Time Domain, frequency domain, and spatial domain

Directory (?) [-]

1. Time domain and frequency domain

Time Domain, frequency domain, and spatial domain

1. What is time domain?

Time DomainDescribes the time-to-time relationship between mathematical functions or physical signals. For example, a time-domain waveform of a signal can express the signal changes over time.

2. What is frequency domain?

Frequency Domain (frequency domain )--The independent variable is the frequency, that is, the horizontal axis is the 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.

3. What is a spatial domain?

Spatial DomainIt is also called image space ). Space composed of image pixels. In the image space, processing the image metadata directly using the length (distance) as the independent variable is called space field processing.

The time field is used as the variable.

The frequency field is used as the variable.

The Research on spatial coordinates as variables is the spatial domain.

The Research Based on the wave number as a variable is called the wave number field.

Time domain and frequency domain

This article is reprinted. I would like to thank my colleagues who have patiently edited the following knowledge and have forgotten the link. Therefore, I can only express my gratitude here.

 

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

Frequency DomainIs the frequency domain,

We usually useTime DomainIs time-related,

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 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

Oscilloscope for viewingTime Domain content, which can be viewed by frequency metersFrequency DomainContent!!!

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.

Title: spatial frequency domain.

English: spatial frequency domain.

Description: The image features are described using the spatial frequency (I .e. the number of waves) as independent variables, the changes in the pixel values of an image can be decomposed into linear superposition of vibration reduction functions with different amplitude, spatial frequency, and phase, the composition and distribution of various air frequency components in an image are called spatial spectrum.

This decomposition, processing, and analysis of spatial frequency features is called spatial frequency domain processing or wave number field processing.

Similar to time and frequency domains, spatial and spatial frequency domains can also be converted to each other.

The mature Frequency Domain technology can be referenced in the spatial frequency domain. The general process is as follows:

① Perform two-dimensional discrete Fourier transform or wavelet transform on the image to convert the image from the image space to the domain space.

② Analyze and process the image spectrum in the spatial frequency domain to change the image's frequency features.

That is, different digital filters are designed to filter the image spectrum. Frequency domain processing is mainly used for processing image spatial frequency.

Image Restoration, image reconstruction, radiation transformation, edge enhancement, image sharpening, image smoothing, noise suppression, spectrum analysis, texture analysis, and other processing and analysis processes.

Note that the unit of spatial frequency (wave number) is meters-l or (millimeters)-1.

Time Domain, frequency domain, and spatial domain

1. What is time domain?

Time DomainDescribes the time-to-time relationship between mathematical functions or physical signals. For example, a time-domain waveform of a signal can express the signal changes over time.

2. What is frequency domain?

Frequency Domain (frequency domain )--The independent variable is the frequency, that is, the horizontal axis is the 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.

3. What is a spatial domain?

Spatial DomainIt is also called image space ). Space composed of image pixels. In the image space, processing the image metadata directly using the length (distance) as the independent variable is called space field processing.

The time field is used as the variable.

The frequency field is used as the variable.

The Research on spatial coordinates as variables is the spatial domain.

The Research Based on the wave number as a variable is called the wave number field.

Time domain and frequency domain

This article is reprinted. I would like to thank my colleagues who have patiently edited the following knowledge and have forgotten the link. Therefore, I can only express my gratitude here.

 

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

Frequency DomainIs the frequency domain,

We usually useTime DomainIs time-related,

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 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

Oscilloscope for viewingTime Domain content, which can be viewed by frequency metersFrequency DomainContent!!!

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.

Title: spatial frequency domain.

English: spatial frequency domain.

Description: The image features are described using the spatial frequency (I .e. the number of waves) as independent variables, the changes in the pixel values of an image can be decomposed into linear superposition of vibration reduction functions with different amplitude, spatial frequency, and phase, the composition and distribution of various air frequency components in an image are called spatial spectrum.

This decomposition, processing, and analysis of spatial frequency features is called spatial frequency domain processing or wave number field processing.

Similar to time and frequency domains, spatial and spatial frequency domains can also be converted to each other.

The mature Frequency Domain technology can be referenced in the spatial frequency domain. The general process is as follows:

① Perform two-dimensional discrete Fourier transform or wavelet transform on the image to convert the image from the image space to the domain space.

② Analyze and process the image spectrum in the spatial frequency domain to change the image's frequency features.

That is, different digital filters are designed to filter the image spectrum. Frequency domain processing is mainly used for processing image spatial frequency.

Image Restoration, image reconstruction, radiation transformation, edge enhancement, image sharpening, image smoothing, noise suppression, spectrum analysis, texture analysis, and other processing and analysis processes.

Note that the unit of spatial frequency (wave number) is meters-l or (millimeters)-1.