Fourier coefficients in a discrete curve

In summary, Fourier coefficients in a discrete curve are numerical values that describe the contribution of each frequency component to the curve. They are calculated using the Fourier transform and are important for representing complex signals or functions as a combination of simpler sinusoidal functions. These coefficients can be calculated using the DFT or FFT algorithm and can be negative, representing the phase difference between the sinusoidal component and the reference signal. When the sampling rate is increased, the number of data points used to calculate the coefficients also increases, resulting in a more accurate representation of the frequency components.
  • #1
suido
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I'm struggling in an application of Fourier transform.here is my problem:
a series of points from experimental data plotted as a cruve. I'm planning to do a Fourier transform to see how smooth the curve is? my question is: is it possible/useful to calculate the Fourier coefficients? if yes, how?
I appreciate for any tips or corrections.
 
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  • #2
Try the Discrete Fourier Transform (DFT). This will give you the harmonics you need for your discrete dataset.
 

1. What are Fourier coefficients in a discrete curve?

Fourier coefficients in a discrete curve refer to the numerical values that describe the contribution of each frequency component to a discrete curve. They are calculated using the Fourier transform and are used to represent complex signals or functions as a combination of simpler sinusoidal functions.

2. How are Fourier coefficients calculated for a discrete curve?

Fourier coefficients for a discrete curve are calculated using the discrete Fourier transform (DFT) or the fast Fourier transform (FFT) algorithm. These algorithms involve breaking down the curve into its individual frequency components and calculating the amplitude and phase of each component.

3. What is the significance of Fourier coefficients in a discrete curve?

Fourier coefficients in a discrete curve are important because they allow us to analyze and represent complex signals or functions in terms of simpler sinusoidal functions. This makes it easier to understand the underlying patterns and behavior of the curve, and can also be used for filtering, compression, and other signal processing techniques.

4. Can Fourier coefficients be negative?

Yes, Fourier coefficients can be negative. The negative values represent the phase difference between the sinusoidal component and the reference signal. These negative values are essential for accurately representing complex signals and should not be confused with negative amplitudes.

5. How do Fourier coefficients change when the sampling rate is increased?

When the sampling rate is increased, the number of data points used to calculate the Fourier coefficients also increases. This results in a more accurate representation of the frequency components of the curve, and the coefficients may change in value. However, the overall shape and behavior of the curve should remain the same.

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