Signals Systems Part 1 Lessons on where they can be optimized

Signal and system are used in China's higher education, and the rise of signal and system in China's higher education is not long, but it is a compulsory core basic course for electronic majors, and the course is mainly based on mathematical analysis, which involves mathematical and physical methods, concepts, etc. are widely used in many fields such as communication, signal and information processing, electronics, computer science bridge and technology, automatic control, circuits and systems. The relevant concepts and analytical methods covered in this course are its main areas of study.

In the signal and system, the corresponding mathematical model is established, and then the solution is analyzed according to the mathematical model, so as to give the obtained results physical interpretation and corresponding physical meaning.

Personally, I think the course of signals and systems should be reviewed by analogy. It can be mainly divided into these three parts to review:

1.There are three types of equations: differential equations, difference equations, and equations of state.

Master the classical solutions of several equations, as well as the Fourier transform to solve differential equations and the Russ transform to solve differential equations.

2.Several transformations: Fourier transform, Russ transform, z-transform. In particular, the nature of the several transformations inside should be compared to the memory). There is also the relationship between the several transformations, and the scope of use.

3.Other aspects of knowledge: mainly system function method and so on.

Calculus is enough.

This course is very logical, first of all, we must figure out the derivation process of each formula, and it is best to have a graphic explanation in the textbook. In fact, to put it bluntly, the whole book only talks about one concept: the transformation relationship between the time domain and the frequency domain, that is, the welfare leaf transformation, and other transformations are extensions of this transformation.

In the time domain, it is commonplace, and in terms of voice signals, it is the intensity of speech at each point in time.

The frequency domain is not easy to understand, but I have also been exposed to it, just like a radio, which receives different signals in different frequency domain bands. This book explains the conversion method of signal representation in the time domain and frequency domain, and it is not difficult for you to see the derivation of this conversion clearly. Many people call it the Book of Heaven, because it is difficult to get started, there are many concepts, and the signal is divided into two types: continuous and discrete, and each of them corresponds to its own multiple transformations, but when you get started, you will find that these transformations are talking about one thing.

If you really want to learn, you have to persevere. Good luck!

Calculus, no, this course is more independent, in fact, it doesn't require much other basic knowledge, calculus is not even very needed, start to do more problems, understand the definition of various transformations and memorize various intermediate results proficiently, the important thing is to understand what he is talking about. Signals drift by with System 99.

The key to this course is the big transformation; And from this course, a deep understanding of the concepts of time and frequency domain is required; The whole book revolves around two spaces: time domain + frequency domain; In addition, from the signal form, it is divided into digital (discrete) and analog (continuous) signals; So that's the discussion of the 4 cases; It is necessary to master the time domain analysis of analog signals, the frequency domain analysis of analog signals (i.e., the Fourier transform, the subsequent Laplace transform is actually a generalization of the Laplace transform, so that functions that do not meet the Dirichlet condition can also do frequency domain analysis), time domain analysis of digital signals, frequency domain analysis of digital signals (i.e., z-transform) In addition, the specific methods of analysis and more detailed problems are listed as follows:

1 Introduction. Signal and System Concepts, Description, Classification and Typical Signals, Signal Operations, Singular Signals, Signal Decomposition.

Models of systems and their classification, linear time-invariant systems, systems analysis methods.

2 Time domain analysis of continuous-time systems.

Establishment and solution of differential equations, jump change of starting point, zero input response and zero state response, method of system impulse response, use of convolution to find the zero state response of the system, method of convolution, nature of convolution.

3 Fourier transform.

Fourier series of periodic signals, spectral structure and band width, Fourier transform--- spectral density function, properties of Fourier transform, Fourier transform of periodic signals, Fourier transform of sampled signals, time-domain sampling theorem.

4 S-domain analysis of continuous-time systems.

Definition of Lassell transform, properties of Lassell transform, complex frequency domain analysis, inverse Rasl transform.

The system function h(s) and the zero-pole distribution of the system determine the time domain and frequency characteristics of the system, and the stability of the linear system.

5 The Fourier transform is applied to communication systems.

Response with system functions, distortion-free transmission, ideal low-pass filter, band-pass filter, modulation and demodulation.

The definition of Hilbert transform, using the Hilbert transform to study the constraint characteristics of system functions, from the sampled signal to recover continuous-time signal, frequency division multiplexing and time division multiplexing, PCM signal.

6 Vector space analysis of signals.

Vector orthogonal decomposition, signal orthogonal decomposition.

Representation of Arbitrary Signals in a Complete Orthogonal Function System, Passevaar's Theorem, Energy Signal vs. Power Signal, Energy Spectrum vs. Power Spectrum, Correlation Coefficients vs. Correlation Functions, Correlation vs. Convolution Comparison, Correlation Theorem.

7 Time-domain analysis of discrete-time systems.

Commonly used typical discrete-time signals, system block diagram and difference equation, solving constant coefficient linear difference equation, unit sample response of discrete-time system, convolution of discrete quantities,

8 Z-domain analysis of discrete-time systems.

Z-transform definition, properties, z-transformation of typical sequences, z-inverse transformation.

The z-transform is used to solve the difference equation, the system function h(z) of the discrete system is defined, the influence of the zero pole of the system function on the system characteristics, and the frequency response characteristics of the discrete-time system.

9 Analysis of state variables of the system.

Signal flow diagram, establishment of equation of state of continuous time system, solution of equation of state of continuous time system.

(2) For any t, f(t) = (t-8)δ(t-4) = 0

Because (t-8) is not equal to 0 only at t 8 and δ(t-4) is not equal to 0 only at t=4

The solution to the other problems is similar, and you need to pay attention to when the integrand is equal to 0

It's not easy to answer the question, there is a complete process in the picture, please adopt it as soon as possible. If you don't understand, you can ask, thank you.