Introduction to signals PDF

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Exercise - Introduction to Signals 1. The frequency of a periodic signal is 20 MHz, state it's period. F=1/T T=1/F T=1/20x10^6 T=5x10^-8seconds 2. A signal has a period T of 0.033 µs, state it's frequency. F=1/T F= 1/0.033 F= 30 MHz 3. Calculate the period of the UK's 50 Hz mains electricity supply. F=1/T T=1/F T=1/50 T= 0.02 seconds 4. Calculate the frequency of the rotation of the Earth. F=1/T F=1/23 F= 0.00434782609 degress/second 5. Calculate the frequency of the orbit of the Earth around the Sun 3.168808 * 10^-8 Hz 1. Calculate the angular velocity ω for the following format of vinyl records 78's: 2 x pi x 78 / 60 radians per second = 8.17 radians per second. 45's: 2 x pi x 45 / 60 radians per second = 4.71 radians per second. LP's: 2 x pi x 33 1/3 /60 radians per second = 3.49 radians per second.

2. What is the instantaneous amplitude of a sinusoidal signal with period T = 5 ns and peak amplitude of 1.141 V at t = 26.8 ns. 1 3. Calculate for a sinusoidal signal with an angular velocity of 314.1593 radians/s and a peak voltage of 340 V. The instantaneous amplitude at t = 15 ms V(t) = A.sin(ω.t) V(t) = 340 sin (314.1593 x 15 x 10-3) V(t) = 340 sin (4.71) V(t) = 27.92 4. The amplitude at an angular rotation of 7.0669 radians. 5. The period of the signal. 6. The frequency of the signal. 7. BBC Radio 4 transmits on 93.5 MHz FM and 198 kHz LW. Calculate the wavelengths at which the signals are broadcast. 93.5 MHz: 1.33 meters 198 KHz: 1 meters 8. The BBC world service transmits in the short wave radio spectrum to Western Europe at wavelength 31.8589 m. Calculate the frequency the signal is transmitted at. 9. Calculate the period T for a signal in the ultra violet with a wavelength of 450 nm 450 nm = 0.45‾⁶ m; T = 0.45 X 10‾ ⁶ m / 300,000,000(m/s) = 0.15 X 10‾⁶ ‾⁸ = 1.5 X 10‾¹⁵ s

10. What bandwidth would be required to transmit the following signal v(t)? v(t) = cos(2.π.f.t) - cos(6.π.f.t) + cos(10.π.f.t) If the available transmission bandwidth were to be decreased by 30%, what would happen to the signal V( t )=c os ( 2. π. f . t )-c os( 6. π. f . t )+c os ( 10. π. f . t ) V( t )=c os ( 2. π. f . t )-c os( 2. π. 3. f . t )+c os ( 2. π. 5. f . t ) Bandwi dt h=5f-f=4. fHz...