Question

Exercise 2. Show that the waveform of Example 1 has exponential Fourier series, $\infty$ $v(t) = \sum_{n=-\infty} \frac{-j2}{n\pi} exp(j \frac{2\pi nt}{T})$, n odd Volts Example 1: Square wave. $\int_{t_0}^{t_0+T} v(t) exp(-jn\omega_0 t)dt$ $C_n = \frac{1}{T} \int_{t_0}^{t_0+T}$ $v(t) = \sum_{n=-\infty}^{\infty} C_n exp(jn\omega_0 t)$

          Exercise 2. Show that the waveform of Example 1 has exponential Fourier series,
$\infty$
$v(t) = \sum_{n=-\infty} \frac{-j2}{n\pi} exp(j \frac{2\pi nt}{T})$, n odd Volts
Example 1:
Square wave.
$\int_{t_0}^{t_0+T} v(t) exp(-jn\omega_0 t)dt$
$C_n = \frac{1}{T} \int_{t_0}^{t_0+T}$
$v(t) = \sum_{n=-\infty}^{\infty} C_n exp(jn\omega_0 t)$

Exercise 2. Show that the waveform of Example 1 has exponential Fourier series,
∞
v(t) = ∑n=-∞(-j2)/(nπ) exp(j (2π nt)/(T)), n odd Volts
Example 1:
Square wave.
∫t0^t0+T v(t) exp(-jnω0 t)dt
Cn = (1)/(T)∫t0^t0+T
v(t) = ∑n=-∞^∞ Cn exp(jnω0 t)

Added by Ricky R.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Stylianos Gregoriou

Step 1

In Example 1, the waveform is a square wave. The period, T, is the time it takes for the waveform to complete one full cycle. In this case, the waveform completes one full cycle in T/2 seconds. Show more…

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Exercise 2. Show that the waveform of Example 1 has an exponential Fourier series. v(t) = exp(2nt) for n odd Volts. Example 1: Square wave. v(t) (Volts) T/2 fo+T v(t) exp(-j nÏ‰t)dt v(t) = âˆ« C exp(jnÏ‰t)