1. For the sequence {0, 1,2,3,...) that starts at n = 0, sketch (a) r(n-2) (b) r(n+2) (c) r(-n) (d) (-n+1) (e) r(-n-1) (f) r(2n) 2. Let r(n) and X (e) represent a sequence and its transform. Determine, in terms of X (ej), the transform of each of the following sequences: (a) g(n) = kr(n) (b) g(n) = x(n-no) (c) g(n) = x(2n) 3. Calculate the period for the following sequences (a) r(n) = 3sin(0.05) (b) r(n) 5 cos(0.6n) (c) r(n) = 2sin(0.05x) + 3sin(0.1πn) 4. Consider the difference equation y(n) 2y(n-1)+r(n) (a) Calculate the first four terms and a closed form expression when the input is r(n) = d(n) (b) Calculate the first four terms and a closed form expression when the input is r(n) = u(n) 5. For a N-length sequence r(n) and an M-length impulse response h(n), what is the length of the resulting sequence y(n) = r(n) *h(n) 6. Prove that the unit sample response of two linear shift invariant systems in cascade is the convolution of the two unit sample responses 7. Prove that two linear shift invariant systems in parallel are equivalent to a sin- gle system whose unit sample response is the sum of the individual unit sample responses. 8. If you have a signal with a 10 kHz bandwidth at an Intermediate Frequency (IF) of 20 kHz (i.e., the signal is contained in the frequency range of 15 kHz to 25 kHz), what sampling rate should you use to make sure you don't have any aliasing? (a) Draw the spectrum of the analog signal (b) Draw the spectrum of the sampled signal 9. GRADUATE STUDENTS (a) A causal linear shift invariant is described by the difference equation y(n) ay(n-1)+r(n) - br(n - 1)