# How to get information on low frequencies of a signal using FFT?

• BrunoIdeas
In summary: HzIn summary, the speaker has conducted a lab experiment on interference and used a CCD camera to photograph a periodic fringe pattern. They are now wondering about the limit of amplitude information that can be obtained from lower frequencies when applying an FFT to the image. They have read that for a 1 second signal, only frequencies above 1 Hz can be obtained. They are interested in low frequencies because the width of the fringes is about 1/10 the size of the total image. They are currently processing the image in ImageJ to gather information.
BrunoIdeas
Hello. I've made a lab experiment of interference and with a CCD camera photographed fringe pattern which one can understand as a periodic signal.
My question is: When I apply an FFT to the image is there any limit to the amplitude information I may get from lower frequencies?
I read in the internet that for a 1 sec signal, one may be able to obtain information about only freqs above 1 Hz.
Why do I ask this? Because the width of the fringes is of about 1/10 the size of the total image, and I am interested in low frequencies.

Now I am processing the image in ImageJ in order to get some information.

Welcome to PhysicsForums!

I'm not quite sure how you're getting temporal measurements (hz) from the FFT of an image (usually in vector space), unless you're asking about contributions from low-frequencies in general.

When you mention fringes being 1/10 the size of the image, you may have things reversed: the contribution from that should actually have a spatial frequency of 10, not 1/10 (think 10 fringes per image):
http://sharp.bu.edu/~slehar/fourier/fourier.html#harmonics

Last edited by a moderator:
The lowest positive frequency represented in the FFT output will be 1 cycle over the length of data. So, for a 1 second signal, there would be information for ..., 0 Hz, 1Hz, ...

1 * fs/N = 1/(Ts * N) = 1/(Total time)

## 1. How does the FFT algorithm work?

The Fast Fourier Transform (FFT) algorithm is a mathematical method for converting a time-domain signal into its frequency-domain representation. It breaks down a signal into its component frequencies and their respective amplitudes, allowing for analysis of different frequency components.

## 2. What is the sampling rate and how does it affect the FFT?

The sampling rate is the number of samples taken per second in a signal. It is important in FFT analysis because it determines the maximum frequency that can be accurately represented. The Nyquist-Shannon sampling theorem states that the sampling rate must be at least twice the highest frequency component in the signal to avoid aliasing.

## 3. How can I determine the low frequencies in a signal using FFT?

The FFT output contains information about the frequency components present in a signal. To determine the low frequencies, you can look at the lower end of the frequency spectrum and identify the peaks or significant values. These correspond to the low frequency components in the signal.

## 4. Can I use FFT to filter out low frequencies in a signal?

Yes, FFT can be used for filtering out specific frequency components in a signal. By identifying the low frequency components using FFT, you can then apply a filter to remove them from the original signal. This can be useful in noise reduction or isolating certain frequency components for analysis.

## 5. Are there any limitations to using FFT for low frequency analysis?

One limitation of FFT for low frequency analysis is the need for a large number of samples to accurately represent low frequencies. This can lead to longer processing times and may not be suitable for real-time applications. Another limitation is the presence of noise, which can affect the accuracy of low frequency analysis.

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