a) Find the Fourier transform of the half-cosine pulse in figure (a). Sketch amplitude spectrum of the G(f). b) Apply the time-shifting property to the result obtained in part (a) to evaluate the spectrum of the half-sine pulse shown figure (b). Sketch amplitude spectrum of the G(f). c) What is the spectrum of a half-sine pulse in figure (b) having a duration equal to aT ? Sketch amplitude spectrum of the G(f). d) What is the spectrum of the negative half-sine pulse shown in figure (c) ? Sketch amplitude spectrum of the G(f). e) Find the spectrum of the single sine pulse shown in figure (d). Sketch amplitude spectrum of the G(f). g(t) g(t) A -T/4 0 T/4 T/2 (a) (b) g(t) g(t) -T/2 -T/2 T/2 -A -A (c) (d)

One single spike in the domain may represent a sine wave in the domain.a. frequency; time b. frequency; time c. time; phased. time; phase

Fourier theory states that any sinusoidal signal may be represented or analyzed as the sum of a fundamental sine wave at the signal frequency plus odd, even, or odd plus even nonharmonic sine waves of different phases and amplitudes. True False

The bandwidth of a composite signal is the difference between the highest and the lowest frequencies contained in that signal. (a) If a periodic signal is decomposed into five sine waves with frequencies of 100, 300, 500, 700, and 900 Hz, what is its bandwidth? Draw the spectrum, assuming all components have a maximum amplitude of 10 V. (b) A periodic signal has a bandwidth of 20 Hz. The highest frequency is 60 Hz. What is the lowest frequency? Draw the spectrum if the signal contains all frequencies of the same amplitude. A non-periodic composite signal has a bandwidth of 200 kHz, with a (c) middle frequency of 140 kHz and 20 V as peak amplitude. The two extreme frequencies have amplitude of 0. Draw the frequency domain of the signal. (d) The period of a signal is 100ms. What is its frequency in kilohertz?