Question

The Fourier series expansion for a rectangular pulse wave with period $T_0$, amplitude A and pulse width $\tau = 50\%$ is: Given a periodic pulse train, x (t), with amplitude A=1 and period of $T_0$=10, Use Matlab to plot the signal in time domain. $x(t) = \sum_{n=-\infty}^{\infty} A \text{rect} \left(\frac{t - nT_0}{\tau}\right)$. $C_k = \frac{\tau}{T_0} \text{sinc} (kf_0\tau)$ 4) Approximate x(t) (reconstructed fourier series) by using 5, 11, 21 and 61 terms of FS coefficients C$_k$ and compare the results. Hint: use subplot to compare between the four graphs.

          The Fourier series expansion for a rectangular pulse wave with period $T_0$, amplitude A and pulse width $\tau = 50\%$ is:
Given a periodic pulse train, x (t), with amplitude A=1 and period of $T_0$=10, Use Matlab to plot the signal in time
domain.

$x(t) = \sum_{n=-\infty}^{\infty} A \text{rect} \left(\frac{t - nT_0}{\tau}\right)$.

$C_k = \frac{\tau}{T_0} \text{sinc} (kf_0\tau)$

4) Approximate x(t) (reconstructed fourier series)
by using 5, 11, 21 and 61 terms of FS coefficients
C$_k$ and compare the results.
Hint: use subplot to compare between the four
graphs.

Show more…

The Fourier series expansion for a rectangular pulse wave with period T0, amplitude A and pulse width τ = 50% is:
Given a periodic pulse train, x (t), with amplitude A=1 and period of T0=10, Use Matlab to plot the signal in time
domain.

x(t) = ∑n=-∞^∞ A rect((t - nT0)/(τ)).

Ck = (τ)/(T0)sinc (kf0τ)

4) Approximate x(t) (reconstructed fourier series)
by using 5, 11, 21 and 61 terms of FS coefficients
Ck and compare the results.
Hint: use subplot to compare between the four
graphs.

Added by Claire B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Deepak Jangra

Step 1

First, we need to define the rectangular pulse wave function. The function will have a value of A for the duration of €To, and 0 for the rest of the time. We can define this function as follows: ```matlab function y = rect_pulse(t, A, To, pulse_width) y = A * Show more…

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The Fourier series expansion for a rectangular pulse wave with period To, amplitude A and pulse width € =50% is= Given a periodic pulse train, x (t), with amplitude A-1 and period of To=10, Use Matlab to plot the signal in time domain. x(t) To ti2 ti2 To F(t) Arect (' " Ck = I sinc (kfot) To 4) Approximate x(t) (reconstructed fourier series) by using 5, 11,21 and 61 terms of FS coefficients Ck and compare the results. Hint: use subplot to compare between the four graphs:

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