Solve the questions by coding in python.
(i) (4 pts.) Consider the frequency fo 420 Hz and the sampling rate fs 600 samples/sec. List all the aliases of fo with respect to f, in the frequency range 0.0 to 3.0 kHz (ii) (2 pts.) If we sample, at rate fs-600 samples/sec, a continuous-time real-valued sinusoid whose frequency is one of the values found in part (i) above, what is the resulting frequency w of the sample sequence? Give your answer in the range [0, ?] (radians/sample) (iii) (5 pts.) The discrete-time sinusoid-ln-2.9cos(04?n-0.7) is obtained by sampling a continuous-time sinusoid r(t) at a rate of 600 samples per second. If it is known that the frequency of r(t) is in the range 600 to 900 Hz, write an equation for r(t) (iv) (4 pts.) Let x[n] be as in (ii, with the sampling rate unchanged. If, instead, it is known that the frequency of r(t) is in the range 1,500 to 1,800 Hz, write a new equation for r(t). (v) (5 pts.) Consider the three continuous-time signals r?(t) cos(36t)cos(56t) nr3(t) cos (116t) The three signals are sampled at the same rate fa = 1/T, to produce the sequences rIn-ri(n%) (wherei-1,2,3). Determine the only value of fa greater than 7 samples/second such that the three sequences are identical, i.e., Problem 3B (i) (10 pts.) It is known that 0 0 0 Express in terms of u, v and w. Can you determine the dimensions (size) of A based on this information? (ii) (5 pts.) If 00 0 00 1 00 0 01 0 00010 0 00 1 0 0 0 0 1 0 0 0 0 10 0 0 0 0 and Bx= 7 3 0 2-5 1]T, determine the vector x (i) (4 pts.) Consider the frequency fo 420 Hz and the sampling rate fs 600 samples/sec. List all the aliases of fo with respect to f, in the frequency range 0.0 to 3.0 kHz (ii) (2 pts.) If we sample, at rate fs-600 samples/sec, a continuous-time real-valued sinusoid whose frequency is one of the values found in part (i) above, what is the resulting frequency w of the sample sequence? Give your answer in the range [0, ?] (radians/sample) (iii) (5 pts.) The discrete-time sinusoid-ln-2.9cos(04?n-0.7) is obtained by sampling a continuous-time sinusoid r(t) at a rate of 600 samples per second. If it is known that the frequency of r(t) is in the range 600 to 900 Hz, write an equation for r(t) (iv) (4 pts.) Let x[n] be as in (ii, with the sampling rate unchanged. If, instead, it is known that the frequency of r(t) is in the range 1,500 to 1,800 Hz, write a new equation for r(t). (v) (5 pts.) Consider the three continuous-time signals r?(t) cos(36t)cos(56t) nr3(t) cos (116t) The three signals are sampled at the same rate fa = 1/T, to produce the sequences rIn-ri(n%) (wherei-1,2,3). Determine the only value of fa greater than 7 samples/second such that the three sequences are identical, i.e., Problem 3B (i) (10 pts.) It is known that 0 0 0 Express in terms of u, v and w. Can you determine the dimensions (size) of A based on this information? (ii) (5 pts.) If 00 0 00 1 00 0 01 0 00010 0 00 1 0 0 0 0 1 0 0 0 0 10 0 0 0 0 and Bx= 7 3 0 2-5 1]T, determine the vector x
