Design Of Graphic Equalizer Based On Wavelet Decomposition And IIR Filter

When a signal passes through a transmission system,the transmission of different frequency components of the signal becomes different both in amplitude and phase,so the loss of different frequency components is also different,resulting the information of some frequency components will be partially lost,or even totally lost,which means that the signal is distorted.Equalizer,which is used to fix the inherent defects in the transmission system,and to compensate the output signal of the transmission system to make it close to the input signal by the means of amplifying the components being attenuated and attenuating the components being amplified.In order to reduce the interference from adjacent frequency band,traditional equalizers are implemented by high order finite impulse response filter(FIR filter),which requires high computational power while designing the equalizers,and bring the problem of high delay.Actually,equalizer based on infinite impulse response filter(IIR filter)is not infeasible,on the contrary,equalizer based on IIR filter has the advantages in smaller volume,easier implementation,lower implementation cost.However,IIR filter has some disadvantages,such as nonlinear phase,instability,and not easy to optimize.Aimed at the problems existing in traditional equalizer and general problems of IIR filter,the following work is carried out:(1)Proposes a design method of stable IIR filter from the perspective of optimization,which to design IIR filter equalizing single frequency band of the transmission system.In order to design the IIR filter,the total absolute error between the ideal equalization and the actual equalization in the passband of the IIR filter is minimized subject to the constraints imposed on the stability criterion of the IIR filter as well as on the maximum modulus error between the ideal equalization and the actual equalization in the corresponding passband.Then an improved genetic algorithm is called to solve the optimization problem.The designed IIR filter is used to equalize single frequency band of the transmission system.(2)In order to avoid the interference from adjacent frequency bands,wavelet decomposition is added in frequency band division stage.Applied multilayer wavelet decomposition to the input and output signal of the transmission system to get two groups of components,which correspond to each other in frequency band.Then use the frequency components of input and output signal in the same frequency band to train the designed IIR filters,and cascade all IIR filters of different frequency band to form the designed graphic equalizer.The computer numerical simulation results show that,the graphic equalizer based on the method proposed in this paper can avoid the interference from different frequency bands,and provides effective equalization for the severely attenuated signal.The waveform of the signal recovered to a great extent both in time domain and frequency domain.The similarity between the signal after attenuation and the original signal is only0.4031,and the similarity is improved to 0.7252 after equalization.Also,the required computational power in designing the equalizer and the delay of the designed equalizer are greatly reduced at the same time.