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 vertical line at -6 dBm at 0 Hz (DC),
A vertical line at a frequency of 10 kHz with a power level of -3.9 dBm,
A vertical line at a frequency of 30 kHz with a power level of -13.4 dBm,
Additional vertical lines at 50 kHz, 70 kHz with power levels at or below -18 dBm.

a. What sort of waveform do the individual lines in the frequency spectrum represent?

b. What sort of waveform does the input signal have?

c. Is the input signal periodic or non-periodic?

d. If the input waveform is periodic, what is its period?

Hint: Translate the dBm values into voltages.

Solution Preview

The first thing to notice is that there is a DC component so a DC level. This means that whatever type of signal it is, it must be unipolar with all the signal (as viewed in the time domain) existing above the x axis (i.e. in positive territory).

The next thing to notice is that there exist terms in the power spectrum spaced at frequencies of 10 kHz, 30 kHz, 50 kHz, 70 kHz etc.. These are all ODD harmonic terms so would suggest that the waveform in the time domain would be an ODD function with no symmetry about the y axis when viewed in the time domain. Such ODD functions are typically SIN waves; COS waves are EVEN function (symmetrical about the y axis).

This then leads to consider looking at a Fourier series of SIN terms.

Let us look at the Fourier representation of a general Square wave (amplitude).

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.
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(See attached file for full problem description)
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