Frequency content calculation

[Petcu Daniel]

Dear Members,

Giakas is using the higher frequency included in the 95% of the signal amplitude in order to characterise the frequency content of GRF components (http://www.gaitposture.com/article/S.../abstract?cc=y= ). For a frequency of the fundamental harmonic of 1.43Hz, "95% of the signal amplitude is contained in the first 15 harmonics (20.27 Hz) in the Z, 14 harmonics (18.92 Hz) in the Y and 19 harmonics (25.68 Hz) in the X components" . It is not clear for me how he has calculated those values (20.27; 18.92 and 25.68) . I'll be grateful if someone could help me with an explanation!

Many thanks
Sincerely,
Daniel

[Vasilios Baltzopoulos]

Re: Frequency content calculation

Hi Daniel
The values we present in that paper (20.27; 18.92 and 25.68) are the frequencies of the respective harmonics as explained in Figure 2 of the paper.
"95% of the signal amplitude is contained in the first 15 harmonics (20.27 Hz) in the Z, 14 harmonics (18.92 Hz) in the Y and 19 harmonics (25.68 Hz) in the X components" This method has been used to describe how oscillatory different signals are depending on their frequency content.

The frequency of the fundamental (first harmonic) for that set is actually ~1.35 Hz (1.43 was a typo in the paper).
So the frequency of the 15th harmonic is 1.3513 Hz*15=20.27 Hz, the frequency of the 14th harmonic is 1.3513 Hz * 14= 18.92 Hz etc. That's how those numbers are calculated; they are the harmonic frequencies.

In essence if a particular GRF signal was represented by N points then the FFT will calculate N/2 harmonics up to the Nyquist frequency which is half the sampling frequency. The frequency of the first (fundamental) harmonic would be 1/T where T is the period of the signal in seconds. 100% of the signal is then by definition contained in the total sum of the amplitudes or powers of the N/2 harmonics. The cumulative sum of the power of a number of harmonics will be making a certain percentage of the total signal as you start adding them up so you are summing the power of consecutive harmonics until you reach 95% of the total. If you reach 95% of the signal with the first few harmonics (lower frequencies) then this indicates that you have a relatively smoother signal compared to requiring a larger number of harmonics (going up to higher frequencies) when you have a more oscillating waveform. Its just one way of trying to quantify the shape of the frequency spectrum with a single number (the frequency or the number of the highest harmonic contained in 95% of total signal power).

I hope this helps.
Best wishes
Bill

[Petcu Daniel]

Re: Frequency content calculation

Hi Vasilios,
For sure it helps, many thanks !
Sincerely,
Daniel