X(t) 3 t -2 consider the periodic signal *, (+) - EL-I)" xct-7n) no a) Draw...
I need help with the following problem: Consider a periodic signal !(t), with period T, such that !(t) 0, 圹 From Example 2.3.1 of the class notes, the nth Fourier coefficient of r(t) is given by in012... a) Use Fourier series, and the symmetry of the sinc function, to express r(t) in terms of cosine functions. Do we also need sine functions in this representation? b) Suppase that is a signal with Fourier transform S Find and plot the Fourier...
2. Consider a periodic signal shown below (20 points) i(t) -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 (a) Find the fundamental period of this signal. (b) Consider following two signals, xi(t) and x2(t), obtained from the above signal, find their corresponding Fourier transforms: xi(t) -1 0 1 *2 (1) Its of, 0 1 2 3 4 5
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
Consider the following signal that is periodic with period T=2 a) Draw a picture of this signal for . b) For which values of t will the Fourier series provide a good approximation for this signal? Justify based on part a c) Find the complex Fourier coefficients Cn from the definition. (integrate through using a table of integrals) d) Find the real Fourier coefficients an, bn. You may use your knowledge of Cn to do this, without integrating. Alternatively, you...
Problem 1: (3 +2+3+2 10, sampling) Consider the continuous-time signal x(t) = 3 + cos(10?1+ 5) + sin(15?), t E R (a) Find the Fourier transform X-Fr. Hint: (F ejuot) (w) 2??(w-wo) (b) What is the Nyquist Frequency wn in radians/s of x? (c) Write an expression for the Fourier transform of the ideal sampling of x with sam- pling period T, = 2n/Cav.), i.e., ?00_ox(AZ)6(t-kZ) Hint: (F eiru>tz(t) (w) - X(w - rus) and recall Poisson's identity, CO eyru'st,...
Signal system 8. Consider the periodic signal x(t) = cos(2nt) + cos(2nt) I. a. Find the Fourier series coefficients for this signal. (4 points). b. If this signal passes through a LTI system with the impulse response h(t)=e* u(t), particularly, would the output signal also be a periodic signal ? If so, what would be the Fourier coefficients of the output signal ? (4 points). c. Give the mathematical expression for the output signal y(t). (2 points).
3. Consider the periodic signal x(t) = 0 otherwise (a) Plot r(t). (b) What is the period T of x(t)? (c) Find the CTFS coefficients ak for (t). 3. Consider the periodic signal x(t) = 0 otherwise (a) Plot r(t). (b) What is the period T of x(t)? (c) Find the CTFS coefficients ak for (t).
Let a periodic signal x(t) with a fundamental frequency ??e2? have a period 4.6 (a) Plot x(t), and indicate its fundamental period To (b) Compute the Fourier series coefficients of x(t) using their integral (c) (d) Answers: x(t) is periodic of fundamental period definition. Use the Laplace transform to compute the Fourier series coefficients Xk. Indicate how to compute the dc term. Suppose that y(t) = dx(t)/dt, find the Fourier transform of x(t) by means of the Fourier series coefficients...
Consider the periodic signal x(t) shown in the Figure below: x(t) . 3 2 0 1 2 3 4 5 6 t A. Determine the fundamental period T and the fundamental frequency wo. B. Compute the Fourier Series coefficients and simplify the expression to its simplest form.
4. Given that x(t) has the Fourier transform X(a), p(t) is a periodic signal with frequency of ??. p(t)-??--o nejnaot, where Cn is the Fourier series coefficient of p) (1) Assume y(t)-x(t)p(t), determine Y(?), the Fourier transform of the modulated signal y(t) in terms of X(). (2) Given the spectrum sketch of x(?) shown below, p(t)-cos(2t) cos(t), determine and sketch the Y() X(w) -1