# Nyquist Plot vs. Complex Function Plot

• Bullington
In summary, the conversation revolves around the differences between a Nyquist plot and the plot of a complex function. The speaker is confused about whether they are the same and is looking for a way to demonstrate this. They also mention their goal of gaining a geometric understanding of complex functions and using Matlab to plot the transfer function. However, they are having trouble with the scatter plot not matching the Nyquist function. The responder suggests looking at an introductory book on complex analysis or stability and control instead.
Bullington
Gold Member
This is not a homework problem, I just am confused a little about the differences between a Nyquist plot and the plot of a complex function. I believe they are the same given the domain of the plot of a complex function is for all real numbers equal to or greater than zero. However, I am having a hard time demonstrating this. So what is the difference? Is there a difference?

My original goal was to get a geometric understanding of complex functions and seeing the difference between differential complex functions and non-differential complex functions. What programs can I use to get a geometric understanding of complex functions.

I'm using matlab, but I am open to any suggestions. My code is below and I'm trying to plot the transfer function 50/(s+3) with a nyquist function, and a scatter plot. I expected that the scatter plot was going to make the same shape as the nyquist function, but it doesn't. Any suggestions?

Code:
y=-10:0.001:10;
x=0:0.001:20;
z=x'*ones(1,length(y))+ones(1,length(x))'*1i*y;
fz=50*(z+3)\ones(length(z));
scatter(real(fz(:)),imag(fz(:)))
figure
nyquist(zpk([],[-3],50))

Thanks for checking this out!

I'm afraid that using Nyquist plots to understand functions of a complex variables is taking a wrong turn. Nyquist plots are used to analyse the stability of systems as a parameter changes. Complex valued functions of a complex variable are much more general and a very different subject. I recommend that you look at an introductory book on complex analysis. I can't recommend any shortcuts.

PS. If your goal is to understand system dynamics, you may be better off with an introductory book on stability and control.

Bullington

## What is a Nyquist Plot?

A Nyquist Plot is a graphical representation of the frequency response of a system, which shows the relationship between the magnitude and phase of a complex function as a function of frequency.

## What is a Complex Function Plot?

A Complex Function Plot is a graphical representation of a complex-valued function which shows the relationship between the input and output values of the function.

## What is the difference between a Nyquist Plot and a Complex Function Plot?

The main difference between a Nyquist Plot and a Complex Function Plot is that a Nyquist Plot shows the frequency response of a system, while a Complex Function Plot shows the input-output relationship of a function. Additionally, a Nyquist Plot is typically used for analyzing the stability of a system, while a Complex Function Plot is used for visualizing the behavior of a function.

## How do you interpret a Nyquist Plot?

In a Nyquist Plot, the frequency response of a system is represented by a curve in the complex plane. The curve starts at the origin (representing zero frequency) and moves towards the right as frequency increases. The shape of the curve and its position relative to the origin can provide information about the stability and performance of the system.

## How do you interpret a Complex Function Plot?

In a Complex Function Plot, the input-output relationship of a function is represented by a curve in the complex plane. The curve shows how the output value changes in response to different input values. The shape and position of the curve can provide insights into the behavior and properties of the function.

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