Why higher freqs. in the time domain are represented with lower peaks in the freq. domain?

Question

I am trying to understnad the signal transformation concept. I found a tutorial, and it descrped the first posted image as, it has four frequency components at four different time intervals, and the second posted image is just the Fourier Transform of the first image. and it is descrped as follows :

Note that the:
amplitudes of higher frequency components are higher than those of the lower frequency   
ones This is due to fact that higher frequencies last longer (300 ms each) than the  
lower frequency components (200 ms each).

my question is: since the amplitude of the higher freq. components is higher than the amplitude of the lower freq. ones. why in the second image the first to peaks from the left are shorter than the other two on the right side. According to the tutorial the first two peaks "from the right" in the second image should be higher than the other two because the corresponding frequency components "shown in first image" of the first two peaks from the right "shown in second image" are of higher frequency. In other words, since the first two freq. component ,from the left in the first imag, are of higher frequency than the other freq. component, then, their corresponding peaks ,in the second image, should be higher?

kindly please provide some clarification.

Img_1:

Img_2:

Answer 1

The peaks in the image do not correspond "left-to-right" or really in any way. The first 300 ms are at a frequency of 100 Hz. You see this in the signal domain (the FT chart) as a peak at 100 Hz, which happens to be the rightmost peak.

The last 200 ms, by contrast, are at a frequency of 10 Hz. This peak is the left-most peak (because 10 < 100, not because of when these are occurring). The height of this peak is smaller than the height of the peak at 100 Hz, because this lasts for 200 ms rather than 300 ms.

I can understand your confusion, as someone new to the subject. If you were to rearrange the 4 groups of signals, then the FT chart would look very similar in terms of peaks. (The stuff in the middle would be a little different, but the peaks would be similar.)

Answer 2

I think you might be a bit confused about how spectra work. The peaks on the right side of the frequency-domain graph are caused by the signal on the left side of the time-domain graph, simply because that's the order in which they occur.

If you were to take the FT of only the first 300 ms of the signal, then the frequency-domain graph would have only one peak, at 100 Hz. If you were to then add the subsequent 300 ms to the FT, a second peak would appear, to the left of the first peak.

The Fourier transform doesn't care about "when", only "what". You could reverse the signal and get virtually the same frequency spectrum. You could shuffle the different frequency components around and likewise have no effect on the spectrum.