# Plotting an Exponential Fourier Series

• polaris90
In summary, to determine the phase angle of an exponential Fourier series, you can divide the coefficient by 2 to get the amplitude and then expand the coefficient into its real and imaginary parts. From there, you can use the formula tan-1(-bn/an) to calculate the phase angle, similar to how you would with sines and cosines.
polaris90
I'm having some problem in determining the phase of an exponential Fourier series. I know how to determine the coefficient which in turn gives me the series after I multiply by $e^-(jωt)$
I can determine the amplitude by dividing the coefficient by 2 $|Dn| = Cn/2$
Now my question is how to determine the phase angle. My book only gives me $ø=∠Dn$ and it doesn't explain how they get the values. Do I have to expand Cn into its real and imaginary parts and then calculate the angle using tan-1(-bn/an) as I would when using sines and cosines?

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polaris90 said:
Do I have to expand Cn into its real and imaginary parts and then calculate the angle using tan-1(-bn/an) as I would when using sines and cosines?
Yes.

## 1. What is an Exponential Fourier Series?

An Exponential Fourier Series is a mathematical representation of a periodic signal as a sum of complex exponential functions. It is used to analyze and represent signals in the frequency domain.

## 2. How is an Exponential Fourier Series calculated?

The coefficients of an Exponential Fourier Series are calculated using the Fourier Transform, which converts a signal from the time domain to the frequency domain. The coefficients are then used to construct the series.

## 3. What is the difference between an Exponential Fourier Series and a Trigonometric Fourier Series?

An Exponential Fourier Series uses complex exponential functions, while a Trigonometric Fourier Series uses only sine and cosine functions. This makes the Exponential Fourier Series more versatile in representing a wider range of signals.

## 4. What is the significance of the Exponential Fourier Series in signal processing?

The Exponential Fourier Series is used to analyze and represent signals in the frequency domain, which is important in many applications such as filtering, compression, and modulation. It also allows for easier manipulation and processing of signals.

## 5. Are there any limitations to using an Exponential Fourier Series?

One limitation is that it can only be used for periodic signals. It is also limited in its ability to represent signals with sharp transitions or discontinuities. Additionally, it may not accurately represent signals with non-harmonic components.

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