(1) f(x)= x/2
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- A continuous periodic signal x (t) of real value y has a fundamental period of T = 8. The coefficients of the nonzero Fourier series for x (t) are a1 = a-1 = 2, a3 = a * -3 = 4j Express x (t) in the formSketch the function f(x) = |sin(x)| and find a Fourier series representation of it.How to find the complex Fourier series coefficients and the Fourier transform of x(t)?
- x(0)=4, x(1)=3, x(2)=2, x(3)=1, x(4)=0, x(5)=0 give as, x(n) series ( 0≥ ? ≥ 5 ). a)calculate x(k) with discrete fourier transform coefficients. (step-by-step should be written)Consider a linear, time-invariant, continuous-time system.a) Since the impulse response of the system is given as ℎ (?) = ? (?) - ? (? - ?), calculate the frequency response of the system (??).b) Write the Fourier series representation by finding the fundamental frequency of the input signal ? (?) = cos (4000??).c) Show that the output signal of the system (?) can be obtained by using the Fourier series coefficients of the input signal (?) and the frequency response of the system ? (??).d) What is the fundamental frequency of the ? (?) sign? Explain why.e) Write the Fourier series representation of the sign ? (?).Laplace transform: Solve the following initial value problem.