Analogue telecommunications modulations - example

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SUMMARY

The discussion focuses on the analysis of analogue telecommunications modulations, specifically the simultaneous transfer of two telegraphic signals using bandpass filters. The signals are modulated with carriers at frequencies f1 and f2, where f2 is 120Hz higher than f1. The key calculation involves determining the attenuation of the filter in the stop band, which is established as 19.5 dB based on the logarithmic ratio of median power between the telegraphic signal and parasitic components. The discussion emphasizes the importance of understanding Fourier series in the context of amplitude, phase, and frequency modulations.

PREREQUISITES
  • Understanding of Fourier series in signal processing
  • Knowledge of bandpass filter design and characteristics
  • Familiarity with analogue telecommunications concepts
  • Basic principles of amplitude, phase, and frequency modulation
NEXT STEPS
  • Study the design and application of bandpass filters in telecommunications
  • Learn advanced Fourier analysis techniques for signal modulation
  • Explore the impact of filter characteristics on signal integrity
  • Investigate the principles of parasitic signal management in telecommunication systems
USEFUL FOR

Telecommunications engineers, signal processing specialists, and students studying analogue modulation techniques will benefit from this discussion.

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Here is my task (Basics of analogue telecommunications):

Block diagram of device for simultaneous transfer of two telegraphic signals u1(t) and u2(t) is shown on image 1. Both signals have waveform as periodioc signal um(t) on image 2. Frequencies f1 and f2 of carriers $$u_{01}(t)=U_0 cos(\omega_1 t)$$ and $$u_{02}(t)=U_0 cos(\omega_2 t)$$ are choosen so f2=f1+120Hz.
For good transfer of telegraphic signal through one channel it is enough to transfer components in range of 80Hz around frequency of carrier. For that purpose, bandpass filter in first channel has attenuation characteristic as in image 3. Characteristic of attenuation of filter in second channel has same shape, only it is shifted to right for 120Hz.
Because of finite attenuation of filter in stop band, signal u(t) contains unwanted products of modulation, some of which fall from one channel in bandpass of second channel. If condition is that logarithmic ratio of median power of whole signal and median power of parasitic components in one channel equals 40dB, calculate attenuation of filter, a[dB], in stop band.

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Any suggestion?
We are studying amplitude, phase and frequency modulations now. Although I'm familiar with basic concepts, I don't know how to apply it here.
I wrote signal um(t) in terms of Fourier series. x1(t) would be Fourier series of um(t) times carrier u01(t), and x2(t) would be Fourier series of um(t) times carrier u02(t).
Final result is a = 19.5 dB
 
Hello.
I didn't make any progress in solving this problem.
 
Fig 3 represents a bandpass filter, so we are told, meaning upwards represents greater attenuation. (I think I'd prefer it drawn upside down.) When your squarewave is filtered, some of its harmonics will lie outside its filter's passband yet within the finite attenuation region of the other signal's filter.

That's how I'd summarize the problem, as I read it.
 

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