Question

If a periodic signal is decomposed into five sine waves with frequencies of 50, 300, 500, 700, and 1800 GHz, what is the bandwidth? Draw the spectrum in periodic and non-periodic form, assuming components have a maximum amplitude of 5,10,1510 and 5V, express this as a function of frequency. Why can’t these spectrum be sketch as a function of time?

Answer 1

Periodic signal is decomposed into five sine waves with frequency

=50 Ghz

=300 Ghz

=500 Ghz

=700 Ghz

=1800 Ghz

So highest frequency =1800 Ghz

Lowest frequency =50 Ghz

Bandwidth is the difference between highest and lowest frequency.

Bandwidth =

Bandwidth =1800-50=1750 Ghz

The bandwidth is 1750 Ghz

The spectrum in periodic form is drawn by using maximum amplitude values and frequencies given and the spectrum has only 5 spikes at 50,300,500,700 and 1800.The maximum amplitude is 15 V at frequency 500 Ghz which is peak value of amplitude.

The frequency 50,300,500,700 and 1800 Ghz have maximum amplitude 5,10,15,10,5 V and the periodic and non periodic spectrum as a function of frequency is shown below

• These spectrum cannot be expressed as function of time because the time domain does not provide the all the information that is needed from spectrum we cannot find that why the signal is pure sinusoid wave by making spectrum as function of time but frequency domain plot the amplitude versus frequency of each sine wave of the spectrum which helps in knowing why signal is not pure sinusoidal wave.
• The frequency domain helps in identifying those questions about signals which cannot be seen in time domain.The frequency domain is more compact and useful when there are more than one sine wave so the spectrum will not become more complex. and easy to analyze.

F1

F2

F3

F4

F5

F5

F1

F5 F1

PERIODIC SPECTROM Amplitude (u 25 20+ ist 10+ 50GHz 300 560 700 1800 GM2 GHz Frequency 4 BANDWIDTH= 1800-50-1750 GHz CScanned with CamScanner

NON PERIODIC SPECTROM Amplitude (vi 20+ Peak values 15 5 50 300 -> 500 foo ISOO Frequency (GHz) BANDWIDTH = 1800-50 = 1750 GHz CScanned with CamScanner