realized that any complex waveform could be decomposed into a group of sinusoids of
different frequencies and amplitudes.
What does this exactly mean ?
lets take an example:
Frequency Content:
Suppose we add another sine wave of the same amplitude with a frequency of 2000 Hz to our 1000 Hz sine wave.The complex wave represents the sum of Frequencies 1 and 2 as they rise and fall at different times with different slopes.
Now, think what Ol’ Joe Fourier said. The complex waveform is comprised of
simple sine waves of various amplitudes.
Surprised? Isn’t it easier to see the complex waveform in the frequency domain.
Time domain: What we see is a waveform that varies in amplitude as time moves.
Frequency Domain: What we see is a waveform that varies in amplitude corresponding to its frequency content.
The spectral display gives us much more useful information than the time domain display
Important: Remember that the two figures (time and frequency domain representation) represent the same thing: a complex waveform, first in the time domain and second in the frequency domain. Do not try to relate what you see in the time-domain display to what you see in the frequency-domain display. They are totally different domains.
Happy learning !! :)
(oscillograph). It can tell us which frequencies are dominant and which are not.
The continuous band of high amplitude will tell us the dominant frequency band etc. It is important to remember that each vertical bar is a single sine wave.
You might be thinking, that there may be a complex wave where one frequency content exists for a certain period of time and then other frequency content is present for another period of time; for example, the image below shows a signal with four frequency contents 100Hz, 50Hz, 25Hz and 10Hz Will fourier transform of such a signal will be, same as when all the frequencies were present throughout the signal?? Yes, absolutely! as the figures given below.
You might be thinking, that there may be a complex wave where one frequency content exists for a certain period of time and then other frequency content is present for another period of time; for example, the image below shows a signal with four frequency contents 100Hz, 50Hz, 25Hz and 10Hz Will fourier transform of such a signal will be, same as when all the frequencies were present throughout the signal?? Yes, absolutely! as the figures given below.
Thus a signal in frequency domain, obtained from Fourier transform does NOT give any information, as to when a frequency component was present in time.
Important: Remember that the two figures (time and frequency domain representation) represent the same thing: a complex waveform, first in the time domain and second in the frequency domain. Do not try to relate what you see in the time-domain display to what you see in the frequency-domain display. They are totally different domains.
Happy learning !! :)
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