pulse width?
What you are actually witnessing on the Spectrum Analyser is the power output which is the "Sinc" function, as represented in diagram(see ATTACHMENT), squared (so the negative lobes just become positive as you square them).
This then gives you the power density spectrum as seen on the Spectrum Analyser.
The zero crossings of the "Sinc" function and thus the actual zero crossings as seen on the Spectrum Analyser are equal to n/T as shown (see ATTACHMENT). So the first zero would occur at n =1 or 1/T which you are told is 2 kHz.
First zero at f = 2 kHz so 1/T = 2 kHz
The next zero at f = 4 kHz so 2/T = 4 kHz
The next zero at f = 6 kHz so 3/T = 6 ...
Analysing the output of a spectrum analyser and utilising the sinc function in its analysis