5_practice.c

#include <stdio.h>	// for printf function
#include <stdlib.h>	// for memory allocation
#include <time.h>	// for time calculation
#include <math.h>	// for sine and cosine functions
int main() {
	// Declare all the variables
	int k, n, N;
	double *x, *yr, *yi;
	time_t t;

	// Input the number N
	printf("Please input a number N\n");
	scanf("%d",&N);
	
	// Locate the memory for x, yr, yi;
    x  = (double *)malloc(N * sizeof(double));
	yr = (double *)malloc(N * sizeof(double)); 
	yi = (double *)malloc(N * sizeof(double));  
	// Initial setting for x, for example, x[k] = k
	
	for (k=0;k<N;k++){
		x[k] = k;
		yr[k] = 0;
		yi[k] = 0;
	}
	
	t = clock();	
	// yr[n]+i*yi[n] = sum(exp(-i 2 Pi k n / N)*x[k], k=0..N-1), n=0..N-1 

	for ( n = 0; n < N; n++){
		for ( k = 0; k < N; k++){
			yr[n] += cos(2 * M_PI * k * n / N ) * x[k];
			yi[n] -= sin(2 * M_PI * k * n / N ) * x[k];
		}
	}


	// output the results
	t = clock() - t;
	printf("Result \n");
	printf("x = (");
	for (k = 0; k < N; k++)
	{
		if (k % 10 == 0 && k > 1)
			printf("\n  ");
		printf(" %.0f ", x[k]);
	}
	printf(" )\n");

	printf("F(x) = \n");
	printf("( ");
	for (n = 0; n < N; n++)
	{
		if (n % 5 == 0 && n > 1)
			printf("\n  ");
		printf(" %.2f %+.2fi ", yr[n], yi[n]);
	}
	printf(" )\n");
	
	printf("%d ms for discrete Fourier Transform of %d elements\n", t, N);

	// free the memory located by x, yr, yi
	free(x);
	free(yr);
	free(yi);
	
	return 100;
}