The author of this article, maxfiner, graduated from Xi'an University of Electronic Science and Technology with a master's degree in signal and information processing. Maxfiner has worked in the wireless communication department of Huawei Communication Technology Co., Ltd., and has many years of experience in engineering project development. It also has algorithm theory research, simulation verification, and corresponding hardware design implementation capabilities. It has practical experience in all aspects of communication physical layer development and design. .
Proficient in signal processing design Small TIps (4): Several signals that are most frequently used
Always talking about digital signal processing, then what is the form of the object processed by the signal processing, the signal, what kind of characteristics, what kind of signal deserves our attention? This is a question we must understand and be familiar with. The role of some basic signals is so important. They are the basis for our further understanding of signal processing. In the sampling time of the analog signal, in the derivation process of the sampling theorem, in the spectrum analysis, in the up and down frequency conversion, they are seen everywhere.
Since there is no complete introduction to the Fourier transform, only the time domain waveforms and numerical expressions of these signals are given here. The detailed analysis of the application examples mentioned is not too much expansion here. The key is to emphasize that they all have What use and influence, so that we have enough attention, understanding and interest in them.
Important signals (continuous form): unit impulse signal, sine wave, rectangular signal, periodic rectangular signal.
Important signals (discrete form): unit sampled signal, rectangular signal, periodic rectangular signal, digital pulse train sequence signal.
These signals are very simple and easy to understand at a glance. The key is what they do. Still use specific examples to illustrate it.
The unit shock signal plays an important role in the analysis and synthesis of the continuous system. A unit input unit impulse signal is output. The output of the system is the familiar unit impulse response. The unit shock signal can be regarded as one of the simplest input signals. Any actual specific signal can be regarded as the superposition of the unit shock signal and its different time shifts. According to the premise that the system is a linear time-invariant system, then The output is also a linear superposition of the unit impulse response, and the formula is the form of convolution, which is also the origin of the convolution, and why the convolution is such a strange look.
Looking directly at the convolution formula, it is difficult to understand why it is such a form. Why do you have to reverse one of the signals? However, by combining the unit shock signal, unit impulse response, linear system's homogeneity, superposition, and time invariance, we will find that the strange convolution formula is this form. The theoretical basis and the reason are not defined as they are. In other words, this form of convolution is not conceived out of thin air and is derived based on the above premise. From this perspective, unit shock signals are indeed the basis for signal and system analysis. We will introduce and delineate this process in detail when introducing convolution. This process is familiar, and it will not be pleasing to the convolution formula.
Not to mention the sine wave signal, which is the fundamental signal of the Fourier transform. For a continuous form of signal, as long as the Dirichlet condition is satisfied, it can be decomposed into a superposition of multiple sine waves, completely with sine waves of different amplitudes and different phases. Equivalent representation. This is also the essence of spectrum analysis. The spectrum of a signal is itself a sine wave of different amplitude and phase.
The frequency and phase of a sine wave seem to be a very simple concept, but it is the most flexible and widely used concept in digital signal processing. After a period of engineering practice, such as analog or digital channel delay, frequency offset estimation and compensation, digital upconversion and digital downconversion, conjugate symmetry of real signal spectrum, phase-locked loop, FIR filter The linear phase and so on, it will be strongly felt that the understanding of the frequency and phase concept, as well as the flexible use, can not be determined at one time. To understand the full position, you need to constantly feel and understand. It does not overemphasize whether it directly affects our ability to use signal processing knowledge to solve specific practical problems.
Why emphasize rectangular signals? When we follow the discrete Fourier transform, we will know that the object processed by the discrete Fourier transform, that is, a certain discrete signal, has a premise that the discrete signal is a period of an infinitely long periodic discrete signal. Therefore, when we do discrete Fourier transform on a certain signal, we actually think that it is a cycle of the periodic discrete signal. In fact, the signal we get is a piece of the acquired signal. This actually implies an operation. In fact, we add an operation to the actual signal, which is to multiply the finite length of the rectangular signal by the actual infinite length signal, which will bring some effects, such as aliasing of the spectrum. Wait. What is the impact of these effects, how much impact, and the bandwidth of the signal, the sampling rate of the signal, the width of the rectangular signal are closely related. When we talk about the Fourier transform, we will quantitatively analyze these problems.
So, what is the specific application value of the periodic rectangular signal? For example, the DA converter, like the AD converter, plays an important pivotal role in the conversion of analog and digital signals. In the analysis of the undesired characteristics of the DA output signal, the periodic rectangular signal plays an important role. From this we can see how the period of the periodic rectangular signal and the width of the rectangle affect the distortion of the output signal of the DA. From this perspective, many practical and specific problems can be analyzed and interpreted from a theoretical point of view, which helps us to understand these specific phenomena and problems more deeply, so as to achieve an effective solution. Method.
The digital burst sequence signal, which plays a very important role in the analysis of the sampling theorem. It can be used to represent the equally spaced digital sampling process of continuous signals, thus deducing the important conclusion that the sampling rate is not less than twice the bandwidth of the signal.
The next issue is to speak - proficient in signal processing design small TIps (5): convolution , so stay tuned!
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Proficient in Signal Processing Design Small TIps(1): Signals and Information
Proficient in Signal Processing Design Small TIps(2): The Role of Mathematics
Proficient in signal processing design Tips (3): the three cornerstones that must be mastered
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