May 23, 2023

# What is an FFT plot? If you're unfamiliar with signal processing, an FFT plot might sound like an intimidating concept. However, despite the seemingly technical jargon, an FFT plot is simply a graphical representation of a signal's frequency components. In this article, we'll delve into what an FFT plot is, how it works, and its various applications.

## Understanding the Basics of FFT

Before we dive into FFT plots, let's first understand the basics of the Fast Fourier Transform (FFT). FFT is a mathematical algorithm used to transform a signal from the time domain into the frequency domain. Put simply, it means that FFT can break down a complex signal into simpler sinusoidal components.

FFT is a powerful tool in signal processing, as it can help us understand the different frequencies that make up a signal. By analyzing these frequencies, we can gain valuable insights into the signal and use this information to make informed decisions.

### What is the Fast Fourier Transform (FFT)?

The Fast Fourier Transform is an algorithm that computes the Fourier transform of a signal. It was developed in the 1960s and has since become a fundamental tool for signal processing and analysis. FFT is widely used in many fields, including audio and music analysis, medical imaging, and vibration analysis.

FFT is a complex algorithm that involves breaking down a signal into its individual frequency components. This process involves a lot of mathematical calculations, but it can be done quickly and efficiently using FFT.

### The Importance of Frequency Analysis

Many signals are composed of multiple frequencies, and analyzing these frequencies can provide valuable insights into the signal. For instance, in a sound signal, analyzing the frequency components can help identify the pitch, harmonics, and overtones. In vibration analysis, analyzing the frequency components can help identify the resonance frequency and natural frequencies of a structure.

Frequency analysis is an important tool in many fields, including music, engineering, and medicine. By understanding the different frequencies that make up a signal, we can gain a deeper understanding of the underlying processes that are producing the signal.

### Time Domain vs. Frequency Domain

In signal processing, signals can be represented in either the time domain or the frequency domain. Time domain refers to the signal's amplitude at different points in time, while frequency domain represents the signal's amplitude at different frequencies. FFT is a tool that can convert a signal from the time domain into the frequency domain.

Understanding the time domain and frequency domain representations of a signal is important in many fields. For instance, in audio engineering, understanding the time domain and frequency domain representations of a sound signal can help with tasks such as noise reduction and equalization.

In summary, FFT is a powerful tool in signal processing that can help us understand the different frequencies that make up a signal. By analyzing these frequencies, we can gain valuable insights into the signal and use this information to make informed decisions.

## Components of an FFT Plot

Now that we understand the basics of FFT, let's examine the components of an FFT plot. An FFT plot typically consists of three components:

### Amplitude Spectrum

The amplitude spectrum represents the amplitude of each frequency component. It is typically displayed as a graph, with frequency on the x-axis and amplitude on the y-axis. The amplitude spectrum can provide insights into the strength of each frequency component and can help identify dominant frequencies.

For example, in an audio signal, the amplitude spectrum can help identify the dominant frequencies of a musical instrument or a human voice. In a medical signal, such as an electrocardiogram (ECG), the amplitude spectrum can help identify the dominant frequencies of the heart rhythm.

### Phase Spectrum

The phase spectrum represents the phase relationship between each frequency component. It is typically displayed as a graph, with frequency on the x-axis and phase angle on the y-axis. The phase spectrum can provide insights into the timing relationship between different frequency components and can help identify the presence of non-linear effects.

For example, in a communication signal, such as a radio signal, the phase spectrum can help identify the timing relationship between the carrier signal and the modulated signal. In a control system, the phase spectrum can help identify the timing relationship between the input signal and the output signal.

### Power Spectrum

The power spectrum represents the energy of each frequency component. It is typically displayed as a graph, with frequency on the x-axis and power on the y-axis. The power spectrum can provide insights into the distribution of energy across different frequency components and can help identify the presence of noise and artifacts.

For example, in a power system, the power spectrum can help identify the frequency components of the voltage and current signals. In a vibration signal, the power spectrum can help identify the frequency components of the vibration signal and can help identify the presence of mechanical faults.

## How to Interpret an FFT Plot

Now that we know what an FFT plot consists of, let's examine how to interpret it. Here are some techniques for interpreting an FFT plot:

### Identifying Dominant Frequencies

One of the primary uses of FFT plots is to identify dominant frequencies in a signal. These are the frequencies that have the highest amplitude and energy levels. By identifying the dominant frequencies, we can gain insights into the characteristics of the signal, such as its pitch, harmonics, and overtones.

For example, if we were analyzing a piece of music, we might use an FFT plot to identify the dominant frequencies in the melody. This could help us understand the key of the song and the overall mood of the piece.

### Analyzing Harmonics and Overtones

In audio and music analysis, harmonics and overtones are important concepts. Harmonics are the frequencies that are multiples of the fundamental frequency, while overtones are frequencies that are not multiples of the fundamental frequency. By analyzing the FFT plot, we can identify the harmonics and overtones in a signal, which can help us understand its musical characteristics.

For example, if we were analyzing the sound of a guitar, we might use an FFT plot to identify the harmonics and overtones present in the sound. This could help us understand the type of guitar being played and the playing style of the musician.

### Understanding Noise and Artifacts

In signal processing, noise and artifacts can distort the signal and affect the accuracy of the FFT plot. By analyzing the power spectrum, we can identify the frequency components that are related to noise and artifacts and remove them from the signal if necessary.

For example, if we were analyzing an audio recording of a speech, we might use an FFT plot to identify any noise or artifacts present in the recording. This could help us clean up the recording and improve its overall clarity.

Overall, an FFT plot is a powerful tool for analyzing signals and gaining insights into their characteristics. By using the techniques outlined above, we can interpret FFT plots with greater accuracy and efficiency.

## Applications of FFT Plots

FFT plots, also known as Fourier transform plots, are powerful tools used in various fields to analyze signals and extract meaningful information. In this section, we will explore some of the most common applications of FFT plots.

### Signal Processing and Filtering

Signal processing and filtering involve analyzing and manipulating signals to remove unwanted noise or amplify specific frequency components. FFT plots play a crucial role in this process by providing a visual representation of the frequency spectrum of a signal. By analyzing the FFT plot, we can identify the frequency components that need to be filtered or amplified. This technique is commonly used in audio processing, where FFT plots are used to filter out unwanted noise or amplify specific frequency components to enhance the quality of the sound signal.

Moreover, FFT plots are also used in video processing to analyze and filter out noise or artifacts that may appear in video signals. In this case, the FFT plot provides a visual representation of the frequency spectrum of the video signal, allowing for the identification of specific frequency components that need to be filtered out.

### Audio and Music Analysis

FFT plots are essential tools in audio and music analysis. By using FFT plots, we can analyze the pitch, harmonics, and overtones of a sound signal, and gain insights into its musical properties. FFT plots are used extensively in music production and sound engineering to manipulate audio signals. For example, in music production, FFT plots can be used to identify the frequency components of a sound signal and apply equalization to enhance the sound quality.

Moreover, FFT plots are also used in speech analysis to analyze the properties of speech signals. By analyzing the frequency components of speech signals using FFT plots, we can identify the formants, which are the resonant frequencies of the vocal tract. This information is crucial for speech recognition and synthesis applications.

### Vibration Analysis and Structural Health Monitoring

In vibration analysis, FFT plots are used to identify the resonance frequency and natural frequencies of a structure. This technique is commonly used in structural health monitoring to detect any issues that may arise in buildings or bridges. By analyzing the FFT plot of the vibration signal, we can identify the frequency components that correspond to the natural frequencies of the structure. Any deviation from these frequencies can indicate a structural issue that needs to be addressed.

Moreover, FFT plots are also used in mechanical engineering to analyze the vibrations of machines and identify any issues that may arise. By analyzing the frequency components of the vibration signal using FFT plots, engineers can identify the source of the vibration and take corrective action to prevent further damage.

### Medical Imaging and Diagnostics

In medical imaging, FFT plots are used to analyze medical data such as electroencephalography (EEG) and electrocardiography (ECG). These signals provide valuable information about the activity of the brain and heart, respectively. By analyzing the frequency components of these signals using FFT plots, doctors can diagnose specific medical conditions.

For example, in EEG analysis, FFT plots can be used to identify the frequency components of brain waves, such as alpha, beta, delta, and gamma waves. By analyzing the FFT plot of the EEG signal, doctors can identify abnormalities in the brain wave patterns that may indicate neurological disorders such as epilepsy or Alzheimer's disease.

In ECG analysis, FFT plots can be used to identify the frequency components of the heart rate signal, such as the QRS complex and the T wave. By analyzing the FFT plot of the ECG signal, doctors can diagnose specific heart conditions such as arrhythmia or myocardial infarction.

In conclusion, FFT plots are versatile tools that have a wide range of applications in various fields, including signal processing, audio and music analysis, vibration analysis, and medical imaging. By providing a visual representation of the frequency spectrum of a signal, FFT plots enable us to extract valuable information and gain insights into the properties of the signal.

## Conclusion

FFT plots are a critical tool in signal processing and analysis. By analyzing the frequency components of a signal, FFT plots can provide valuable insights into the characteristics of the signal. Whether you're in the field of audio and music analysis or medical imaging and diagnostics, FFT plots are an essential technique for analyzing complex signals.