Question

(a) Determine the period, amplitude, and frequency of a signal given by, v(t) (120nt). Plot this signal both in the time-domain and frequency domain. (b) For the following square wave v(t), determine if it is a periodic signal, and if yes, what 10 V sin 4. [61 are its amplitude, period T and fundamental frequency f? Why do we need to convert this signal into sine/cosine wave for transmission? 2 o-oims (c) () According to Fourier Theorem, the above signal v(t) can be converted to the following Fourier series, u(t)s ao + Σ%,1 (an cos 2 πηft + bn sin 2 πηft). Write an expression for determining the Fourier coefficient amplitude terms ao, an and ba. (i) After calculating the Fourier coefficients for the above square wave, we find that: v(t) 5V 6.37 V sin 2Tmft +2.12V sin 2T(3f)t + 0.27 V sin2n(5f)t Plot these 4 terms of the Fourier series v(t) of the above square wave in time-domain in a single diagram (Amplitude vs time), show that by adding these terms we can synthesize and get back the wave from of the original square wave in waveform. (ii) Also plot the above 4 harmonics in a single frequency-domain spectral diagram and determine the required spectrum (Bandwidth) for the transmission of these 4 harmonics. [5]

Answer 1

Fig 1 : to find sine wave parameters compare with a general sine wave expression

fig 2: parameters for a sine wave found in the same way as sine wave

fig 3: plotting the spectrum is extremely important for band width determination.