Relationship between time domain and frequency domain

Recently, in digital image processing, I did not have an intuitive concept in the time domain and frequency domain. I will search for it and summarize it as follows:
 
1. The simplest explanation

The frequency domain is the frequency domain,

We usually use the time domain, which is related to time,

This is only related to the frequency, which is the reciprocal of the time domain. In the time domain, the X axis is time,

Frequency is the frequency. Frequency domain analysis is to analyze its frequency characteristics!

2. Image Processing:

Concepts such as space domain, frequency domain, transform domain, and Compression Domain!

It just means to transform the image to another domain and then facilitate processing and computing.

For example, after a certain degree of transformation (Fourier transformation, discrete yuxua DCT transformation), the statistical characteristics of the image's spectrum function: Most of the image's energy is concentrated at low, medium frequency, and the components of the high frequency are weak, it only shows some details of the image.

2. Discrete Fourier Transformation

There are usually Discrete Fourier transformation and its inverse transformation.

3. DCT Transformation

The oscilloscope is used to view the time domain content, and the frequency meter is used to view the frequency domain content !!!

Time Domain is a general summary of signal changes over time in the timeline.

In the frequency domain, the expression of the time domain waveform is used as the Fourier change to obtain the expression of the complex frequency domain. The drawn waveform is the spectrum diagram. Describes the relationship between frequency changes and amplitude changes.

The Time Domain performs Spectrum Analysis to the frequency domain; the space domain performs Spectrum Analysis to the wave field;

Signals pass through the system and are convolution in the time domain, while multiplication in the frequency domain.

Both Fourier transform and wavelet transform are essentially the same. They convert signals between time and frequency domains and find some intuitive information from seemingly complex data, then analyze it. Because the signal is often simpler and more intuitive in the frequency domain than in the time domain, most of the signal analysis work is carried out in the frequency domain. Music is an excellent example of time/frequency analysis. Music score is the signal distribution of music in the frequency domain, and music is a function after the music score is transformed to the time domain. From music to music, it is a Fourier or wavelet transformation; from music to music, it is a Fourier or wavelet inverse transformation.

Time Domain (Time Domain) -- the independent variable is time, that is, the horizontal axis is time, and the vertical axis is the signal change. Its Dynamic signal x (t) is a function that describes the value of a signal at different times.
Frequency (frequency domain) -- the independent variable is frequency, that is, the horizontal axis is frequency, and the vertical axis is the amplitude of the frequency signal, that is, the spectrum diagram. The spectrum diagram describes the signal frequency structure and the relationship between the frequency and the frequency signal amplitude.
When performing time-domain analysis on signals, sometimes some signals have the same time-domain parameters, but it does not indicate that the signals are exactly the same. Because the signal not only changes with time, but also is related to the frequency and phase information, it is necessary to further analyze the frequency structure of the signal and describe the signal in the frequency domain.
The conversion of dynamic signals from time domain to frequency domain is mainly achieved through Fourier series and Fourier transformation. Periodic Signals rely on Fourier series, and non-cyclic signals rely on Fourier transformation.

Very simple time domain analysis function is that the parameter is T, that is, y = f (t). in frequency domain analysis, the parameter is W, that is, y = f (W)
The two can be converted to each other. Time-Domain functions are transformed into frequency-domain functions through Fourier or Laplace transformations.

 

Fourier transform, as a mathematical tool, is not only embodied in one or two aspects.
Just like a differential equation, it is useful in many disciplines. Large to man-made satellite, small and micro particles.

Common applications can transform one function field to another. Specifically, for example, in signal processing, you can set the signal
To the frequency of the signal. Signal processing is also widely used, such as processing. Right

Transformation can process some differential equations that have been learned in mathematical and physical methods, so I will not go into details.

The basic principles of quantum mechanics are related to Fu's transformation. (Refer to several books by Peng Yunwu)

Generally, engineering students, especially those who are specialized in automation and signal processing, are better at Fu's transformation than science. Because in the letter
Number and system, as well as the principle of automatic control, Fu's transformation and LA's transformation are the most basic concepts and tools.

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