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Its regular assignment of semester 5 course Analog Communication(BEE-Telecom)....

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Analog Communications Assignment # 1 Q 1:

For the signal 𝑔(𝑡) as shown, sketch: (a) 𝑔(𝑡 − 4); (b) 𝑔(2 − 𝑡); (c) 𝑔(2𝑡)

Q 2:

Evaluate the following integrals:

(i) ∞

∫ 𝑔(𝜏)𝛿(𝑡 − 𝜏)𝑑𝜏 −∞

(ii) ∞

∫ 𝛿(𝑡 − 2) sin(𝜋𝑡)𝑑𝑡 −∞

(iii) ∞ 𝜋 ∫ 𝑒 (𝑥−1) cos ( (𝑥 − 5)) 𝛿(𝑥 − 3)𝑑𝑥 2 −∞

Q 3: For the signals 𝑔(𝑡) and 𝑥(𝑡) as shown, find the component of the form 𝑥(𝑡) contained in 𝑔(𝑡). In other words, find the optimum value of 𝑐 in the approximation 𝑔(𝑡) ≈ 𝑐𝑥(𝑡) so that the error signal energy is minimum. What is the error signal energy?

Q 4:

Energies of the two signals 𝑥(𝑡) and 𝑦(𝑡) are 𝐸𝑥 and 𝐸𝑦 respectively.

Q 5: Find the correlation coefficient 𝑐𝑛 of signal 𝑥(𝑡) and each of the four pulses 𝑔1 (𝑡), 𝑔2 (𝑡), 𝑔3 (𝑡), and 𝑔4 (𝑡) shown in figure. Which pair of pulses would you select for a binary communication in order to provide maximum margin against the noise along the transmission path?

Q 6: For each of the periodic signals shown below, find the Fourier series and sketch the amplitude and phase spectra. If either the sine or cosine are absent in the Fourier series, explain why?

Q#7: From the definition, find the Fourier transforms of the following signals

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Q#8: From the definition, find the inverse Fourier transform of the following signals:

Q#9:

Q#10:

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