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[SOLVED] Single frequency missing in time domain effect

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Nanda Sinha

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How to explain effect of a missing frequency in time domain ? As we know it is simple task when we talk about frequency domain and missing a frequency component in there (in spectrum).What about time domain . Let's take a example:

I have a signal in time domain with 'N' frequencies in frequency domain(seeing these frequencies in spectrum).Now if I remove 1 frequency component from signal by subtracting the sine/cosine signal in time domain with that frequency and amplitude at that frequency.Now that the signal containing all 'N' frequencies in time domain whose amplitude is in volts(assuming), will get affected in amplitude because subtracted sine/cosine wave had values which were there before subtracting.So it became different signal altogether with 'N-1' frequencies in frequency domain. I want to know the effect of this less/more (changed ) amplitude of the signal.

In simple words I just want to know that if I see a signal as the sum of different frequency components then I can understand the effect of every frequency on some system or circuit but I want to understand the effect of frequencies in time domain.I hope I am you get an intuition.English is not my 1st language . I will rephrase the question if anyone wants.
 

If I understand your question, and I'm not sure I do, there's more to the frequency component than just its frequency. You also have to consider its phase and amplitude to determine its contribution to the complete signal.
 

Hi,

I'm also not sure if I understand correctly...

You think if you remove one frequency .... some or all other remaining frequencies amplitudes are affected? Why?

For an ideal circuit, that is able to remove just one frequency ... all other frequencies will remain the same.
The problem may be how "ideal" a real circuit can be.

Klaus
 

You need to understand the basic Fourier transformation in detail. However, you are likely talking about a discrete Fourier transformation and that makes some difference.

A single frequency missing in the time domain has no effect on the power spectrum (frequency domain) - in fact an infinite number of denumerable frequencies can be removed from the power spectrum and the result Fourier transformed back to the time domain and compared to the original.

Unfortunately the story is less elegant for discrete Fourier transformation.

In the discrete space, you are not able to remove a single frequency and you must remove a band. Removing a band from the frequency domain will have some effect on the time domain.

Best way to get some idea is to try it out- with a sample of say 16 or 32 samples (time series data). The results can be enlightening.
 

Hi,

I'm also not sure if I understand correctly...

You think if you remove one frequency .... some or all other remaining frequencies amplitudes are affected? Why?

For an ideal circuit, that is able to remove just one frequency ... all other frequencies will remain the same.
The problem may be how "ideal" a real circuit can be.

Klaus

What I wanted to say that amplitude of time domain signal which, is the linear combination of sine and cosines ,will be affected ( because removing 1 frequency component means removing a sine/cosine wave which was previously there before it was removed ) ,there will be no effect on other frequencies and other amplitude.
 

Yes I meant amplitude,phase of a single cosine/sine
 

Hi,

The "amplitude" of a mixture of frequencies is hard to define.
The peak value is no solution, because it depends of phase alignment between these frequencies.

but:
The amplitude of a single frequency is defined.
The RMS value of a mixture of frequencies is defined.

What about a drawing? Or a simple simulation on Excel?

Klaus
 

Let's say there is 1 frequency component in singal i.e. S1 = A1cosf1t . This signal has amplitude A1 and frequency f1 . Now I add another one S2 = A2cosf2t which has A2and f2. Now S = S1 +S2 it will have S = Acosft . So I was talking about effect on A when we remove S1 or S2 .When I say effect I mean if there is single sinusoid the voltage will be of a sine'cosine function which means it will oscillate and amplitude will change in very time instant which will affect system/circuit .Now when 2 sine/cosine are present the change with time of voltage will be there but it will be different .
 

Hi,

you say:
* S1 = A1cosf1t
* S2 = A2cosf2t
These are two different frequencies. When you add them the resulting waveform is not a sinewave anymore.

For further discussion a drawing is urgent.

Klaus
 

S1 = A1cosf1t . This signal has amplitude A1 and frequency f1 . Now I add another one S2 = A2cosf2t which has A2and f2. Now S = S1 +S2 it will have S = Acosft

Say I plot 0.5 * sin(x) + 0.5 * sin(2*x) and the result is NOT a sine or a cosine wave: test1.png
Any arbitrary waveform can be decomposed by a series sum of sine waves. That is where Fourier transformation comes handy!
 

Hi

Say I plot 0.5 * sin(x) + 0.5 * sin(2*x)
and even more funny waveform if you use: 0.5 * sin(x) + 0.5 * sin(2.13*x)

Klaus
 

and even more funny waveform if you use: 0.5 * sin(x) + 0.5 * sin(2.13*x) ...

But it looks best in a 2D plot: just like a Lissajous figure:

test2.png
 

Or funnier yet sin(xt)+sin(xt+180degrees)

What is the funny there? It is identically zero. (sin(x)-sin(x))
 

This can be absurdly weird.

You can create examples of square or triangle waves without an odd harmonic -- there is a visually obvious frequency that doesn't actually exist in the frequency domain!
 

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