# Numerical Approximation and addition of new data points

• Geeniey
In summary, Stephen's problem is that he needs more data points to see the small reflections on his oscilloscope. He is researching numerical methods to help him.

#### Geeniey

Hi

I am new member and I am new to the Signal processing so I hope I could get some help from the members to able to understand the concepts.

I have a Signal. I have a 10Msaples/sec ADC. I view the Signal on an Oscilloscope which has 20Gsamples/sec sampling rate.

The Point where I am struck is, I must increase the number of sample Points so that I can have more Resolution on the Oscilloscope.

I have researched and found that Numerical Approximation methods help to develop new algorithm. But I am unable to Chose which Kind fits.

Your problem is to estimate the value of the signal between the given sample points. The "best" way to do that depends on what you know about the data. To get the best advice you must explain what the data measures. What experiment does it come from?

If you merely want a pretty picture, your problem is to interpolate a curve between the data points or "fit" a curve to approximate the data. To "interpolate" means the curve will pass exactly through the data points. To "fit" means the curve may not pass exactly through the data, but will be close to them.

Thank you Mr Stephen for your response.

The data I am measuring is the reflection (based on radar). At the moment I have fine reflections and like you mentioned, my next step is to interpolate to observe the reflections in time more clearly. I have this experiment running on MPLAB and I am not sure how can I interpolate. I do not have an idea of how to collect the data points and to insert new points.

Suppose your data sequence is x[0], x[1], x[2],... When you interpolate between x[k] and x[k+1] can you access the values x[k+2],x[k+3],...? i.e. Do you have a complete record of all data, past and future so you can "look ahead"?

Or are you working with "real time" data and cannot know x[k+1], x[k+2],... ?

Stephen Tashi said:
Suppose your data sequence is x[0], x[1], x[2],... When you interpolate between x[k] and x[k+1] can you access the values x[k+2],x[k+3],...? i.e. Do you have a complete record of all data, past and future so you can "look ahead"?

Or are you working with "real time" data and cannot know x[k+1], x[k+2],... ?

Hi Stephen,

I have the raw data from the UART in real time. The set of data is in decimal counts, for example:
1;4048#gy;1;4052#gy;1;4050#gy;1;4050#gy;1;4050#gy;1;4050#gy;1;4052#gy;1;4050#gy;
and so on...

I cannot find the way to crack this!

Is the signal periodic?

No, its just a single reflecting pulse.

Can you use the samples to modulate a 10 G Hz sine wave and display the modulated wave?

Stephen Tashi said:
Can you use the samples to modulate a 10 G Hz sine wave and display the modulated wave?

Its a square wave and I must over sample the ADC to increase the sampling rate which increases the number of sampling points. But that is not enough in my case, I guess.

I don't understand yet how much computation can be done on the data. You said that you had looked up some numerical methods. Can you give an example of a method that is feasible? (I don't mean a method that is "best" - just a method that you could conceivably implement with the hardware/software that you are using.)

Geeniey said:
20Gsamples/sec sampling rate
Wow, that's fast. But I don't understand your question.

Sir,

Iam working the Time Domain Reflectometry.

I have a square waveform with 14ns rise time and 350ns Duration generated by a 7GHz Transistor which is controlled by a micro-controller. This is my incident pulse. The Information that I am interested in is the reflected pulse. This pulse is acquired from the coax after an mismatch has occured. This pulse is sent into a comparator which compares the PWM (with 50% duty cycle) of the incident with this reflected and generates a stop pulse.

This stop pulse is sent to a CTMU (Charge time measurement unit) of the micro-controller and the time is converted into a voltage. This voltage is given to ADC and the Output is viewed on the scope via UART.

Now, I want to view the Signal in high Resolution on the scope with more data Points to analyze the small reflections. So I am now struck where to start with and how can I do it !

Do I have to do FFT of the Signal? Or make Firmware changes like cascading the ADCs available. (the ADC used is 12 bit Resolution high Speed pipelined)

Since the Resolution depends on the rise time( which is the circuit Response to fast changing input), I must look for a way to improve the rise time. If the reflections are smaller than the rise time, I cannot see them on the reflected Signal. I would like your suggestions on methods to achieve this.

I hope I made my problem clear now.

Your advice can help me improve my state of understanding of how to develop an algorithm to fulfil my requirement.

## 1. What is numerical approximation?

Numerical approximation is a method used to estimate a value that is close to the actual value of a mathematical expression or function. It is a useful tool for solving complex problems that cannot be solved exactly.

## 2. How is numerical approximation used in scientific research?

Numerical approximation is widely used in scientific research for data analysis and simulations. It allows researchers to make predictions and draw conclusions from large sets of data that would be difficult or impossible to analyze by hand.

## 3. What is the process of adding new data points to a numerical approximation?

Adding new data points to a numerical approximation involves taking existing data and using it to make a more accurate estimation by adjusting the parameters of the approximation. This can be done through various techniques such as interpolation or extrapolation.

## 4. What are the advantages of using numerical approximation in scientific calculations?

Numerical approximation allows for complex calculations to be performed quickly and efficiently. It also allows researchers to work with real-world data, which is often messy and incomplete, and still obtain useful results. Additionally, numerical approximation can be used to solve problems that do not have exact analytical solutions.

## 5. What are the limitations of numerical approximation?

Numerical approximation is not always accurate and can introduce errors into calculations. It also requires a significant amount of computing power, and the results may vary depending on the chosen method of approximation. Additionally, it may not be suitable for all problems, such as those that involve discontinuous functions or complex systems.