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m_goldberg
m_goldberg
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Why amplitude is different while using 'Fourier' and 'FourierTransform' operations for 2*sin[x]? Reconciling results from Fourier with those form FourierTransform

I need to use the discrete fourierFourier transform for function that represented as list of values. I

I started from thewith an easy task to check ammy understanding. I use it right - trytried to reachget the amplitude values fot 2*Sin[x] functionfor 2*Sin[x]. Looks like itI think they should be somwhere about 2. But using the discrete 'Fourier'Fourier operation it isproduces something quite different. Can someone tell me - where is my mistakes are?

Please see my observations:Here is what I tried.

data = Table[2*Sin[x], {x, 0, 100}]; ListPlot[data, Joined -> True]

data = Table[2*Sin[x], {x, 0, 100}];
ListPlot[data, Joined -> True]

enter image description here

ListPlot[Abs[Fourier[data]], Joined -> True, PlotRange -> All]

ListPlot[Abs[Fourier[data]], Joined -> True, PlotRange -> All]

enter image description here

ListPlot[Table[ Abs[FourierTransform[2*Sin[x], x, w]] /. DiracDelta -> DiscreteDelta, {w, 0.1, 10, 0.1}], Joined -> True, PlotRange -> All]

ListPlot[
  Table[Abs[FourierTransform[2*Sin[x], x, w]] /. 
    DiracDelta -> DiscreteDelta, {w, 0.1, 10, 0.1}], 
  Joined -> True, 
  PlotRange -> All]

enter image description here

How can I reach fo the 'Fourier' operationget the same results from 'Fourier' as I reach for theget from 'FourierTransform'?

Thank you for help.

Why amplitude is different while using 'Fourier' and 'FourierTransform' operations for 2*sin[x]?

I need to use the discrete fourier transform for function that represented as list of values. I started from the easy task to check am I use it right - try to reach the amplitude values fot 2*Sin[x] function. Looks like it should be somwhere about 2. But using the discrete 'Fourier' operation it is different. Can someone tell me - where is my mistakes?

Please see my observations:

data = Table[2*Sin[x], {x, 0, 100}]; ListPlot[data, Joined -> True]

enter image description here

ListPlot[Abs[Fourier[data]], Joined -> True, PlotRange -> All]

enter image description here

ListPlot[Table[ Abs[FourierTransform[2*Sin[x], x, w]] /. DiracDelta -> DiscreteDelta, {w, 0.1, 10, 0.1}], Joined -> True, PlotRange -> All]

enter image description here

How can I reach fo the 'Fourier' operation the same results as I reach for the 'FourierTransform'?

Thank you for help.

Reconciling results from Fourier with those form FourierTransform

I need to use the discrete Fourier transform for function that represented as list of values.

I started with an easy task to check my understanding. I tried to get the amplitude values for 2*Sin[x]. I think they should be somwhere about 2. But using the discrete Fourier operation produces something quite different. Can someone tell me where my mistakes are?

Here is what I tried.

data = Table[2*Sin[x], {x, 0, 100}];
ListPlot[data, Joined -> True]

enter image description here

ListPlot[Abs[Fourier[data]], Joined -> True, PlotRange -> All]

enter image description here

ListPlot[
  Table[Abs[FourierTransform[2*Sin[x], x, w]] /. 
    DiracDelta -> DiscreteDelta, {w, 0.1, 10, 0.1}], 
  Joined -> True, 
  PlotRange -> All]

enter image description here

How can I get the same results from 'Fourier' as I get from 'FourierTransform'?

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user12991
user12991
  • 71
  • 3

I need to use the discrete fourier transform for function that represented as list of values. I started from the easy task to check am I use it right - try to reach the amplitude values fot 2*Sin[x] function. Looks like it should be somwhere about 2. But using the discrete 'Fourier' operation it is different. Can someone tell me - where is my mistakes?

Please see my observations:

data = Table[2*Sin[x], {x, 0, 100}]; ListPlot[data, Joined -> True]

enter image description here

ListPlot[Abs[Fourier[data]], Joined -> True, PlotRange -> All]

enter image description here

ListPlot[Table[ Abs[FourierTransform[2*Sin[x], x, w]] /. DiracDelta -> DiscreteDelta, {w, 0.1, 10, 0.1}], Joined -> True, PlotRange -> All]

enter image description here

How can I reach fo the 'Fourier' operation the same results as I reach for the 'FourierTransform'?

Thank you for help.

I need to use the discrete fourier transform for function that represented as list of values. I started from the easy task to check am I use it right - try to reach the amplitude values fot 2*Sin[x] function. Looks like it should be somwhere about 2. But using the discrete 'Fourier' operation it is different. Can someone tell me - where is my mistakes?

Please see my observations:

data = Table[2*Sin[x], {x, 0, 100}]; ListPlot[data, Joined -> True]

enter image description here

ListPlot[Abs[Fourier[data]], Joined -> True, PlotRange -> All]

enter image description here

ListPlot[Table[ Abs[FourierTransform[2*Sin[x], x, w]] /. DiracDelta -> DiscreteDelta, {w, 0.1, 10, 0.1}], Joined -> True, PlotRange -> All]

enter image description here

Thank you for help.

I need to use the discrete fourier transform for function that represented as list of values. I started from the easy task to check am I use it right - try to reach the amplitude values fot 2*Sin[x] function. Looks like it should be somwhere about 2. But using the discrete 'Fourier' operation it is different. Can someone tell me - where is my mistakes?

Please see my observations:

data = Table[2*Sin[x], {x, 0, 100}]; ListPlot[data, Joined -> True]

enter image description here

ListPlot[Abs[Fourier[data]], Joined -> True, PlotRange -> All]

enter image description here

ListPlot[Table[ Abs[FourierTransform[2*Sin[x], x, w]] /. DiracDelta -> DiscreteDelta, {w, 0.1, 10, 0.1}], Joined -> True, PlotRange -> All]

enter image description here

How can I reach fo the 'Fourier' operation the same results as I reach for the 'FourierTransform'?

Thank you for help.

Source Link
user12991
user12991
  • 71
  • 3

Why amplitude is different while using 'Fourier' and 'FourierTransform' operations for 2*sin[x]?

I need to use the discrete fourier transform for function that represented as list of values. I started from the easy task to check am I use it right - try to reach the amplitude values fot 2*Sin[x] function. Looks like it should be somwhere about 2. But using the discrete 'Fourier' operation it is different. Can someone tell me - where is my mistakes?

Please see my observations:

data = Table[2*Sin[x], {x, 0, 100}]; ListPlot[data, Joined -> True]

enter image description here

ListPlot[Abs[Fourier[data]], Joined -> True, PlotRange -> All]

enter image description here

ListPlot[Table[ Abs[FourierTransform[2*Sin[x], x, w]] /. DiracDelta -> DiscreteDelta, {w, 0.1, 10, 0.1}], Joined -> True, PlotRange -> All]

enter image description here

Thank you for help.