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Fourier series expansions of Periodic Signals

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Use the Fourier series expansions of periodic square wave and triangular signals to find the sum of the following series:

1 - 1/3 + 1/5 - 1/7 + ...

1 + 1/9 + 1/25 + 1/49 + ...

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Please see the attached file.

We write the triangle wave as:

It looks like:

This function is symmetric; hence we will expand it as a cosine series. For a function defined in the ...

Solution Summary

The solution explains the Fourier series expansions for the Periodic Signals. Periodic square waves and triangular signals to find the sum of functions are examined.

See Also This Related BrainMass Solution

Fourier Series of Signal

(See attached file for full problem description)

Consider a periodic function f(x) with period L.
Over one period, f(x) = sin(2*pi*x/L) over the interval -L/4 to L/4, f(x) = 0 over the intervals -L/2 to -L/4, and L/4 to L/2.
Derive an expression for the nth Fourier series coefficient, an.
In the Fourier series expansion

plot for n = -4 to 4 using matlab, and superimpose onto a plot for f(x)

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