Estimating Atmospheric Params w/ Autocorrelation & Spectral Density Funcs.

In summary, an experiment is conducted to measure atmospheric parameters using autocorrelation and spectral density functions. Table 1 shows the parameters used in the experiment, including the PRF, number of coherent integrations, resolution, lag resolution, number of bits in code, maximum lag, and operating frequency. Using the equation v = f*λ (1), the maximum velocity that can be represented by the spectral density function is calculated. The minimum difference in velocity that can be resolved by the system is not specified. Additionally, a 500 m resolution is achieved using a 13 bit Barker code, but the pulse length is not specified.
  • #1
Firben
145
0

Homework Statement


An experiment probes a coherent process and the receiver is coherent. The autocorrelation function and the spectral density function are estimated and transformaed into atmospheric parameters. See Table 1 below

1) Calculate the maximum velocity (in m/s) that may be represented by the spectral density function.2) What is the minimum difference in velocity that can be resolves by this system ?3) 500 m resolution is archieved by using 13 bit Barker code. What is the pulse length ?Tabel 1.

PRF [Hz] 1200
No. of coherent
integrations 32
Resolution [m] 500
Lag resolution [ms] 24.6
Nr of bits in code 13
Maximum lag [s ] 25
Operating frequency 45

Homework Equations



v = f*λ (1)

The Attempt at a Solution



1)
How can i do this when i don't know the wavelength ? Should i suppose that the maximum velocity is the speed of light ?

2)
How can i know the minimum velocity here ?

3)
What should i do here ?

I don't know were the black lines comes from ? <Moderator's note: [s ] was interpreted as a BB code>
 
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  • #2
The maximum velocity is related to the resolution and sampling properties of the signal and of the computed quantities (like PSD).
 

Related to Estimating Atmospheric Params w/ Autocorrelation & Spectral Density Funcs.

1. What is autocorrelation and how is it used to estimate atmospheric parameters?

Autocorrelation is a statistical tool that measures the correlation between a variable and its past values. In the context of estimating atmospheric parameters, autocorrelation is used to analyze time series data of atmospheric variables, such as temperature or pressure, and determine the degree of correlation between data points at different time intervals. This helps in identifying any patterns or trends in the data and can be used to make predictions about future values.

2. What is a spectral density function and how does it relate to estimating atmospheric parameters?

A spectral density function is a mathematical tool that describes the distribution of frequency components in a time series data. In the context of estimating atmospheric parameters, the spectral density function is used to analyze the frequency components of the data and identify any dominant frequencies or periodic patterns. This information can then be used to estimate parameters such as the dominant frequency of a weather phenomenon or the amplitude of a specific frequency component.

3. What are some common atmospheric parameters that can be estimated using autocorrelation and spectral density functions?

Autocorrelation and spectral density functions can be used to estimate a wide range of atmospheric parameters, including temperature, humidity, wind speed, atmospheric pressure, and even air pollution levels. These parameters play a crucial role in weather forecasting and climate modeling, and accurate estimation of these parameters is essential for understanding and predicting atmospheric conditions.

4. What are the advantages of using autocorrelation and spectral density functions for estimating atmospheric parameters?

One of the main advantages of using autocorrelation and spectral density functions is that they can handle non-stationary and nonlinear data, which is common in atmospheric variables. Additionally, these methods can capture the temporal dependencies between data points, which can improve the accuracy of parameter estimation. Moreover, they are relatively simple and efficient techniques that can be easily implemented in various atmospheric modeling and analysis tools.

5. Are there any limitations to using autocorrelation and spectral density functions for estimating atmospheric parameters?

While autocorrelation and spectral density functions are powerful tools for estimating atmospheric parameters, they do have some limitations. These methods assume that the data is stationary, meaning that the statistical properties of the data do not change over time. This may not always hold true in the case of atmospheric variables, which are influenced by various external factors. Additionally, these methods may require a large amount of data to accurately estimate parameters, which may not always be available in certain situations.

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