The so-called Gaussian white noise means that the probability distribution is a normal function, while white noise means that its second moment is uncorrelated and its first moment is constant, which means the correlation of continuous signals in time. This is a question of testing two different aspects of the signal.
Gaussian random process refers to its arbitrary n-dimensional (n = 1, 2, …) probability density function, which can be expressed as:
f (x，x； t t)
= (3-3)
Where =; ; Is the determinant of the correlation coefficient matrix,
=
Is the algebraic cofactor corresponding to the elements in the determinant.
Equation (3- 1) is a mathematical function model corresponding to Gaussian white noise.
Question 2: What is standard Gaussian white noise? Gaussian noise means that the probability density function of noise obeys Gaussian distribution, while white noise means that any two samples of noise are uncorrelated, and they are described from different angles.
Strictly speaking, white noise is only an idealized model, because the power spectral density of actual noise cannot have infinite bandwidth, otherwise its average power will be infinite, which is physically impossible. White noise is a powerful tool for system analysis because it is convenient in mathematical processing. Generally speaking, as long as the spectral width of a noise process is much larger than that of the system it acts on, and its spectral density can be regarded as a constant within this bandwidth, it can be treated as white noise. For example, thermal noise and shot noise have uniform power spectral density in a wide frequency range, and they can usually be considered as white noise.
How to make standard white noise with matlab;
Randon () is used to generate random numbers with Gaussian distribution; y=randn( 1，2500)； y = y/STD(y)； Y = y- mean (y); a = 0.0 128； b = sqrt(0.9596)； y = a+b * y； %a is the expected value and b is the standard deviation.
2.WGN: generate Gaussian white noise: y = wgn(m, n, p) generate a Gaussian white noise matrix with m rows and n columns, where p specifies the intensity of output noise in dBW.
3. To add noise to the specified signal, use awgn ().
Question 3: Introduction to Gaussian White Noise The so-called Gaussian white noise means that the probability distribution is a normal function, while white noise means that its second moment is uncorrelated and its first moment is constant, which means the correlation of continuous signals in time. This is a question of testing two different aspects of the signal.
Question 4: Why does the communication principle choose Gaussian white noise? It means that the probability density function of noise satisfies the statistical characteristics of normal distribution and its power spectral density function is constant.
In the theoretical analysis of communication system, especially when analyzing the anti-noise performance of computing system, it is often assumed that the channel noise in the system (that is, the fluctuation noise mentioned above) is Gaussian white noise. as a result of
1. Gaussian white noise can be expressed by concrete mathematical expressions, which is convenient for derivation, analysis and operation.
2. Gaussian white noise truly reflects the additive noise in the actual channel and is a true representation.
The characteristics of channel noise are analyzed.
Question 5: Gaussian white noise usually refers to how much noise obeys Gaussian distribution: if a noise obeys Gaussian distribution and its power spectral density is evenly distributed, it is called Gaussian white noise. Instantaneous value refers to probability density function, and Gaussian distribution refers to normal distribution.
Question 6: What standard normal white noise is the variance of white noise? Its mean value is 0, and its variance is 1.
Assume that the power spectrum of standard normal white noise is constant c; therefore
The area under the power spectrum curve is equal to the variance of white noise and its value is 1.
For the standard normal white noise with limited frequency band (0, fc), Cfc = 1 C = 1/fc. (This refers to the one-sided spectrum).
Question 7: What are the two representations of Gaussian white noise? Thermal noise and shot noise are both Gaussian white noise: if a noise obeys Gaussian distribution and its power spectral density is uniformly distributed, it is called Gaussian white noise. The so-called Gaussian white noise means that the probability distribution is a normal function, while white noise means that its second moment is independent and its first moment is constant. Refers to the correlation of continuous signals in time. This is a question of testing two different aspects of the signal. There are complex phenomena such as multipath delay, Doppler frequency shift and diffusion, Gaussian white noise interference and so on. In order to test the performance of short-wave communication equipment, a large number of field experiments are usually needed. In contrast, the channel simulator can perform similar performance tests in the laboratory environment, with low test cost and strong repeatability. It can shorten the development cycle of equipment, so it is necessary to develop a channel simulator by itself. The channel simulator can choose a representative Watterson channel model (that is, Gaussian scattering gain tapped delay line model), and one of the important links is to quickly generate Gaussian white noise sequences. It is convenient to use when adding Doppler spread and Gaussian white noise. The traditional Gaussian white noise generator is implemented on microprocessor and DSP software system, and its simulation speed is much slower than that of hardware simulator. Therefore, choosing FPGA hardware platform to design Gaussian white noise generator can realize full digital processing, and has the advantages of low test cost, strong repeatability, good real-time performance and high speed. It can meet the experimental requirements well. A fast generation scheme of Gaussian white noise sequence based on FPGA is proposed. According to the mapping relationship between uniform distribution and Gaussian distribution, the scheme adopts a broken line approximation method suitable for FPGA. This method is simple and fast, occupies less hardware resources, is written in VHDL language, and has strong portability. And can be flexibly embedded into a modem. The pseudo-random noise generated by. 1 uniformly distributed random number generator 1. 1 m sequence generator has some statistical characteristics similar to random noise, which is convenient for repeated generation and processing, so it has been widely used. M sequence is a commonly used pseudo-random sequence. This sequence is also called the longest linear feedback shift sequence. M sequence is the longest sequence generated by linear feedback shift register. If N-level linear feedback shift register is selected, the period of M sequence is (2n- 1). For M-sequence, the state of N-level linear feedback shift register is regarded as an unsigned integer. Then the value range of the state is 1 ~ (2n- 1), and each state of the shift register will only appear once in one cycle of the m sequence. However, it should be noted that the initial state of the linear feedback shift register is set to a non-zero value, and the period of the m sequence is unchanged when any non-zero initial state is given. The state value of the shift register is a random number that obeys uniform distribution. When making an M-sequence generator, the feedback line connection of the linear feedback shift register can be obtained by checking the primitive polynomial (the coefficient is 1, which means that the corresponding bit has feedback line connection, and 0 means that the corresponding bit has no feedback line connection). Therefore, the number of feedback lines of the linear feedback shift register and the number of modulo-2 adders are directly determined by the terms of the primitive polynomial. In order to reduce the consumption of hardware resources, primitive polynomials with fewer terms can be selected in the design. In order to make the period of pseudo-random sequence long enough to meet the design requirements, the primitive polynomial adopted is: x 18+x7+ 1. That is, a 18 linear feedback shift register can generate an m sequence with a period of (2 18- 1). The connecting line is shown in figure 1. The Gaussian white noise signal of correlation reduction module is a random process, each sample point is a Gaussian variable, and the power spectral density on both sides is constant n0/2. That is to say, it can be seen from Equation (2) that the sampled signals of Gaussian white noise at any two different times are statistically independent. However, it can be seen from the generation process of M-sequence that in each clock cycle, the linear feedback shift register only moves out the highest bit and feeds back a value to the lowest bit, so the adjacent states are not completely independent. This will inevitably affect the independence between Gaussian white noise signals sampled at any two different times. Therefore, non-correlation operation is needed. In order to reduce the correlation, the usual method is to generate a Gaussian sequence, and then connect an interleaver to disrupt the sequence in which the Gaussian sequence appears. However, the construction of interleaver takes up ... & gt
Question 8: What does Gaussian white noise e=0 mean? It is assumed that white noise is represented by x(t), and the average value of 0 is represented by E(x(t))=0, that is, the mathematical expectation of random variables is 0. As you can see from your question, the Gaussian white noise here should be a multidimensional random variable. For any white noise, it can be averaged by 0.
Question 9: The difference between Gaussian noise and white noise Gaussian noise is a kind of noise with normal distribution (also called Gaussian distribution) probability density function. In other words, the value of Gaussian noise follows Gaussian distribution or its energy in each frequency component has Gaussian distribution.
White noise storage refers to the noise whose power spectral density is evenly distributed in the whole frequency domain. Random noise with the same energy at all frequencies is called white noise.