Question Please show details in this problem P-3.17 The two-sided spectrum representation of a real-valued signal x (t) is shown below (frequency in Hz): 11/2/5 Ile-/2/5 II l II. 7/3/5 7e-8a/ -180 -105 105 180 Figure P-3.17 (a) Determine the fundamental frequency (in Hz) for x (t). (b) Write the formula for x(1) as a sum of real-valued sinusoids. (c) The signal x2(t) = x(+ - 0.05) is a time-delayed version of x (1). Determine the spectrum of x2(1). Simplify the numerical values for the complex amplitudes, so that the phases lie in (-1,1). (d) A third signal is defined as x3 (t) = X(t)e/21077. This new signal is complex-valued, and it has a nonzero DC component. Determine the complex amplitude for the DC component of x3(t).

T3IZ26 The Asker · Electrical Engineering
Please show details in this problem

Transcribed Image Text: P-3.17 The two-sided spectrum representation of a real-valued signal x (t) is shown below (frequency in Hz): 11/2/5 Ile-/2/5 II l II. 7/3/5 7e-8a/ -180 -105 105 180 Figure P-3.17 (a) Determine the fundamental frequency (in Hz) for x (t). (b) Write the formula for x(1) as a sum of real-valued sinusoids. (c) The signal x2(t) = x(+ - 0.05) is a time-delayed version of x (1). Determine the spectrum of x2(1). Simplify the numerical values for the complex amplitudes, so that the phases lie in (-1,1). (d) A third signal is defined as x3 (t) = X(t)e/21077. This new signal is complex-valued, and it has a nonzero DC component. Determine the complex amplitude for the DC component of x3(t).
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Transcribed Image Text: P-3.17 The two-sided spectrum representation of a real-valued signal x (t) is shown below (frequency in Hz): 11/2/5 Ile-/2/5 II l II. 7/3/5 7e-8a/ -180 -105 105 180 Figure P-3.17 (a) Determine the fundamental frequency (in Hz) for x (t). (b) Write the formula for x(1) as a sum of real-valued sinusoids. (c) The signal x2(t) = x(+ - 0.05) is a time-delayed version of x (1). Determine the spectrum of x2(1). Simplify the numerical values for the complex amplitudes, so that the phases lie in (-1,1). (d) A third signal is defined as x3 (t) = X(t)e/21077. This new signal is complex-valued, and it has a nonzero DC component. Determine the complex amplitude for the DC component of x3(t).
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(a) fundamental frequency =GCD(105,180)(3.17)GCD=15:. fundamental frequency in Hz=15H3(6){:[x(t)=11e^(-j2pi//5)+11e^(j2pi//5)+7e^(j 31//5)+7e^(-j3pi//5)],[=11[e^(-j2pi//5)+e^(j2pi//5)]+7[e^(j3pi//5)+e^(-j3pi//5)]]:}{:[=2xx11[(e^(-j pi//5)+e^(j2pi//5))/(2)]+7xx2[(e^(j3pi//5)+e^(j3pi//5))/(2)]],[x(t)=22 cos(2pi//5)+14(cos(3pi//5))]:}(c){:[x_(2)(t)=x(t-0.05)],[x_( ... See the full answer