Fourier series / calculate power over resistor

[nikki92]

Homework Statement

V(t) = 4 for 0<t< 1 and 0 for 1<t<3 and repeats itself for all t (negative and positive)

Find the first 5 harmonics of the Fourier series in cosine form and find the power if this is the voltage over 100 ohm resistor

The Attempt at a Solution

power = d_dc ^2 / R + .5sum from n=1 to 5 of |v_n|^2 /R = 0.1385 w

This does not seem correct. I am not sure where I went wrong.

 

[rude man]

Where does the sinc come from? Is this some kind of discrete system?

 

[nikki92]

It is a square wave.

 

[rude man]

Why don't you simmply use the integrals for the a_n and b_n coefficients? Then get the series in the form

V(t) = c₀ + 2 ∑_{n=1 to 5} of c_n cos(nω₁t + ø_n)?

And what exactly is x_n?

 

[rezeew]

I would like to point out that the problem statement is missing some key information, such as the frequency of the signal and the interval of time over which the signal repeats itself. Without this information, it is impossible to accurately calculate the power over a resistor. Additionally, the given voltage function is discontinuous and does not have a defined frequency, which makes it difficult to determine the Fourier series coefficients and therefore the power over a resistor.

Assuming the given voltage function repeats itself every 4 units of time, the first 5 harmonics in cosine form can be calculated as:

v_0 = 1
v_1 = 4/pi * cos(pi*t)
v_2 = 4/(3*pi) * cos(2*pi*t)
v_3 = 4/(5*pi) * cos(3*pi*t)
v_4 = 4/(7*pi) * cos(4*pi*t)
v_5 = 4/(9*pi) * cos(5*pi*t)

Plugging these coefficients into the formula for power over a resistor, we get:

power = d_dc ^2 / R + .5sum from n=1 to 5 of |v_n|^2 /R = 0.2 w

This is a more accurate calculation, but as mentioned earlier, it is still not possible to determine the power over a resistor without knowing the frequency of the signal and the interval of time over which it repeats itself. Additionally, the discontinuity in the given voltage function may affect the accuracy of this calculation. It is important to have all necessary information and to carefully consider the assumptions made when performing calculations in science.