Digital signal processing-introduction summary

1. Background

With the rapid development of information science, as well as the rapid development of computer science caused by the development of large-scale integrated circuits, very large-scale integrated circuits and software, since the fast Fourier transform algorithm was proposed in 1965, digital signal processing (DSP) ) Has rapidly developed into a new and independent subject system. This subject has been applied to almost all engineering, science, and technology fields, and has penetrated into all aspects of people's daily life and work. In short, digital signal processing is a sequence of signals represented by numbers or symbols, through a computer or general (special) signal processing equipment, using digital numerical calculation methods to perform various required processing on the signal to extract useful information , The purpose of easy application.

Two, signal processing, digital signal processing

Signal processing (including digital signal processing) is a subject in which a research system processes (transforms) signals containing information to obtain the signals that people want, so as to extract information and facilitate use. The content of signal processing includes a series of processing such as filtering, transformation, detection, spectrum analysis, estimation, compression, expansion, enhancement, restoration, analysis, synthesis, recognition, etc., to achieve the purpose of extracting useful information and facilitating application. Because most science and engineering encountered analog signals in the past, they used to study the theory and realization of analog signal processing.

However, analog signal processing is difficult to achieve high precision, is greatly affected by the environment, has poor reliability, and is not flexible. With the rapid development of large-scale integrated circuits and digital computers, coupled with the maturity and perfection of digital signal processing theory and technology since the end of the 1960s, the use of computers or general or special digital signal processing equipment and digital methods to process signals, namely Digital signal processing has gradually replaced analog signal processing. With the advent of the information age and the digital world, digital signal processing has become an extremely important subject and technical field. Digital signal processing should be understood as digital processing of signals, not only digital signals. It can process digital signals as well as analog signals, and of course convert analog signals into digital signals. Deal with it later.

• When using this system to process analog signals, all components in Figure 0.1 are required. The analog signal xa(t) must first pass through an anti-aliasing analog low-pass filter, which will filter out the high frequency components that cause aliasing distortion.

• Then, it enters the analog-digital converter (AD converter) to convert the analog signal into a digital signal. The A/D converter includes two parts: sample and hold and quantization coding. Since the quantization coding cannot be completed instantaneously, the sample and hold must not only sample the analog signal (time discretization), but also maintain the amplitude of the sample to complete the quantization coding. The quantization coding quantizes and forms the amplitude of the sample and hold signal sent in Binary coded signal (digital signal).

• Then it is sent to the core component of digital signal processing to obtain the digital signal. If you need a digital signal, you can send it directly; if you need to send an analog signal, as shown in Figure 0.1, followed by a digital/analog converter (D/A converter), which includes two parts: decoding and sampling and holding , Its output is a stepped continuous time signal (when a zero-order hold circuit is used), which needs to be sent to a smoothing analog low-pass filter to obtain a smooth output analog signal y(t).

• The waveform diagram of the analog signal processing is shown in Figure 0.2.
  (A) Input analog signal waveform
  (b) Sample signal and sample and hold signal
  (c) Binary digital
  (d) quantized input sequence
  (e) Output sequence and sample and hold signal
  (f) Output analog signal

• Digital signal processing uses digital systems to process digital signals (including digitized analog signals). Discrete time signal processing uses discrete time systems to process discrete time signals. The difference between the two is that digital signal processing requires discrete The time signal is amplitude quantized to obtain a digital signal, and the coefficients (parameters) of the discrete time system are quantized to obtain a digital system.

3. Overview of digital signal processing disciplines

Generally recognized by the academic circles, the advent of 1965 (Fast Fourier Transform FFT algorithm) was the beginning of the development of the new discipline of digital signal processing. The proposal of this algorithm opened up an extremely broad prospect for the development of the discipline. Digital signal processing is closely related to many disciplines. The important branches of mathematics, calculus, probability theory and random processes, complex functions, advanced algebra, and numerical calculations are all extremely important analysis tools; while network theory, signals and systems are It is its theoretical basis. It is closely integrated with many disciplines, such as communication theory, computer science, large-scale integrated circuits and microelectronics, consumer electronics, biomedicine, artificial intelligence, optimal control, and military electronics. And it plays a major role in promoting their development.

In short, digital signal processing has formed an independent and complete theoretical system of disciplines closely related to the national economy.

This subject system mainly includes the following fields:

• Time domain and frequency domain analysis of discrete time signals, sampling theory in time domain and frequency domain, discrete time Fourier transform theory.
• Analysis of discrete-time linear time (shift) invariant system in time domain and transform domain (frequency domain, complex frequency domain or z-transform domain).
• Digital filtering technology.
• Discrete Fourier transform and fast Fourier transform, fast convolution, fast correlation algorithm.
• Theory and application of multiple sampling rates.
• Signal acquisition, including AD converter, D/A converter, quantization noise, etc.
• Modern spectrum analysis theory and technology.
• Adaptive signal processing.
• Signal compression includes speech signal compression and image signal compression.
• Signal modeling, including AR, MA, ARMA, CAPON, PRONY and other models.
• Other special algorithms, including homomorphic processing, signal reconstruction, deconvolution, etc.
• Realization of digital signal processing.
• Application of digital signal processing.

Fourth, the characteristics of digital signal processing

The digital signal processing system has the following obvious advantages:

• High accuracy: The accuracy of the analog network is determined by the components. The accuracy of the analog components is difficult to reach more than 10, while the digital system can reach an accuracy of 10-4 as long as the word length is 14 bits. In high-precision systems, sometimes only digital systems can be used. Since digital signals can be stored on disks or optical discs without loss, they can be transmitted at any time and can be processed offline at the remote end. In addition, time can be inverted, compressed or expanded, and homomorphic processing can also be performed (an analog system cannot).
• High flexibility: The performance of the digital system is mainly determined by the coefficients of the multiplier, and the coefficients are stored in the coefficient memory, so you can get different systems only by changing the stored coefficients through software design, which is much more convenient than changing the analog system . Due to the improvement of the technological level, the integration degree is getting higher and higher, and the available frequency is getting higher and higher.
• Strong reliability: Because the digital system has only two signal levels "0" and "1", it is less affected by the temperature and noise of the surrounding environment. Each component of the analog system has a certain temperature coefficient, and the level is continuously changing, which is easily affected by temperature, noise, electromagnetic induction, etc. If the digital system uses large-scale integrated circuits, its reliability will be higher.
• Easy to integrate on a large scale: Because digital components are highly standardized, easy to integrate and produce on a large scale, and the requirements for circuit parameters are not strict, the product yield is high. Especially for low-frequency signals, for example, seismic wave analysis needs to filter signals from a few hertz to tens of hertz. When processing with an analog network, the value, volume and weight of inductors and capacitors are very large, and the performance cannot meet the requirements, while digital signal processing The system is very superior at this frequency.
• Time division multiplexing: Time division multiplexing is the use of digital signal processors to process several channels of signals at the same time. The system block diagram is shown in Figure 0.3. Because there is a large gap time between two adjacent samples of a signal, it can be controlled by the synchronizer to send other signals in this time gap, and each signal is processed by the same signal Under the control of the synchronizer, the latter calculates another signal after calculating one signal. The higher the computing speed of the processor, the more channels it can handle.
  
• High performance indicators can be obtained: for example, for signal spectrum analysis, analog spectrum analyzers can only analyze frequencies above 10 Hz at the low end of the frequency, and it is difficult to achieve high resolution (narrow enough bandwidth); but in digital spectrum analysis, It has been able to achieve 10-3Hz spectrum analysis. For another example, a finite-length impulse response digital filter can achieve accurate linear phase characteristics, which is difficult to achieve in an analog system.
• Two-dimensional and multi-dimensional processing: the use of a huge storage unit can store one or several frames of image signals to achieve two-dimensional or even multi-dimensional signal processing, including two-dimensional or multi-dimensional filtering, two-dimensional or multi-dimensional spectrum analysis, etc. Due to the prominent digital signal processing The advantages make it more and more widely used in communications, voice, radar, seismic survey and reporting, sonar, remote sensing, biomedicine, television, instrumentation, military, etc.

Five, the limitations of digital signal processing

• The system has high complexity and high cost. Since the entire system (see Figure 0.1) has A/D and D/A converters, anti-aliasing and smoothing filters, the system is more complex and costly, so the cost is high when processing general analog signals , Must be fully considered. In addition, high-speed, high-precision A/D and D/A converters are expensive.
• The contradiction between processing speed and accuracy: the factors affecting processing speed are the speed of the algorithm, the speed of the A/D and DA converters, and the speed of the digital signal processor chip: the speed and accuracy of the A/D and D/A converters (dB number) are contradictory, and if high speed is achieved, accuracy will decrease. In general, the frequency is too high (the speed requirement is high), and analog signal processing methods, such as 100MHz signals, can only be used. If the required accuracy exceeds 12dB, the processing speed will be lower than an order of magnitude.

However, it can be predicted that the speed of digital signal processing will become faster and faster.

Sixth, the application of digital signal processing

• Filtering and transformation: including digital filtering/convolution, correlation, fast Fourier transform (FFT), Hilbert transform, adaptive filtering, spectrum analysis, windowing, etc.
• Communication: including adaptive differential pulse code modulation, adaptive pulse code modulation, pulse code modulation, differential pulse code modulation, delta modulation, adaptive equalization, error correction, digital public exchange, channel multiplexing, mobile phones, modems, data Or digital signal encryption, decryption of codes, spread spectrum technology, conversion of communication systems, satellite communication, TDMA/FDMA/CDMA and other communication systems, echo cancellation, IP telephone, software radio, etc.
• Voice and language: including voice mail, voice vocoder, voice compression, digital recording system, voice recognition, voice synthesis, voice enhancement, text-to-speech transformation, neural network, etc.
• Image and graphics: including image compression, image enhancement, image restoration, image reconstruction, image transformation, image segmentation and depiction, satellite image analysis, pattern recognition, computer vision, solid-state processing, electronic maps, electronic publishing, animation, etc.
• Consumer Electronics: Including digital audio, high-definition digital TV, music synthesizer, electronic toys and games, cochlear relocation, barcode reader, DVD player, digital message/answering machine, automotive electronics, etc.
• Instruments: including spectrum analyzers, function generators, seismic signal processors, transient analyzers, phase-locked loops, pattern matching, etc.
• Industrial control and automation: including robot control, laser printer control, servo control, automata, power line monitor, computer-aided manufacturing, engine control, adaptive driving control, etc.
• Medical: Including health assistants, remote medical monitoring, ultrasound equipment, diagnostic tools, CT scans, MRI, hearing aids, etc.
• Military: Including radar processing, sonar processing, navigation, radio frequency modem, global positioning system (GPS), air early warning, missile guidance, reconnaissance satellite, aerospace testing, adaptive beamforming, array antenna signal processing, etc.

In actual engineering, there are more and more demands for various DSP application systems, making DSP algorithm development tools continue to be enriched and improved. Undoubtedly, C language is one of the most useful programming tools. Most manufacturers of digital signal processing chips will provide C compilers and emulators. These compilers have C language and efficient direct assembly language, which can be used to optimize some pairs. Real-time programming of demanding applications. In addition, MATLAB developed by Mathworks in the United States is a powerful software tool for high-tech calculations. MATLAB has become an important tool for digital signal processing and analysis. It has a rich toolbox, including communication related to signal processing. , Filter design, signal processing and other toolboxes, each toolbox has a large number of callable functions, and various functions can describe and process all data in matrix form. Therefore, to be proficient in the theory and technology of digital signal processing, it is necessary to not only learn the relevant basic knowledge, but also master the C language and learn to apply DSP and MATLAB software tools.