Given H(z) as shown, determine the response y(n) function 6In-3] for all n >= 0) of...
Use the Principle of Mathematical Induction to prove that (2i+3) = n(n + 4) for all n > 1.
Q 3 a) Let n > 2 be an integer. Prove that the set {z ET:z” = 1} is a subgroup of (T, *). Show that it is isomorphic to (Zn, + mod n). b) Show that Z2 x Z2 is not isomorphic to Z4. c) Show that Z2 x Z3 is isomorphic to 26.
0 for t<0 t-1 for 0sts2 16. The step response of a LTI system is given by y sep 1for 2sts3 0 for t 24 (a) Determine the impulse response of the system h() (b) Write the impulse response in terms of unit step functions.
Prove that is an integer for all n > 0.
) Construct a context-free grammar for the language L={ ab”ab”a | n> > 1}.
BC:9.4 A LTI discrete time system has an impulse response h[n] = (-0.8)"u[n] + (0.65)"u[n-1] Find the transfer function, #(eo), in the normalized frequency domain. Use Matlab to plot the magni- tude and phase (in degrees) of H(eo) in the range of-? < ? < ?. Attach your Matlab source code with the plots. 1212 AM ^???4/4/2013
3) Given the system function of a discrete time filter 1-2z-1 10.4z-1 with R. 0. C: Iz| > 0.4 The unit sample response h[n] is a) h[n] =-58m] 6(0.4")u[n] b) h[n]- -56[n] 60-0.4)"ufn] c) h[n] = (-0.4n)2[n]-2 (-0.4n-1)u[n-1] d) h[n] = (-0.4)"u[n]-2(-0.4)"-111[n-1] e) b and c f) b and d g) a and d h) a and c i) none of the above hint: use Partial Fraction Expansion
Detail Explain please:
6 Impulse Response Let h(t) denote the response of a system for which the input signal is the unit-impulse t 0: he(t) = t [a(t) _ u(t-1)] + 2a(t-2), for t > 0.
For all n E N prove that 0 <e- > < 2 k!“ (n + 1)! k=0 Hint: Think about Taylor approximations of the function e".
5. Given y,-t is a solution of t2y" + 2t1-2y = 0, for t > 0, find a second solution y2.