Plot functions with Symbolic parameters

Questions
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1

Hi,

In order to plot a simple function like sine we could use the following command

Plot[Sin[x],{x,0,10}]

the result of course is a sine wave of magnitude 1. The qustion is what if we want to plot the sine with amplitude other than 1 but we want to leave it in general like this:

Plot[A*Sin[x],{x,0,10}]

In other words, I am interested in seeing ‘A’ on the y-axis instead of the 1. I know it will not be as what I wrote in the second line. It might be related to the axis properties but I could not figure how to do it.

I need to plot this signal in this form because I am working on some tutoreials and notes for a signal processing course.

Regards

2

In order to plot, one would need a value for A. Will it be sufficient for you to use Manipulate wherein A takes on different values to show the effect of various A?

Manipulate[ Plot[A Sin[x], { x, 0, 10},
          (* Options 4 Plot *)
          PlotRange -> {Automatic, {-2, 2}} (* End Plot *)], 
	      {A, -2, 2, 1}, 
          (* Options 4 Manipulate *)
          ControlType -> RadioButton ]

Now you can click a radiobutton to show the effect of various A. I hope this may be helpful.

3

Thanks Issac;

Consider this example, we have Pulse - Sinc fourier pair, and I am interested in showing the effect of the amplitude of the pules together with its width on the location of sinc’s zeros .. in this case I need to put the symbol on the axis while hiding the actual numeric values from the axis because the actual values are not of that importance in this context.

4

If you are just interested in visual label, then this should work:

Plot[Sin[x], {x, 0, 10}, Ticks -> {Automatic, {{1, "HELLO"}}}]

we98wes8d7v6fd5fdf67sdf57.png
we98wes8d7v6fd5fdf67sdf57.png402×224 8.77 KB

5

Considering Sam’s input, and the sketch above, would the following work?

T = 4;
g[t_] := Sinc[T t];
f[\[Omega]_] := FourierTransform[ g[t], t, \[Omega], FourierParameters -> {1,-1} ]
plt0 = Plot[ g[t], {t, -2T, 2T},  AxesLabel -> {Automatic, "g(t)"},
			          PlotRange -> {{-2T, 2T},All} ,
				  PlotStyle -> {Thick, Red, Dashed}];


plt1 = Plot[ f[\[Omega]], {\[Omega], -2T, 2T},  AxesLabel -> {Automatic,"F(\[Omega])"},
					        PlotRange -> {{-2T, 2T},All} ,
						PlotStyle -> {Thick, Blue}];

Show[ {plt0,plt1}, 
		AxesLabel -> {"","g(t), F(\[Omega])"}, 
		(* Change Ticks to None to have no markers *)
		Ticks -> {Automatic, Automatic}]
6

Thanks dear Sam, this is exactely what I need. Many thanks for you Issac, your answer is very valuable. I appreciate your comments.

Regards.