Code in Python

Problem 3A (i) (4 pts.) Consider the frequency fo = 420 Hz and the sampling rate f-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 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(04n-0.7) is obtained by sanpling a continuous-time sinusoid r(t) at a rate of 600 samples per second. If it is known that the frequency of a(t) is n the range 600 to 900 Hz, write an equation for x(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 x(t) (v) (5 pts.) Consider the three continuous-time signals n(t)=cos(36t), x2(t)=cos(56nt) and zalt)= cos(11Grt) The three signals are sampled at the same rate fa-1/T, to produce the sequences rin-ri(n%) (where i = 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 A 2 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 00 01 0 0 00 1 0 0 0 0 1 0 0 0 0 10 0 0 0 0 and Bx -7 30 2-5 1], determine the vector x