The Dryden wind model treats wind (on each body axis) as a single-input-single-output system, whose driving input is random white noise. For each model we investigate, we should use the same input...

The Dryden wind model treats wind (on each body axis) as a single-input-single-output system, whose driving input is random white noise. For each model we investigate, we should use the same input data, so we'll start by defining a single u series of random white noise 5. n = 1000 u_series = [random.gauss (0,1) for i in range (n)] This same series will be used to update all three of our simulations. Also, for simplicity, we will focus on gusts along a single axis, the v axis in other words, we are only modeling WU) For each of the following parts, write code to find Wv in response to u. 4.a One simple way to model wind would be to model it as white noise. To do this, simply use the input: Wvi = u;0.059 (We apply a scale factor it so that it has a similar power spectrum as the Dryden model, at least over long periods of time, allowing for a more apples-to-apples comparison) 4.b Next, we'll implement the Dryden wind model using forward Euler integration. So, with each update step, you will evaluate Xi+1 = 1; +AT(Ax; + Bu;) Wv; = Yi = Cx Start with ro = [0,0] and use AT = 0.01 and Va = 25. 4.c Finally, implement the Dryden wind model using discretized update steps. With each update step you will evaluate Vi+1 = x; + Iu; Wvi = yi = Hai Again, start with 20 = [0,0] and use AT = 0.01 and Va = 25. 4.d Now that you've obtained three simulated time series of Wv, plot all three together. Comment on the result. Does the naive model or the Dryden model behave more like wind does, in your experience? How helpful is the discretized implementation of the Dryden model? SNote that u denotes an input to a system, not to be confused with with u, an aircraft's velocity in the direction