Understanding Fourier Transforms

In summary, the conversation is about a first-time poster seeking help in understanding Fourier transforms and their use in analyzing electrical signals in a lab setting. They are using LabView software and have noticed a relationship between sampling time and the width of a signal peak. They also have limited understanding of the mathematical computations involved in producing the transformed values. They are seeking clarification and direction on these topics and have been directed to a helpful thread on the physics forum.
  • #1
MxwllsPersuasns
101
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Hello all,

First time poster here so please excuse any mistakes as I'm unfamiliar with the conventions of this forum. Also before I get started I'd like to say I wasn't sure exactly where a question like this would go; I debated in the Math Programs and Latex section but figured general physics would find it the most exposure.

So I am currently working in a lab as an undergraduate assistant and much of my work involves/will involve analyzing the Fourier transforms of various electrical signals. To do this I am utilizing LabView; so our signal comes in and is displayed on a waveform graph then runs through the 'FFT' tool in LabView and the output (the transform) is displayed on a second graph with a numerical indicator array to view the particular values. My goal currently is to understand and be able to interpret a Fourier transformed waveform -- or as my professor put it "Determine, quantitatively, how to go from analog voltage to the Fourier Spectrum plotted by LabView".

Given this; I have some background knowledge I'd like to lay out to help contextualize my issue and also some specific questions I'm hoping someone can help me tackle from another angle or shed some light on;

So I know that (in essence) a Fourier Transform decomposes a time varying signal in the time domain to it's constituent trigonometric functions in the frequency domain. I was playing around with a 1V, 102Hz signal being generated from a function generator today by varying the sample rate and the number of samples (essentially varying the sampling time) and noticed that there was an inversely proportional relationship between the sampling time and the width of the 102Hz signal peak, so that, for example, if I halved the sampling time from 1s to .5s I notice that my width increases to 150%, the progression down to fractional integer times (1/n; 1/2, 1/3, 1/4, etc...) did not seem to be linear however. I was wondering if anyone might be able to shine a bit more light on this relationship or at least point me in the right direction?

Finally I have a very limited understanding of what's going on inside the software to compute the transformed values, I believe it goes something like this; First, each value in the array for the input voltage gets put through the transformation formula which produces a complex # for each value then, I believe, the complex numbers get absolute valued then squared in order to produce a real-valued number and that is what is plotted as the amplitude against the frequency. So thus if the value of the input voltage is in units of Volts then the value of the amplitudes would be in units of Volts^2. Can anyone tell me if this is correct? On the right path? Or am I completely off-base? Any insight or help into these two main issues (especially the latter -- about how the values are computed algorithmically) would be incredibly valued and appreciated. Thanks guys!
 
Physics news on Phys.org

1. What is a Fourier Transform?

A Fourier Transform is a mathematical tool used to analyze the frequency components of a signal or function. It decomposes a function into its constituent frequencies, allowing us to better understand its behavior.

2. How does a Fourier Transform work?

A Fourier Transform takes a time-domain signal and converts it into a frequency-domain representation. This is achieved by breaking down the signal into its sine and cosine components, which are then plotted on a graph to show the frequency content of the signal.

3. What is the difference between a Fourier Transform and a Fast Fourier Transform (FFT)?

A Fast Fourier Transform (FFT) is an algorithm used to efficiently compute a Fourier Transform. It is faster than the traditional Fourier Transform algorithm, making it more practical for real-world applications.

4. What are some common applications of Fourier Transforms?

Fourier Transforms have a wide range of applications in various fields, including signal processing, image processing, data compression, and audio and video encoding. They are also used in scientific research and engineering to analyze and understand complex systems.

5. Are there any limitations to using Fourier Transforms?

Fourier Transforms are limited to signals that are time-invariant, meaning that the signal does not change over time. They also assume that the signal is periodic, which may not always be the case in real-world applications. Additionally, Fourier Transforms cannot capture localized or time-dependent information, making them less useful for analyzing signals with sudden changes or irregular patterns.

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