Final answer:
The output spectrum of the signal is the product of its input spectrum and the transfer function of the filter at the input frequency. To find the amplitude and phase of the output signal, calculate the modulus and angle of the complex transfer function at the input frequency.
Step-by-step explanation:
When the signal with the spectrum S(\u03c9)=0.5\u03b4(\u03c9\u22121500) goes through the filter with the transfer function H(\u03c9)=1/10+j1000, the output spectrum is obtained by the product of S(\u03c9) and H(\u03c9) at \u03c9=1500.
Therefore, the spectrum of the output signal is Sout(\u03c9)=S(\u03c9)\u00d7H(\u03c9)=0.5\u03b4(\u03c9\u22121500)\u00d7(1/10+j1000) at \u03c9=1500.
To find the amplitude and phase of the output signal, we evaluate the magnitude and the angle of the complex number H(1500). The amplitude |H(1500)| is the modulus of the complex number which can be found using the formula |H| = \u221a(Re2+Im2), and the phase angle \u03c6 is found using the formula tan\u207b\u00b9(Im/Re).