# Telecommunications – Solve for parameters of Spectrum and plot on graph

The amplitude and frequency of the first 8 harmonics of the signal are displayed as:
f1 = 2.5 kHz: -2.96 dBm
f2 = 5.0 kHz: -5.96 dBm,
f3 = 7.5 kHz: -12.50 dBm
f4 = 10.0 kHz: 0 (no signal, not 0 dBm)
f5 = 12.5 kHz: -16.93 dBm
f6 = 15.0 kHz: -15.51 dBm
f7 =17.5 kHz: -19.86 dBm
f8 = 20.0 kHz: 0 (no signal, not 0 dBm)
Spectrum analyzers display power dB units and ONLY amplitude is displayed. Your spectrum analyzer has 50 ohm input impedance. It measures the power dissipated in a 50 ohm resistor in dBm. In addition, your spectrum analyzer will not display zero frequency (DC) but you know that the signal has a 0.25 V component at zero frequency. Hint: Remember in converting dBm to voltage that there is 30 dBm/watt and be careful of the sign. If you get 10’s or hundreds of volts, ask yourself if that is reasonable. THINK first, don’t just put numbers in equations! The dBm values are intentionally given to second decimal place so the voltages come out correctly for the sin(x)/x spectrum.
What is the peak (not RMS) voltage amplitude of each harmonic?
What is the pulse period, pulse width and pulse amplitude of this signal?.
If you display this signal on oscilloscope (an instrument that displays voltage vs time) what would you see? Plot the signal. Be sure to label the x,y axis properly. While your spectrum analyzer doesn’t show all the harmonics assume that spectrum extends to infinite frequency.
Plot the time domain wave of this waveform (the oscilloscope display) at the output of a lowpass filter that has a cutoff frequency of 10 kHz. You will need to plot what is left of the Fourier Series after signal passes through the filter. You should have the amplitude values for the remaining harmonics from 1.) above. The time scale should run over 3-4 periods of the waveform. Remember that the LPF response goes to zero frequency. Your plot must be properly labeled for full credit. If you have access to Matlab, this is an almost trivial exercise. The instructor’s solution is just 3 lines of Matlab code. You can do the plot in your spreadsheet but it is more work. Part credit will be awarded for writing the correct Fourier Series for the plot but the really interesting part of this problem is to compare waveform the comes out of the filter to the ideal waveform that went in. 