a) Consider the following signal $f(t)=2 \sin(3t)+4 \cos(5t)+6 \sin(7t)$
i) Determine if the signal is periodic or not
ii) If signal is periodic, find its fundamental period and sketch one period of the signal.
iii) If the signal is non-periodic, explain why? (Unit 1)

b) Find the Fourier transform of an impulse function $x(t)=\delta(t)$. Also draw the spectrum. (Unit 1)

a) What is the principle of Amplitude modulation? Derive expression for the AM wave and draw its spectrum. (Unit 2)

b) A modulating signal of $2 \cos(5000t)$ is amplitude modulated over a carrier signal of $5 \cos(20000t)$. Derive the expression for modulation index, LSB and VSB frequencies, Bandwidth and the ratio of side band power in the Total Power of AM wave. (Unit 2)

a) Explain frequency modulation. Derive the relation between frequency modulation and phase modulation. (Unit 3)

b) A 107.6 MHz carrier signal is frequency modulated by a 7 kHz sine wave. The resultant FM signal has a frequency deviation of 50 kHz. Determine:
i) The carrier swing of the FM signal.
ii) The highest and the lowest frequencies attained by the modulated signal.
iii) The modulation index of the FM wave. (Unit 3)

a) State and explain sampling theorem in time domain. Explain about Nyquist rate. (Unit 4)

b) Find the Nyquist rate and Nyquist interval for the signal $x(t)=\frac{1}{2\pi}\cos(4000\pi t)\cos(1000\pi t)$ (Unit 4)

a) Explain DPSK. With the help of block diagram explain generation and detection of DPSK. (Unit 5)

b) Describe with the help of neat diagram, the operation of QPSK modulator. Draw its phasor and constellation diagram. (Unit 5)

a) Discuss the advantages and limitation of Pulse Code Modulation (PCM) as digital modulation technique. Illustrate your answer with suitable examples. (Unit 4)

b) Compare and contrast Natural Sampling, Flat top Sampling and Aperture Effect in analog to digital conversion. Explain their implication on the reconstructed signal. (Unit 4)

a) Explain the working principle of Foster-Seeley discriminator. Derive an expression for its output voltage and explain how the discriminator provides frequency demodulation. (Unit 3)

b) Discuss the concept of pre-emphasis and de-emphasis in FM systems. Explain how pre-emphasis and de-emphasis techniques help in improving signal quality. (Unit 3)

a) Explain the concept of DSB-FC modulation. Discuss its advantages and disadvantages. (Unit 2)

b) Discuss the demodulation technique used for AM signals. Explain the working principle of the square law detector and envelope detector in demodulating AM signals. Compare and contrast the advantages and limitation of these demodulation techniques. (Unit 2)