## 1.CVC and DSP noise reduction:

When consumers buy Bluetooth headsets, they will always hear the CVC and DSP noise reduction functions that the merchants have in promoting the headphones. No matter how many users have heard the descriptions, many consumers still don’t understand the difference between the two. The difference, for such a technical problem, we come to the science of the two under the working principle and difference.

DSP is a shorthand for digital signal processing. Its working principle: the microphone collects external environmental noise, and then through the noise reduction system function inside the earphone, it replicates to generate a reverse sound wave equal to the ambient noise, which cancels the noise and thus achieves more. Good noise reduction effect.

CVC is short for Clear Voice Capture. It is a software noise reduction technology. The principle is to suppress various types of reverberation noise through the built-in noise cancellation software and microphone.

**The difference as follows:**

a. for the object is different, CVC technology is mainly for the echo generated during the call, DSP is mainly for the high and low frequency noise in the external environment.

b. different beneficiaries, DSP technology mainly makes the headset users personal income, and CVC mainly benefits the other party.

In summary, headphones using DSP and CVC noise reduction technology can effectively reduce the noise of the external environment of the call, and significantly improve the quality of the call and the sound of the headphones.

## 2.ANC noise reduction:

ANC refers to Active Noise Control, which actively reduces noise. The basic principle is that the noise reduction system produces reverse sound waves equal to the outside noise, neutralizing the noise. Figure 1 is a schematic diagram of a feedforward active noise canceling earphone. The ANC chip is placed inside the earphone. Ref mic (reference microphone) collects ambient noise on the earphones. Error mic (Error Microphone) Collects the residual noise after noise reduction in the earphone. Speaker plays the anti-noise after ANC processing.

Figure 2 is a schematic diagram of the ANC system, with three layers, separated by dashed lines. The uppermost primary path is the acoustic channel from ref mic to error mic, the response function is represented by P(z)P(z); the middle layer is the analog channel, where the secondary path is the path from the adaptive filter output to the return residual. Including DAC, reconstruction filter, power amplifier, speaker playback, re-acquisition, pre-amplifier, anti-aliasing filter, ADC; the bottom layer is the digital path, where adaptive filter constantly adjusts the filter weight coefficient to reduce the residual until convergence . The most common solution is to implement an adaptive filter using an FIR filter in combination with the LMS algorithm. Simplify Figure 2 and get Figure 3.

Let me briefly talk about the principles of adaptive filter and LMS (Least mean square) algorithm, and then Figure 3. As shown in Figure 4, given the input xx and the desired output dd, the adaptive filter updates the coefficients every iteration so that the difference between the output yy and dd becomes smaller and smaller until the residual is close enough to zero and converges. LMS is an update algorithm for adaptive filters. The objective function of LMS is the square of the instantaneous error e2(n)=(d(n)−y(n))2e2(n)=(d(n)−y(n))2, in order to minimize the objective function, Applying the gradient descent gives the updated formula of the algorithm. (The algorithmic idea of using gradient descent to minimize an objective and get the updated formula of the parameter to be sought is very common, such as linear regression.) The update formula of the LMS algorithm using FIR filter is: w(n+1) =w(n)+μe(n)x(n)w(n+1)=w(n)+μe(n)x(n), where μμ is step size. If the μμ size is adjusted with iteration, it is a step-by-step LMS algorithm.

Let's talk about Figure 3. Here the adaptive filter is output after S(z)S(z) to compare with the desire output. S(z)S(z) will cause instability. In the literature, "the error signal is not correctly 'aligned' In time with the reference signal", the convergence of the LMS is broken. (I haven't figured out what it means T__T) An effective method is FXLMS (Filtered-X LMS), which allows x(n) to be input to the LMS module via Sˆ(z)S^(z), Sˆ(z S^(z) is an estimate of S(z)S(z). Objective of FXLMS:

E2(n)=(d(n)−s(n)∗[wT(n)x(n)])2,

E2(n)=(d(n)−s(n)∗[wT(n)x(n)])2,

So gradient=−2e(n)s(n)∗x(n)−2e(n)s(n)∗x(n), where s(n)s(n) is unknown, with its estimate approximation, so FXLMS Update formula is

w(n+1)=w(n)+μe(n)x'(n),

w(n+1)=w(n)+μe(n)x'(n),

Where x'(n)=sˆ(n)∗x(n)x'(n)=s^(n)∗x(n).

When the adaptive filter converges, E(z)=X(z)P(z)−X(z)W(z)S(z)≈0E(z)=X(z)P(z)−X(z ) W(z)S(z) ≈ 0, so W(z) ≈ P(z) / S(z) W(z) ≈ P(z) / S(z). That is to say, the weight coefficient of the adaptive filter is determined by the primary path and the secondary path of the headphones. The primary path and the secondary path of the headset are relatively stable, so the weight coefficient of the adaptive filter is relatively stable. Therefore, for the sake of simplicity, the weight coefficients of some manufacturers' ANC headphones are determined at the factory. Of course, the listening experience of this ANC earphone is obviously not as good as the ANC earphone with true adaptive meaning, because in actual situations, the external noise relative to the direction of the earphone, different temperature and the like may have an influence on the channel response of the earphone.

Matlab verification

Write Matlab code, using the adaptive filter of variable step size LMS, the simulation results are shown in Figure 5. In the range of 0 to 2 kHz, the feedforward ANC is used to eliminate Gaussian white noise, and the noise attenuation is 30 dB+ on average. The FXLMS in the Matlab library is fixed-step, and the effect is worse.

## Q&A

**a. Why is the ANC only for low frequency noise below 2 kHz?**

On the one hand, the physical sound insulation of the headphones (passive noise reduction) can effectively block high-frequency noise, and it is not necessary to use ANC to reduce high-frequency noise. On the other hand, the low-frequency noise has a long wavelength and can withstand a certain phase delay, while the high-frequency noise has a short wavelength and is sensitive to phase deviation, so ANC eliminates high-frequency noise.

**b. When the electronic delay is larger than the primary delay, how can the performance of the algorithm be greatly reduced?**

P(z) delay is small, S(z) delay is large, such as P(z)=z-1, S(z)=z-2, only when W(z)=z can meet the requirements, non-causal, Unreachable.

**c. What is the difference between Feedforward ANC, narrow-band feedforward ANC, and feedback ANC?**

The Feedforwad structure has a ref mic and an error mic that collect external noise and internal residual signals, respectively. The feedback structure has only one error mic, and the reference signal is generated by error mic and adaptive filter output.

The Broad-band feedforward is the structure described above. In the narrow-band structure, the noise source generates a signal trigger signal generator, and the signal generator generates a reference signal for the adaptive filter. Only applicable to eliminating periodic noise.

Feedback ANC uses error mic to recover the signal collected by ref mic in the feedforward structure because it only has error mic. The path does not satisfy the causal constraint, so only the predictable noise components, ie the narrowband periodic noise, are eliminated. It should be noted that if the feedforward does not satisfy the causal constraint, ie the electronic delay is longer than the main channel acoustic delay, it can only eliminate the narrowband periodic noise.

There is also a Hybrid ANC structure that includes both the feedforward and feedback structures. The main advantage is that you can save the order of the adaptive filter.