Fourier transform of the following signal

Determine the Fourier series coefficients of the following signal, which is periodic in T = 10.

Determine the Fourier transform of the following signal, which is zero outside the indicated range.

A message signal has the form m(t) = cos(2000πt) + 14 cos(4000πt).
This message is DSB-SC modulated onto a carrier defined by c(t) = 100
cos(2πfct), where fc = 3 MHz. Determine the time-domain expression for
the modulated sig- nal. (Your answer should be in terms of a sum, not
product, of cosine functions).

A modulating wave m(t) = 3 cos(2π100t) + 4 sin(2π100t) volts is
applied to an FM modulator with a carrier wave of frequency 1MHz and of
amplitude 10 volts. The modulator’s frequency sensitivity kf = 20 Hz/V.

• Determine the peak frequency deviation ∆f of this FM signal.
• Find the mathematical expression for the modulated FM signal. (Simplify your answer as much as possible).
• Use Carson’s rule to estimate the transmission bandwidth of the modulated signal.

Consider the system in the following figure

• Sketch Xp(ω) for −9π ≤ ω ≤ 9π for the following values of ω0.
  1. ω0 = π (ii) ω0 = 2π (iii) ω0 = 3π (iv) ω0 = 5π
• For which of the preceding values of ω0 is xp(t) identical?

• A sinusoidal signal, with an amplitude of 3.25 volts, is applied to
  a uniform quantizer whose output takes on the values of 0,±1,±2,±3
  volts, Sketch the waveform of the resulting quantizer output for one
  complete cycle of the input.
• Repeat this evaluation for the case when the quantizer’s output takes on the values of ±0.5,±1.5,±2.5,±3.5 volts.

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