In case of a transient thermal problem, for large diffusivity coefficient when I use the FFT to transform the signal from time domain into the frequency domain, I have a different evolution of amplitude and phase angle depending on the number of samples. Let us note that the original signal has 2001 points, then I have used two cases to check the effect of sampling:
case 1: same number of samples: 2001,
case 2: following the next higher power of 2 thus: 2048
I have attached the effect on phase and amplitude in frequency for both cases.
Knowing that both when we make IFFT we can obtain exactly the same signal.
What is the reason of this issue?
What must I use?
Can I use Case 1?
#FFT #Thermal #Fast Fourier Transform
What seems to be happening is that your signal does not change much. Indeed, it seems like DC. In that case the DFT of the points you have will give you an impulse at the origin (FFT of constant). If you zero pad that, then you have a signal which is essentially DC followed by the zeroes (2001 values which are essentially the same, followed by 47 zeroes to get to 2048). The DFT of that is a sinc function. Simple.
Do take a look at what your signal looks like in the time domain and do study Fourier transforms.
I hope this is useful to you.
Best wishes.
Thank you, Fernando, for your answer, okay I understand this point, the signal in time domain is cyclic the mean of this signal corresponds to the amplitude at zero frequency.
You think that adding these more points (2048) are not important since it leads to a sinc function.
I doubt that "the signal in time domain is cyclic". If it were cyclic there would be a certain value corresponding to the frequency of this cyclic behaviour in the frequency domain for the original (N=2001) DFT. It seems there is not...
Sorry for the mistake the signal, in this case, is just exponential and not cyclic as I mentioned, yes when we have cyclic a certain value of frequency must appear which is related to the cycle time. However, in this case, the signal is exponential in the form a*exp(-5*t)+b*exp(10^-5*t)
I attached here the signal in time domain,
One question occurs to me. Did you add the zeros for the 2048 case at the beginning or the end of the signal? Or did you simple extend the signal using the last samples as being representative?
If you just extended with zeroes at the end, then I imagine that the FFT thinks that the signal has both a rise and a fall,but mostly DC.
The plot of your signal in the time domain confirms what I thought. It is basically a constant (around 35). I do not see the exponential behaviour you mention...
Thank you all for participating on this,
David no I did not add zeros for the 2048 case, finally, I want to understand which signal in the frequency domain ( phase and amplitude) correctly represents the signal in frequency.
Ahmad, both amplitude and phase are important to represent the signal in the frequency domain. The Fourier Transform is generally a complex series and a Complex series cannot be fully described by its amplitude or its phase just as a single complex value can't. You need to study Fourier Transforms and complex numbers.
But this, not my question I know both are very important my question which signals in frequency domain for case (2001) or case (2048) that what I want to clearly understand,
Thank you.
If you choose 2048 point FFT, some "zero padding" is happening automatically unless you "actively" work against that (e.g. repeating the last value or extrapolating these points). Thus the 2001 points FT is "reality" while the 2048 points FFT shows artefacts from tze zero padding.
In both cases, for your current signal (more or less DC) the phase information is garbage: DC has no phase and at the minute AC components artefacts from arithmetical imprecisions (and eventually digitization noise) prevail.
Ahmad,
There is nothing to be gained from adding samples and doing a 2048 point transform.
Matlab can handle the 2001 dft just fine.
As U. Has reported, a signal that is basically DC has no phase.
The only significance of anything to do with phase is the very early, and very short transition at the very beginning. And all that the phase will tell you, is when did that transition happen relative to the other data. Remember, phase is about time domain delay.
David
I think it is sampling frequency problem. Your are analyzing transient temperature in frequency domain. The transient is persist for less than 1 sec or in ms range. As i observed your samples and frequency plot. It seems your sampling frequency is in second. But for observing transient you change the sampling frequency as 1KHz or more the analyse same number of sample then see the results.
Use the 2001 samples you have. Having said that your 'signal' is a boring almost constant dc value. Using 2048 samples you are doing an inappropriate zero-padding, i.e. in effect you create a rectangular gate function, hence the amplitude spectrum you show in figure 2. You need to study and talk to your professors!
Ahmad Takash, some old questions are still worth thinking about and answering. Such as 'who am I?', 'how does the universe work?', 'what is life?', 'what is consciousness?', 'is there a god?',... :-)
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