20log(V(k)) (dB) 4) A system for discrete-time spectral analysis of continuous-time signals is shown below. In...

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20log(V(k)) (dB) 4) A system for discrete-time spectral analysis of continuous-time signals is shown below. In addition, the output [] from the system is shown in the plot. (Note the plot of [] is in dB.) One of the ten signals listed below is x(t), which is the input to the system shown and produces [k] as the output. Which signal(s) could be the input to the system? Important: please provide reasoning and explanation for your answer(s). x(t)=1000 cos(230) x(t)=1000 cos(115) x,(t) Analog-to-Digital xin Converter (f,-1000Hz) V[n] V[K] x(t)=10 32-point DFT 60 50 40 30 20- 10 0 x()=1000) x(t)=10(2) x(t)=1000(2) 0 n 31 w[n] 32 otherwise x, (1)=10 cos(250x1) 10 15 20 25 30 35 x, (1) 1000 cos (218.75) x(t)=10/(200 (1)=1000 5) A discrete-time signal is given as x[n] = {3.-5.2,-3). a) Compute X[k], the DFT of x[n] using the Fast Fourier Transform algorithm. Use 1-point DFTs as the lowest level. b) Using X[k], compute the original x[n] via the Inverse DFT using the Fast Fourier Transform algorithm. Use 1- point DFTs as the lowest level. 20log(V(k)) (dB) 4) A system for discrete-time spectral analysis of continuous-time signals is shown below. In addition, the output [] from the system is shown in the plot. (Note the plot of [] is in dB.) One of the ten signals listed below is x(t), which is the input to the system shown and produces [k] as the output. Which signal(s) could be the input to the system? Important: please provide reasoning and explanation for your answer(s). x(t)=1000 cos(230) x(t)=1000 cos(115) x,(t) Analog-to-Digital xin Converter (f,-1000Hz) V[n] V[K] x(t)=10 32-point DFT 60 50 40 30 20- 10 0 x()=1000) x(t)=10(2) x(t)=1000(2) 0 n 31 w[n] 32 otherwise x, (1)=10 cos(250x1) 10 15 20 25 30 35 x, (1) 1000 cos (218.75) x(t)=10/(200 (1)=1000 5) A discrete-time signal is given as x[n] = {3.-5.2,-3). a) Compute X[k], the DFT of x[n] using the Fast Fourier Transform algorithm. Use 1-point DFTs as the lowest level. b) Using X[k], compute the original x[n] via the Inverse DFT using the Fast Fourier Transform algorithm. Use 1- point DFTs as the lowest level.