(a) Sketch 1 [u(t-1)-u(t-2)] (b) Using the generalized function definition of impulse: "(t)8(1)dt = poſs(t)dt =...
aliasing? A continuous-time system is given by the input/output differential equation 4. H(s) v(t) dy(t) dt dx(t) + 2 (+ x(t 2) dt (a) Determine its transfer function H(s)? (b) Determine its impulse response. (c) Determine its step response. (d) Is the stable? (a) Give two reasons why digital filters are favored over analog filters 5. (b) What is the main difference between IIR and FIR digital filters? (c) Give an example of a second order IIR filter and FIR...
1. (a) Suppose the unit step function uc(t) has a generalized derivative u(t) everywhere. Find L[u'(t)] for c > 0. What generalized function is u(t) equal to do you think?
the function y=f(x)={ 0-4), 14x+16, x20 x<0 Consider 1. (a) Sketch the graph off. (3 pts.) (b) Verify that the function is continuous everywhere using the properties of the definition and possibly calculating the limit at a particular point. (2 pts.) (c) Show f'(x) is not continuous at x-0. (5 pts.) the function y=f(x)={ 0-4), 14x+16, x20 x
In the previous homework, the Fourier Transform of x(t)- t[u(t)-u(t-1) was found to be x(t) 2 0 -1 -2 -3 5 4 3-2 0 2 3 4 5 a) b) Using known Fourier transforms for the terms of y(t), find Y(j). (Hint: you will have to apply some c) Apply differential properties to X(ju) to verify your answer for part b Differentiate x(t), y(t) = dx/dt. Note, the derivative should have a step function term. Include a sketch of y(t)...
1. (20 p) Compute and sketch the output y(t) of the continuous-time LTI system with impulse response h(t) = el-tuſt - 1)for an input signal x(t) = u(t) - ut - 3). 2. (20p) Consider an input x[n] and an unit impulse response h[n] given by n-2 x[n] = (4)”- u[n – 2] h[n] = u(n + 2] Determine and plot the output y[n] = x[n] *h[n].
PLEASE ANSWER ALL! SHOWS STEPS 2. (a) Prove by using the definition of convergence only, without using limit theo- (b) Prove by using the definition of continuity, or by using the є_ó property, that 3. Let f be a twice differentiable function defined on the closed interval [0, 1]. Suppose rems, that if (S) is a sequence converging to s, then lim, 10 2 f (x) is a continuous function on R r,s,t e [0,1] are defined so that r...
x(t)-A()x(t) + B(t)u(t) 2. Consider the following system y(t)-C(t)x(t) where A(t)- 0 1) Derive the state transition matrix Φ(t, τ). 2) Derive the impulse response function g(t, z). x(t)-A()x(t) + B(t)u(t) 2. Consider the following system y(t)-C(t)x(t) where A(t)- 0 1) Derive the state transition matrix Φ(t, τ). 2) Derive the impulse response function g(t, z).
Problem 2: A sinusoidal signal w(t) = 10cos(200nt) is sampled using a periodic impulse function s(t) = Ek=-08(t - kt), where the sampling period Tg = 1ms. a) Sketch the signal w(t) and its corresponding impulse-sampled function ws(t) = w(t)s(t) b) What is the sampling frequency fs of this signal? c) Write an expression for the spectrum W (f) and the spectrum of the sampled signal Ws(f). Sketch W, (f) and specify the coordinates of its frequency components.
solve please 8 Sketch the direction field of the differential equation dx dt Verify that x t-1 Ce is the solution of the equation. Sketch the solution curve for which x(0) 2, and that for which x(4) 0, and check that these are consistent with your direction field. MAPI R has tools for exam 8 Sketch the direction field of the differential equation dx dt Verify that x t-1 Ce is the solution of the equation. Sketch the solution curve...
Verify the following using MATLAB 2) (a) Consider the following function f(t)=e"" sinwt u (t (1) .... Write the formula for Laplace transform. L[f)]=F(6) F(6))e"d Where f(t is the function in time domain. F(s) is the function in frequency domain Apply Laplace transform to equation 1. Le sin cot u()]F(s) Consider, f() sin wtu(t). From the frequency shifting theorem, L(e"f()F(s+a) (2) Apply Laplace transform to f(t). F,(s)sin ot u (t)e" "dt Define the step function, u(t u(t)= 1 fort >0...