time domain(Time domain) is the descriptionmathematicsfunctionorPhysicssignalThe relationship to time.For example, the time domain waveform of a signal can express the change of the signal with time.
time domainYes DescriptionmathematicsfunctionorPhysicssignalThe relationship to time.For example, the time domain waveform of a signal can express the change of the signal with time.
If consideringdiscrete time The value of the function or signal in the time domain at each discrete time point is known.If consideringContinuous time, the value of the function or signal at any time is known.
When studying signals in time domain, we often useOscilloscopeConvert the signal into its time domain waveform.[1]
Conversion between time domain and frequency domain
A function or signal can pass through a pair of mathematicalOperatorTransform between time domain and frequency domain.for exampleFourier transformA time-domain signal can be converted into the corresponding amplitude and phase at different frequencies. Its spectrum is the performance of time-domain signal in the frequency domain, and the inverse Fourier transform can convert the spectrum back to the time-domain signal.
Spectrum analysis of time-domain signals
Take the signal as an exampletime domainThe graph below can show how the signal changes with time, while the graph below the frequency domain (generally calledspectrum）It can display the frequency and proportion of the signal distribution.In addition to the size of each frequency, the frequency domain representation will also have the size of each frequencyphase, using the size and phase information, we canSine waveGiven different sizes and phases, the original signal can be restored after addition.
In frequency domain analysisSpectrum analyzerTo convert the actual signal into the frequency spectrum in the frequency domain.
Frequency characteristics of time domain system
The characteristics of many physical components will change with the frequency of the input signal. For example, the impedance of the capacitor becomes larger at low frequencies, and smaller at high frequencies. On the contrary, the impedance of the inductance becomes larger at high frequencies, and smaller at low frequencies.OneLinear time invariant systemIts characteristics also change with frequency, so it also has its characteristics in frequency domain,frequency responseThe figure of is its representative.frequency responseIt can be regarded as the change of output signal amplitude when the input signal amplitude of a system is the same but the frequency is different. It can be seen that the output frequency of the system is larger.
Some systems are defined mainly in frequency domain, such aslow pass filter Only signals below a certain frequency are allowed to pass.
Amplitude and phase
Whether it islaplace transform 、Z conversionorFourier transformation The spectrum generated by it is a complex function of frequency, representing the amplitude of a signal (or system response) and itsphase。However, in many applications, the phase information is not important. If the phase information is not considered, the spectrum information can be expressed only in terms of amplitude (or power density) at different frequencies.
power spectral density It is a frequency-domain representation method that is often used in many aperiodic signals and does not meet the square integrable requirements.As long as one signal is consistentGeneralized stationary stochastic processThe corresponding power spectral density can be calculated.
Time-domain to frequency-domain method
Many transformations are used to analyze signals in the time domain, and are generally regarded as methods of frequency domain analysis.The following are the most common transformations and their application fields:
