Triangular Wave (Periodic Function) – C Program

One might need to work with periodic functions in C for several reasons. Periodic functions are an important class of functions with numerous applications.

In this post I will show you how to define a particular periodic function in C, called the Triangular Wave.

But before that let me just give you a brief idea about dealing with periodic functions.

Periodic Functions are those that give the same value after a particular period.

Let’s say that there is a function f(x) which is periodic with a period of 2*T and is already defined in the interval [-T,T].

Then the function should have the same value at: f(x), f(x+2T), f(x+4T), ….

i.e. f(x)=f(x+2T)=f(x+4T)=……. since period=2*T.

But I said that the function is defined only in the interval [-T,T]. So how is the computer supposed to calculate it’s value at x>T?
That’s easy. Since the value of the function at f(x+2T) is simply f(x), therefore we can generalize that whenever x>T: then,
f(x)=f(x-2T).
  Note: We have to keep taking x back by 2T i.e (x-2T) until it lies  within [-T,T] where the function is well-defined.

Similarly what about the value of function at x less than (-T) cause the function is not defined for values less than (-T)?
Again, this time we use:f(x)=f(x+2T). Note: We keep translating x forward by 2T  i.e (x+2*T) until it lies  within [-T,T] where the function is well-defined.

Using the above two arguments we can create a function which will make any given function defined within [-T,T] and with a period 2*T a periodic function.

The following program generates x and y-values for a Triangular Wave of period 2\pi defined by:

This means that the wave has an amplitude of \pi .
The calculated x and y-values are stored in a txt file called ‘periodic.txt’ and then plotted using Gnuplot.

PROGRAM:

/************************************
 *******PLOT A PERIODIC FUNCTION*****
 ************TRIANGULAR WAVE*********
 ***********************************/
#include<stdio.h>
#include<math.h>
/**Function definition for the Triangular Wave(Periodic Function)**/
double f(double x){
  if(x>=0&&x<M_PI){
    return x;
  }
  else if(x>=M_PI&&x<2*M_PI){
    return 2*M_PI-x;
  }
  else if(x>=2*M_PI){
    return f(x-2*M_PI);
  }
  else if(x<0){
    return f(x+2*M_PI);
  }
}
main(){
  FILE *fp=NULL;
  /*To write the data points to a txt file [periodic.txt]**/
  fp=fopen("periodic.txt","w");
  double x;
  /**To plot in the rang of -6pi to 6pi **/
  for (x=-6*M_PI;x<=6*M_PI;x=x+0.1){
    fprintf(fp,"%lf\t%lf\n",x,f(x));
  }
}

The above program will produce a file called ‘periodic.txt’ containing the data points for the Triangular Wave.
Now open, Gnuplot and plot it using the following command:

plot 'periodic.txt' w l

The result looks as shown.

GNUPlot Output:

I'm a physicist specializing in theoretical, computational and experimental condensed matter physics. I like to develop Physics related apps and softwares from time to time. Can code in most of the popular languages. Like to share my knowledge in Physics and applications using this Blog and a YouTube channel.



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