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What are the linear modulation methods? In view of this problem, this article introduces the corresponding analysis and answers in detail, hoping to help more partners who want to solve this problem to find a more simple and feasible way.

There are four modes of linear modulation, namely: 1, conventional double-sideband amplitude modulation "DSB-AM"; 2, double-sideband amplitude modulation "DSB"; 3, single-sideband modulation "SSB"; 4, residual sideband modulation "VSB".

According to the transmission characteristics, the modulation mode can be divided into linear modulation and nonlinear modulation. The generalized linear modulation refers to the modulation process in which the modulated parameters change linearly with the modulated signal. In a narrow sense, linear modulation refers to the modulation process in which the frequency spectrum of the modulated signal is moved to both sides of the carrier frequency to become the upper and lower sideband.

Overview of Linear Modulation Theory

Continuous wave modulation CWM (Sine wave): there are two types of modulation methods with sine wave as carrier:

Linear modulation: Z out = ∑ ki Zin (f-f oi)

Nonlinear modulation: there is no above linear relationship.

Analog linear modulation

1. Conventional double-band amplitude modulation (DSB-AM)

two。 Double sideband amplitude modulation (DSB)

3. Single sideband modulation (SSB)

4. Residual sideband modulation (VSB)

Conventional double-band amplitude modulation (DSB-AM)

S AM (t) = [A0 + f (t)] cos (ω c t + θ c)

A where: 0 external DC; f (t) modulated signal; angular frequency of ω c carrier signal; initial phase of θ c carrier signal. This is a simple and intuitive modulation method, and the original modulated signal can be easily recovered by envelope detection. [

The premise of undistorted detection is: A0 + f (t)] ≥ 0; otherwise, there will be over-amplitude modulation, an example.

If the ① modulation signal is a single-frequency cosine, then f (t) = Am cos (Ω mt + θ m) S AM (t) = [A0 + Am cos (Ω mt + θ m)] cos (ω c t + θ c) = A 0 [1 + β AM cos (Ω mt + θ m)] cos (ω c t + θ c) β where: AM Am =; for amplitude modulation index, its value should be ≤ 1. A0

When the ② modulation signal is deterministic, the spectrum of the modulated signal is S AM (t) = [A0 + f (t)] cos (ω ct + θ c) 1 = [A0 + f (t)] [e j (ω ct + θ c) + e? J (ω ct + θ c)] 2 if the frequency spectrum of f (t) is F (ω), 1s AM (ω) = [2 π A0 δ (ω + ω c) + F (ω + ω c)] e can be obtained from Fourier transform F [A0] = 2 π A0 δ (ω) F [f (t) e ±j ω ct] = F (ω m ω c). For the sake of simplification, let θ = 0, then 1 S AM (ω) = π A 0 δ (ω? ω c) + F (ω? ω c) 21 + π A 0 δ (ω + ω c) + F (ω + ω c) 2 if expressed by convolution, let θ = 0, then S AM (t) = [A0 + f (t)] cos (ω c) = m (t)? C (t) 1S AM (ω) = [m (ω)? C (ω)] 2 π

Where m (t) = A0 + f (t), c (t) = cos ω c t M (ω) = F [m (t)] = 2 π A0 δ (ω) + F (ω) C (ω) = F [cos ω c] = π [δ (ω? ω c) + δ (ω + ω c)] this result is exactly the same as the above results.

③ power distribution (average power) 2s AM = S AM (t) = [A0 + f (t)] 2 cos 2 ω c t because f (t) = 0, cos 2 ω c t = 0 S AM A02 f 2 (t) = + = Sc + Sf 22 Sc carrier power Sf ═ sideband power average power results including carrier power and sideband power can be known by definition, only sideband power is related to the modulated signal. So we can define the modulation efficiency as η AM= Sf S AM= f 2 (t) A02 + f 2 (t) 2 when the modulation signal is single frequency cosine, f (t) 2 = Am / 2, then η AM 22 Am β AM= = 2222A0 + Am 2 + β AM when it is at the critical point, β AM=1, the modulation signal with the highest modulation efficiency of η AM=1/3 is the square wave with amplitude A0, η AM=0.5.

Conclusion: the carrier component C does not carry information, but it occupies a lot of power, which is wasted. If the carrier component can be suppressed, this part of power can be saved. Therefore, another modulation method is evolved: suppressing carrier double-band modulation.

When the ④ modulated signal is random, the power spectral density signal of the modulated signal is known. The power spectral density can be obtained from the autocorrelation function of the signal to study the modulation efficiency and characteristics. For ergodic stationary random processes / generalized stationary random processes, there is a pair of Fourier transform relationships between the power spectral density and the autocorrelation function. Autocorrelation characteristic of signal waveform → autocorrelation function; power spectral density → average power → modulation efficiency.

Suppressed carrier double-band modulation (DSB-SC)

If the carrier is to be suppressed, the double-band amplitude modulation of the suppressed carrier can be obtained as long as there is no DC component A0, and its time expression is S DSB (t) = f (t) cos ω c t when f (t) is a known signal, the spectrum of the modulated signal is 1s DSB (ω) = [F (ω? ω c) + F (ω + ω c)] 2 comparison of conventional double-band amplitude modulation with suppression carrier conventional double-band amplitude modulation when A0 = 0 This is the suppression of carrier conventional double-band amplitude modulation. When A0 ≠ 0, this is a conventional double-band amplitude modulation. For details of the modulator, see balanced modulator and ring modulator. This kind of demodulator can only use the method of coherent demodulation. For example, after inserting a strong carrier at the demodulation end, we can adopt the method of envelope detection. For example, a strong carrier can be inserted at the transmitting end of the signal when sending more than one transmission. The balanced modulator shows that the input of the nonlinear unit is: X1 = f (t) + cos ω c t. The output of the nonlinear unit is: X2 =? F (t) + cos ω c t Y1 = A1 [f (t) + cos ω c t] + a2 [f (t) + cos ω c t] 2y2 = A1 [? F (t) + cos ω c t] + a2 [? F (t) + cos ω c t] 2 therefore, the second term of the following formula can be obtained by bandpass filtering and y = y1? Y2 = 2a1 f (t) + 4a2 f (t) cos ω c t ring modulator if the carrier is to be suppressed, as long as there is no DC component A0, the double-band amplitude modulation of suppressed carrier can be obtained. The time expression is (? 1) n? 1C (t) = ∑ cos [2 π f c t (2n? 1)] π n = 12n? 14 ∞ when f (t) is a known signal. The spectrum of the modulated signal is S (t) = C (t) f (t) 4 ∞ (? 1) n? 1 = ∑ cos [2 π f c t (2n? 1)] f (t) π n = 12n? 1 working principle: D1D2/D3D is turned on respectively.

Single sideband modulation (SSB)

SSB modulation transmits only one sideband of SSB modulated signal, which is the best way to save frequency band.

1. Intuitive method: the characteristic of H SSB (ω) formed by filtering method is: h SSB (ω) = H USB (ω) =? 0? 1 = H LSB (ω) =? 0 ω > ω c ω ≤ ω c < ω c ω ≥ ω c SSB signal demodulation can not be demodulated by simple envelope detection. The signal envelope can not reflect the waveform of the modulated signal. The demodulation of SSB modulation should adopt the coherent demodulation method. For example, a sideband signal requires carrier frequency: 10MHz, bandwidth: 300~3400Hz. Upper and lower sideband interval: 600Hz is limited by filter normalization value 600Hz transition band rises 40dB only choose two-stage filter first-stage carrier frequency selection: 100kHz second-stage carrier frequency selection: 10MHz

two。 The formation of Hilbert transform / orthogonal pair / Hilbert filter / broadband phase shift network by SSB modulation phase shift method must shift the signal wide band phase-π / 2, and? Phase shift-π / 2 must be stable and accurate; Phase shift-π / 2 for all frequency components

3. The single sideband modulated Weaver method uses the orthogonal component of the carrier frequency and only needs the carrier phase shift-π / 2. It is not necessary to make the frequency range of the signal broadband phase shift-π / 2 signal 12 ω L? ω H ω a = (ω L + ω H) ω c = ω a + ω b 1 filter cutoff frequency is (ω H? ω L) 2

Residual sideband modulation (VSB)

Residual sideband modulation is a method between SSB and suppressed carrier sideband modulation. In addition to transmitting one side band, a part of another side band, that is, the transition band, is retained. It is easier to implement. The phase-shifting method can also be used for residual sideband modulation, but in practice, the filtering method is mostly used. The filtering method can be divided into: the spectral characteristics of the residual part of the upper sideband method are shown in the middle picture. The spectral characteristics of the method of the lower sideband of the residual part. The transfer function of the residual sideband filter must have complementary symmetry near the carrier frequency in order to ensure that the results of coherent demodulation do not distort H VSB (ω? ω c) + H VSB (ω + ω c) = constant residual sideband filter attenuation characteristics: it can be steeper → SSB or flatter → SSB, which is suitable for selection. The attenuation roll-off characteristics of the filter: linear roll-off and cosine roll-off (TV signal). [1]

Linear modulation can be divided into two types: generalized linear modulation and narrow linear modulation. In the narrow sense, the linear modulation only changes the frequency of each component in the spectrum, but does not change the relative proportion of the amplitude of each component, so that the spectrum structure of the upper sideband is the same as that of the modulated signal, while the spectral structure of the lower sideband is the mirror image of the modulated signal spectrum. In a narrow sense, linear modulation includes amplitude modulation (AM), carrier suppressed double-band modulation (DSB-SC), single-sideband modulation (SSB) and residual sideband modulation (VSB).

This is the answer to the question about which linear modulation methods are shared here. I hope the above content can be of some help to you. If you still have a lot of doubts to be solved, you can follow the industry information channel to learn more about it.

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