1. Show that if x(t) is an even function of t, then X(jw)2 (t) cos(wt) dt...
(b) (2 pts) (t) is given as r(t) e sin(t) Find X(jw). Show that X(jw) = 25 + (w- 1)225(w+1)2 (c) (4 pts) x(t) is given as x(t)-π inc(t) cos(nt). Find X(jw) (d) (4 pts) 2(t) is given as 2(t) e Áil+ 3) + e' ỗ(t-3). Find X (jw). Simplify the answer as (e) (4 pts) 2(t) is given as r(t) = rect(2(t )) reetgehj)). Hint: use Fourier Transform pair: sine(t)艹rect( ) much as possible Find X(jw). Simplify the answer...
x(t) has the fourier transform x(jw) show dx(t)/dt has the fourier transform jw x(jw)
1. (a) You have seen that the Fourier transform of cos(wt) and sin(wt) func- tions results in even and odd combinations of delta functions in the frequency domain. Prove the opposite. That is, find the combination of delta functions in the time domain that give cosine and sine functions in the frequency domain. (b) Use the signum function to relate these two combinations of delta functions and use the convolution theorem to show that sin (wt) = cos (wt) *...
Problem 3: a) Show that is f(t) is an even, real valued periodic function of time with period To, then 0 f(t)dt ao = T. Jo b) Show that is f(t) is an odd, real valued periodic function of time with period To, then an-0 f (t) sin(nwot)dt
2. Let g(t)=e-2,[sin(6π) + 2 cos(3m)]. FindJa-2)g(t)dt. 3. Let g(1)=-2111(1)-11(1-2)|. Plot g(t) Using g(t) from problem 3, plot g| and g 4. i-2 5. Let g(t)=Πcos(2km. Is this an even or odd function. (Justify your answer) に!
7. Find the function f(t) that satisfies the equality f(t)dt = x-COS x + 1. 7. Find the function f(t) that satisfies the equality f(t)dt = x-COS x + 1.
A particle moves on x-y plane according to the equations x = a cos (wt), y = b sin (wt). 1 - Show that its trajectory is an ellipse? 2 - Calculate the values of its velocity v(t) = |v(t)| and acceleration a(t) = |a(t)| ? 3 - What are the maximal and minimal values of v(t) and a(t) ? I think for the first part the answer is as the following image. Please correct me if my answer is...
1. (a) We want to develop a method for calculating the function sint dt f)-inf t 0 for small or moderately small values of x. This is a special function called the "sine integral", and it is related to another special function called the "exponential integral". It arises in diffraction problems. Derive a Taylor-series expression for f(x), and give an upper bound for the error when the series is terminated after the n-th order term. [HINT: (-1)"*z ? + R...
answer 1,2,3,4 thank you. HW4.5: Problem 1 Previous Problem Problem List Next Problem 1 point) Evaluate each of the integrals (here &(t) is the Dirac delta function) (60-3)dt (2)cos(3t)S(t -2) dt- (3)/eTst cos(4t)(t - 3) dt - c0 sin()(t - 5) dt- HW4.5: Problem 1 Previous Problem Problem List Next Problem 1 point) Evaluate each of the integrals (here &(t) is the Dirac delta function) (60-3)dt (2)cos(3t)S(t -2) dt- (3)/eTst cos(4t)(t - 3) dt - c0 sin()(t - 5) dt-
0and / is an odd function of t, find the Fourier sine sin wt d for 0<t< 1 10, (a) If f(t) = for t a 0 transform of f. Deduce thato s if0<t < a. What is the value of the integral for t2 a? for 0 < t < b (b) If g(t)-{ b-t and g is an even function of t, find the Fourier 0 cosine transform of g. Deduce that foo 1-w2bw cosa t dw =...