Fourier Series/ transform demonstration

In summary, the person is asking for help understanding the use of different notations (X(jw), X[e^jw], X(w), X(f)) in continuous and discrete signals and how it relates to the concepts of Fourier series and transforms, Laplace transform, and Z transform. They are seeking a deeper understanding of these concepts in order to better grasp the subject and be able to sleep better at night.
  • #1
MrAlbot
12
0
Hey guys!

if anyone can help me I guess it is you! :)

I'm trying to find the Fourier Series demonstration to continuous and periodic functions.

I don't understand why people keep using X(jw) and X[e^jw] and even sometimes X(w) and X(f)

If anyone can help me I'm really not understanding that!

Best regards

Peter
 
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  • #2
I'm trying to understand why in my Signals and Systems they use X(jw) (and X[e^jw] in disrete signals) and in my telecomunications class they use X(f) and what does it change, and why can they change that. I have no problem going into deep mathematics if that means understanding it. I feel like only after understanding this Fourier series/transform Laplace and Z transform will make sense in my head and I'll be able to sleep at night if I get this right into my head. ^^

Thanks again.
 
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Related to Fourier Series/ transform demonstration

1. What is a Fourier Series/transform?

A Fourier Series/transform is a mathematical tool used to represent a periodic function as a sum of sine and cosine waves. It decomposes a complex signal into simpler components, making it easier to analyze and understand.

2. What is the difference between a Fourier Series and a Fourier transform?

A Fourier Series is used for periodic functions, while a Fourier transform is used for non-periodic functions. A Fourier Series represents a periodic function as a sum of sine and cosine waves with specific frequencies, while a Fourier transform represents a non-periodic function as a continuous spectrum of frequencies.

3. How is a Fourier Series/transform calculated?

A Fourier Series is calculated by finding the coefficients of the sine and cosine waves that make up the function. A Fourier transform is calculated by taking the integral of the function multiplied by a complex exponential function.

4. What is the practical use of Fourier Series/transform?

Fourier Series/transform is used in a variety of fields, including engineering, physics, and signal processing. It is used for analyzing and filtering signals, compressing data, and solving differential equations.

5. Are there any limitations to using Fourier Series/transform?

Fourier Series/transform can only be used for functions that satisfy certain conditions, such as being continuous and having a finite number of discontinuities. It also assumes that the function is periodic or non-periodic over an infinite interval. Additionally, the accuracy of the results depends on the number of terms or frequencies used in the calculation.

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