Question

1- A continuous-time periodic signal x(t) is real valued and has a fundamental period T=8. The nonzero Fourier series coefficients for x(t) are specified as a? = a_{-1} = j, a? = a_{-5} = 2 Express x(t) in the form $x(t) = \sum_{k=0}^{\infty} A_kcos(\omega_k t + \phi_k)$ 2- Find the complex Fourier series coefficients of the shown periodic signal. The signal is sinusoidal when non-zero. 3- Consider a continuous-time LTI system with impulse response h(t) = e??|t| Find the Fourier series representation of the output y(t) for each of the following inputs: a) x(t) = $\sum_{n=-\infty}^{\infty} \delta(t - n)$ b) x(t) = $\sum_{n=-\infty}^{\infty} (-1)^n \delta(t - n)$ Note: $H(j\omega) = \int_{-\infty}^{\infty} h(t)e^{-j\omega t}dt$

          1- A continuous-time periodic signal x(t) is real valued and has a fundamental
period T=8. The nonzero Fourier series coefficients for x(t) are specified as
a? = a_{-1} = j, a? = a_{-5} = 2
Express x(t) in the form  $x(t) = \sum_{k=0}^{\infty} A_kcos(\omega_k t + \phi_k)$
2- Find the complex Fourier series coefficients of the shown periodic signal.
The signal is sinusoidal when non-zero.
3- Consider a continuous-time LTI system with impulse response
h(t) = e??|t|
Find the Fourier series representation of the output y(t) for each of the
following inputs:
a) x(t) = $\sum_{n=-\infty}^{\infty} \delta(t - n)$
b) x(t) = $\sum_{n=-\infty}^{\infty} (-1)^n \delta(t - n)$
Note: $H(j\omega) = \int_{-\infty}^{\infty} h(t)e^{-j\omega t}dt$

1- A continuous-time periodic signal x(t) is real valued and has a fundamental
period T=8. The nonzero Fourier series coefficients for x(t) are specified as
a? = a-1 = j, a? = a-5 = 2
Express x(t) in the form x(t) = ∑k=0^∞ Akcos( t + )
2- Find the complex Fourier series coefficients of the shown periodic signal.
The signal is sinusoidal when non-zero.
3- Consider a continuous-time LTI system with impulse response
h(t) = e??|t|
Find the Fourier series representation of the output y(t) for each of the
following inputs:
a) x(t) = ∑n=-∞^∞δ(t - n)
b) x(t) = ∑n=-∞^∞ (-1)^n δ(t - n)
Note: H(jω) = ∫-∞^∞ h(t)e^-jω tdt

Added by James G.

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