Why is a single signal frequency sinusoidal

The sinusoidal signal is the signal with the most singular frequency component, and is named because the waveform of this signal is a mathematical sinusoidal curve. Electricity for industry and lighting is a sinusoidal signal. The sine wave output by the oscillation circuit generally contains harmonic components, and the square wave is formed by the superposition of a series of harmonic components.

These advantages bring a lot of convenience to the operation, so the sinusoidal signal is widely used as a typical signal or test signal in practice.

The sinusoidal signal has a very useful property as a basic signal:

1. The addition of two sinusoidal signals of the same frequency, although their amplitude and phase are different, the result of addition is still the sinusoidal signal of the original frequency.

2. If the frequency f1 of one sinusoidal signal is equal to an integer multiple of the frequency f of another sinusoidal signal.

3. The differentiation and integration of a sinusoidal signal to time is still a sinusoidal signal of the same frequency.

A single signal frequency is not sinusoidal, and usually a square wave is formed by the superposition of a series of harmonic components.

In practical applications, a square wave is usually formed by superimposing a series of harmonic components, including the fundamental wave and the harmonics. The fundamental wave is the lowest frequency component of the square wave signal and the main body of the square wave signal, while the harmonic is the integer multiple frequency component of the fundamental wave, and their amplitude gradually decreases, and the influence on the signal is getting smaller and smaller.

The sinusoidal signal is a spectral line with zero bandwidth, and the non-sinusoidal signal is synthesized by the collapse of several sinusoidal signals, and the spectral group manuscript shed is discrete or continuous with a certain bandwidth.

From sinusoidal circuits to non-sinusoidal circuits, the circuit structure has not become complex, but the signal source has changed from a sinusoidal function to a non-sinusoidal vertical chord function, and the non-sinusoidal function can usually be decomposed into a series of sinusoidal functions by Fourier series, so we can solve the non-sinusoidal periodic current circuit based on the previous sinusoidal steady-state circuit analysis method and through the superposition theorem.

g(j) is called the frequency characteristic, and a( ) is the ratio of the amplitude of the output signal to the amplitude of the input signal, which is called the amplitude-frequency characteristic.

) is the difference between the phase angle of the output signal and the phase angle of the input signal, which is called the phase frequency characteristic.

The characteristic that the phase shift angle varies with frequency is called the phase frequency characteristic.

When the input to the system is a sinusoidal signal, the output steady-state response is also a sinusoidal signal, and its frequency is the same as the frequency of the input signal, but the amplitude and phase change, and the change depends on the angular frequency. If the output steady-state response and the input sinusoidal signal are expressed as complex numbers, and their complex ratios are obtained.

g(jω)=a(ω)e rφ(ω

The following equation is the expression of the sinusoidal signal:

x(t) = a sin(2 π f t + = a sin(ω t + 1)

Where: a - the amplitude of the sine wave;

- the initial phase angle of the sine wave;

f -- frequency of the sine wave (hz);

- garden frequency, equal to 2 f;

t - time.

The value of the sinusoidal signal varies with frequency according to equation (1).

Expression for sinusoidal signal:

x(t) = a sin(2 f t + = a sin( t + f : frequency, w : angular frequency.

1. All signals contain only one frequency, and there are no other frequency components, which is called a single frequency signal. s(t)=asin(wt+p)

A single AC signal expression represents a single frequency signal.

A signal refers to an electromagnetic or electronic code for data. Signals are divided into analog signals and digital signals. Analog signal refers to the continuous value of the parameters of the electrical signal, which is characterized by continuous amplitude.

Common analog signals include **, fax and TV signals. Digital signals are discrete, and changes from one value to another are instantaneous, just like turning power on and off. Digital signals are characterized by amplitude being limited to a finite number of values.

Common digital signals are telegram symbols, digital data, etc.

It is a signal of a fixed frequency, not doped with other frequencies.