Question

6.3-3 A periodic signal $x(t)$ is expressed by the following Fourier series: $x(t) = 3cos t + sin left(t - frac{pi}{6} ight) - 2cos left(t - frac{pi}{3} ight)$ (a) Sketch the amplitude and phase spectra for the trigonometric series. (b) By inspection of spectra in part (a), sketch the exponential Fourier series spectra. (c) By inspection of spectra in part (b), write the exponential Fourier series for $x(t)$. (d) Show that the series found in part (c) is equivalent to the trigonometric series for $x(t)$.

          6.3-3 A periodic signal $x(t)$ is expressed by the following Fourier series:

$x(t) = 3cos t + sin left(t - frac{pi}{6} 
ight) - 2cos left(t - frac{pi}{3} 
ight)$

(a) Sketch the amplitude and phase spectra for the trigonometric series.
(b) By inspection of spectra in part (a), sketch the exponential Fourier series spectra.
(c) By inspection of spectra in part (b), write the exponential Fourier series for $x(t)$.
(d) Show that the series found in part (c) is equivalent to the trigonometric series for $x(t)$.

$6.3-3 A periodic signal x(t) is expressed by the following Fourier series: x(t) = 3cos t + sin left(t - fracpi6 ight) - 2cos left(t - fracpi3 ight) (a) Sketch the amplitude and phase spectra for the trigonometric series. (b) By inspection of spectra in part (a), sketch the exponential Fourier series spectra. (c) By inspection of spectra in part (b), write the exponential Fourier series for x(t). (d) Show that the series found in part (c) is equivalent to the trigonometric series for x(t).$

Added by Vincent G.

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