Show work and answer all questions to receive rating 2) A periodic composite sig

Question

Show work and answer all questions to receive rating

2) A periodic composite signal contains sine harmonics with frequencies from 10 KHz to 70

KHz. The fundamental frequency of the first harmonic of this composite signal is 10 KHz

and all harmonics in the range 10-70 KHz are included in the composite signal. The signal is

transmitted over a channel that has attenuation of - dB for all frequencies less than or equal

to 40 KHz and attenuation of -3 dB for all frequencies larger than 40 KHz. All harmonics

have a maximum power of 20 milliwatts (mW) at the sender

Explanation / Answer

The signal has a fundamental frequency of 10 kHz

The harmonics are integral multiples of this fundamental frequency
Hence the harmonics will be 20, 30, 40, 50, 60, 70 kHz. We do not consider any more because that lies outside the bandwidth.

NOw, I think you forgot to give the first attenuation value
In any case, the attenuation for frequency values above 40khz is -3db

If you send 20 mW power, then output power for f > 40 khz will be

let output power = x

then 10 log(x/20) = 3
so x = 20 * 10 ^ -0.3 = 10 mW

Similarly for the attenuation value you have for frequncies less than 40 khz, calculate it the same way


Your bandwidth at the sender side is 70 - 10 = 60 kHz

Now you have forgotten to mention another data, which is the minimum power for which the signal will be held valid at the reciever. For example, -3db attenuation gave out a 10 mW power at the reciever, if this is less than the minimum value of the power that the reciever needs, then it will ignore these frequency values.

Only when that value is given you will be able to compute the harmonics reaching the reciever, the bandwidth of the reciever.

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