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Examining frequency to time domain signals

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 (sinc 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 is the input waveform?
b. Is the input signal periodic or non-periodic?
c. What is the 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?

Solution Preview

(a)

The Sin(x)/x type waveform (also known as Sinc(x) function) in the frequency domain is charactristic of a stream of pulses. The zero crossing points (nulls) in the Sinc(x) = Sin(x)/x waveform occur at points denoted by

1/t, 2/t, 3/t.......n/t (n an integer ranging from 1 to infincity) where t represents the pulse width (time duration) of the pulses. In addition with the Sinc(x) function if there is any periodicity in the pulse stream (ie repeated data patterns) then this ...

Solution Summary

In this solution from a description of a Sinc function we back engineer the signal to its tiime domain representation to answerthe following

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 (sinc 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 is the input waveform?
b. Is the input signal periodic or non-periodic?
c. What is the 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?

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