Average Power for Frequency < Fundamental Frequency: An Analysis

[sarveshkumarv]

We have a periodic signal of period 10 ms and amplitude 2.The signal is a rectangular pulse from -5/2 to 5/2 and 0 from 5/2 to 19/2.This signals fundamental frequency(f0) is 100Hz.It is passed through a filter whose response is 1/(1+jf/f0.I calculated the average power using the trignometric Fourier series expansion.I get the average total power for f=100,200 etc.But what will be the average power for f=50Hz.Will there be an average power for a freq less than fundamental frequency.Because we get nf0=f.For f=50Hz n=1/2.But the trignometric Fourier expansion talks only about the integer values of n.So wat is the avg power at f=50 Hz?

 

[antonantal]

This signal doesn't have a component at 50Hz. It only has the DC component, the fundamental and the components at positive integer multiples of the fundamental frequency (the harmonics).

 

[ravenprp]

The average power for a frequency below the fundamental frequency can still be calculated using the trigonometric Fourier series expansion. In this case, the value of n would be a non-integer, but it can still be approximated using the concept of fractional harmonics. The average power for a frequency of 50Hz would be the average total power for the harmonic with a frequency of 50Hz, which would be the first fractional harmonic with n=1/2.

It is important to note that the average power for a frequency below the fundamental frequency may not be accurate, as the filter response may not be well-defined for frequencies below the fundamental frequency. In this case, it would be more appropriate to use a different method of calculating average power, such as the Parseval's theorem.

In conclusion, although the trigonometric Fourier series expansion may not directly address frequencies below the fundamental frequency, it is still possible to approximate the average power for these frequencies using the concept of fractional harmonics. However, it is important to consider the limitations of the filter response and use alternative methods if necessary.