Consider the time-domain periodic signal, x(t) = 2 + cos - cos (121 + (a) The complex exponential Fourier series expansion of x(t) is given by: = Σ ₁. Exp ( 12x +-1). ex j2π- k=-00 Find T, and c,. x(t) = +3) + sin(16t). (b) Determine the Fourier transform X(f) of x(t). (c) Sketch the magnitude spectrum and phase spectrum of x(t) with proper labelling.

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Consider the time-domain periodic signal, x(t) = 2 + cos 12t+-
(a) The complex exponential Fourier series expansion of x(t) is given by :
k
- -1).
x(t) = Σ c exp|j2π.
km-00
T
Find T, and c.
21+ 7) + sin(161).
3
(b) Determine the Fourier transform X(f) of x(t).
(c) Sketch the magnitude spectrum and phase spectrum of x(t) with proper labelling.
Transcribed Image Text:Consider the time-domain periodic signal, x(t) = 2 + cos 12t+- (a) The complex exponential Fourier series expansion of x(t) is given by : k - -1). x(t) = Σ c exp|j2π. km-00 T Find T, and c. 21+ 7) + sin(161). 3 (b) Determine the Fourier transform X(f) of x(t). (c) Sketch the magnitude spectrum and phase spectrum of x(t) with proper labelling.
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