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salil87

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Do Fourier Transforms give us actual amplitude/phase of the particular frequency (

**e**) just like Fourier series?

^{jωt}Thanks

Salil

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- Thread starter salil87
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In summary, Fourier Transforms and Fourier series are related in that they both involve representing a function as a combination of sinusoidal components. However, the inverse continuous Fourier transform is an integral while the Fourier series is a summation. The actual amplitude in the Fourier transform is proportional to the product of X(f) and the width of the frequency spectrum, while in the Fourier series it is given by the coefficients. The series is a discrete process while the transform is continuous, and they can yield different results if the basic rules are ignored. The Fourier transform of sum(Vhcos(hwt)) will result in a regular "comb" of components at frequencies w, hw, 2hw, etc. with amplitudes given by the coefficients V.

- #1

salil87

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Do Fourier Transforms give us actual amplitude/phase of the particular frequency (

Thanks

Salil

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- #2

rbj

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to compare, give the (inverse) Fourier integral a finite width (with the limits of the integral) and then represent that finite width integral with a Riemann summation and then you will be able to see the relationship between the inverse Fourier transform and the Fourier series. in a loose sense, they are the same thing.

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sophiecentaur

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Anitha Sankar

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what is the Fourier transform of sum( Vhcos(hwt)) where h varies from 1 to infinity

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sophiecentaur

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Anitha Sankar said:what is the Fourier transform of sum( Vhcos(hwt)) where h varies from 1 to infinity

Hi

I assume that when you write Vh , the h is a suffix.

The transform will be a regular 'comb' of components at frequency w, hw, 2hw etc. with amplitdes given by the coefficients V. In fact, the original function is of a form that tells you the frequency spectrum just by 'observation'.

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Cecilia48

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http://www.infoocean.info/avatar2.jpg The series is a Discrete process where the Transform is Continuous.

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sophiecentaur

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I guess I meant "sum' as against 'integral'.

Is that better?

Is that better?

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The Fourier Transform Doubt is a concept in mathematics and signal processing that describes the uncertainty or doubt associated with the Fourier Transform. It refers to the fact that the Fourier Transform cannot perfectly reconstruct a signal due to the loss of information during the transformation process.

The Fourier Transform Doubt can affect signal processing by causing errors or inaccuracies in the reconstructed signal. This can be especially problematic in applications where precise signal reconstruction is necessary, such as in audio or image processing.

The Fourier Transform Doubt is caused by the limitations of the Fourier Transform. It is a mathematical uncertainty that arises due to the fact that the Fourier Transform is a one-to-one mapping, meaning that multiple signals can have the same Fourier Transform.

No, the Fourier Transform Doubt cannot be completely eliminated. However, there are techniques such as windowing and zero-padding that can help reduce its effects and improve the accuracy of the reconstructed signal.

The Fourier Transform Doubt and the Heisenberg uncertainty principle are both related to the concept of uncertainty in mathematics and physics. While the Heisenberg uncertainty principle deals with the uncertainty in the measurement of certain physical quantities, the Fourier Transform Doubt deals with the uncertainty in the reconstruction of a signal. Both principles are based on the idea that there are inherent limitations and uncertainties in our ability to measure or represent certain phenomena.

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