# FFT interpretation of time vector (simple)

• MATLAB
• member 428835
In summary, the conversation discusses the use of FFT on video data to extract the frequency of a moving object. The speaker confirms that Fs would represent the camera frame rate and L would be the total number of frames. They also suggest taking a slice of the image across frames and using the vertical position as the sample. In this case, L would be the sample count, with Fs being the frame rate.
member 428835
I have video data that shows an object moving up and down. I'd like to extract the frequency the object moves. Following the given example here (scroll down to "Examples"), am I correct in assuming Fs would be camera frame rate and L would be the total number of frames?

Thanks so much!

Video data is three-dimensional: horizontal, vertical, and time.
None of the examples deal with images - let alone video data.

It is certainly possible to do a 3-d FFT, but I doubt that is your intent.
Tell us more about this video and exactly what you want to extract from it. Is it a pendulum swinging back and forth and you want the frequency?

This sounds like a situation where an FFT could be used - but it probably isn't the best method.
If you do use an FFT, you would probably want to take a slice of the image across those frames so that you ware dealing with width and time. The slice would be selected as containing the periodic motion. Then an FFT would highlight periodic motion (with frequency spikes) along the frequency (time) axis.

.Scott said:
Video data is three-dimensional: horizontal, vertical, and time.
None of the examples deal with images - let alone video data.

It is certainly possible to do a 3-d FFT, but I doubt that is your intent.
Tell us more about this video and exactly what you want to extract from it. Is it a pendulum swinging back and forth and you want the frequency?

This sounds like a situation where an FFT could be used - but it probably isn't the best method.
If you do use an FFT, you would probably want to take a slice of the image across those frames so that you ware dealing with width and time. The slice would be selected as containing the periodic motion. Then an FFT would highlight periodic motion (with frequency spikes) along the frequency (time) axis.
I appreciate the response. The image only moves up and down, and I’m only tracking one pixel. Then I have the vertical position y as a function of time t, y(t). Each frame the pixel changes location, always up and down. I track the position. I extract the frequency using the MATLAB example shown above. I don’t think I need to use another technique, I’m just wanting to confirm L and Fs are as I describe. Would you input Fs as frame rate and L and total frame number?

joshmccraney said:
I appreciate the response. The image only moves up and down, and I’m only tracking one pixel. Then I have the vertical position y as a function of time t, y(t). Each frame the pixel changes location, always up and down. I track the position. I extract the frequency using the MATLAB example shown above. I don’t think I need to use another technique, I’m just wanting to confirm L and Fs are as I describe. Would you input Fs as frame rate and L and total frame number?
Yes.

As I understand it, you are tracking the vertical position of a one-pixel-size feature.
For simplicity, I will assume you are not dealing with an interlaced image.

So your samples are vertical positions - likely image line numbers. And your sampling rate will be your video frame rate.

Let's assume that the frame rate is 30 frames per second and the length of the video is 1 minute.
Fs = 1000; % Sampling frequency
T = 1/Fs; % Sampling period
L = 1500; % Length of signal
t = (0:L-1)*T; % Time vector
L would be better described as the "sample count".

So for you, Fs=30 and L=1800.

## 1. What is FFT interpretation of time vector?

FFT stands for Fast Fourier Transform, which is a mathematical algorithm used to convert a signal from its original domain (such as time) to a representation in the frequency domain. The time vector refers to the time values of a signal, which can be interpreted using FFT to analyze its frequency components.

## 2. How does FFT interpret the time vector?

FFT works by breaking down a signal into its individual frequency components, which are represented as peaks in the frequency domain. The height of each peak indicates the strength of that frequency component in the original signal. By analyzing the frequency components, we can gain insights into the characteristics of the signal in the time domain.

## 3. What is the importance of interpreting the time vector using FFT?

FFT interpretation of the time vector is important because it allows us to analyze and understand the frequency components of a signal. This can be useful in various fields such as signal processing, acoustics, and vibration analysis. It can also help in identifying patterns and anomalies in time series data.

## 4. What are some applications of FFT interpretation of time vector?

Some common applications of FFT interpretation of the time vector include audio and video compression, noise reduction, spectral analysis in physics and engineering, and biomedical signal processing. It is also widely used in digital signal processing and image processing.

## 5. Are there any limitations to FFT interpretation of time vector?

While FFT is a powerful tool for analyzing signals in the frequency domain, it does have some limitations. It is most effective for signals with a fixed frequency content, and may not work well for signals with rapidly changing frequency components. Additionally, FFT can only provide information about the frequency components of a signal, and not its amplitude or phase information.

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