diff --git a/Makefile b/Makefile
index ab4a4cf..7393a4b 100644
--- a/Makefile
+++ b/Makefile
@@ -5,3 +5,10 @@ two_pole:
./tp > tp.dat
vi tp.dat
gnuplot < tp.gpt
+
+
+fa: freq_analysis.c
+ gcc freq_analysis.c -o fa -lm
+ ./fa > fa.dat
+ vi fa.dat
+ gnuplot < fa.gpt
diff --git a/fa.gpt b/fa.gpt
new file mode 100644
index 0000000..590bdc9
--- /dev/null
+++ b/fa.gpt
@@ -0,0 +1,8 @@
+
+
+
+plot "fa.dat" using 1:8
+
+!sleep 10
+!sleep 10
+!sleep 10
diff --git a/freq_analysis.c b/freq_analysis.c
new file mode 100644
index 0000000..9210845
--- /dev/null
+++ b/freq_analysis.c
@@ -0,0 +1,171 @@
+#include <stdio.h>
+#include <math.h>
+
+double xz[10]; // = {0.0}; // Z transform numerator or zeros Z^0 + Z^1 + Z^2 etc.
+double yp[10]; // = {0.0}; // Z transform denominator or poles Z^0 + Z^1 + Z^2 etc.
+
+
+typedef struct complex_number {
+ double real;
+ double imaginary;
+} COMPLEX;
+
+#define NYQUIST 1000
+#define PI 3.14159265358979323844
+
+double arg ( COMPLEX x) {
+ return atan2(x.imaginary, x.real);
+}
+
+double mag ( COMPLEX x ) {
+ return sqrt ( x.real * x.real + x.imaginary * x.imaginary );
+}
+
+// add x1 and x2 result in x1
+void complex_add ( COMPLEX * x1, COMPLEX x2 ) {
+ x1->real = x1->real + x2.real;
+ x1->imaginary = x1->imaginary + x2.imaginary;
+}
+
+void complex_print ( COMPLEX x ) {
+ printf("x.r = %f x.i = %f ",x.real,x.imaginary);
+}
+
+void complex_scalar_mul ( double m, COMPLEX * x) {
+ x->real = m * x->real;
+ x->imaginary = m * x->imaginary;
+}
+
+void complex_pow ( double p, COMPLEX * x ) {
+ double r = arg(*x) + PI * 2.0;
+ double m = mag(*x);
+
+ r *= p;
+ while (r>360.0) r -= 360.0; // r %= ( PI * 2.0);
+ m = pow(m,p);
+
+ x->real = cos(r) * m;
+ x->imaginary = sin(r) * m;
+}
+
+COMPLEX complex_mul ( COMPLEX a, COMPLEX b ) {
+
+ COMPLEX ans;
+
+ ans.real = a.real * b.real - a.imaginary * b.imaginary;
+ ans.imaginary = a.real * b.imaginary + b.real * a.imaginary;
+
+ return ans;
+}
+
+COMPLEX complex_div ( COMPLEX n, COMPLEX d ) {
+ COMPLEX ans;
+ // find overall divisor
+ //
+ double oad;
+
+ oad = d.real * d.real + d.imaginary * d.imaginary;
+ oad = 1.0/oad;
+ //printf("\noad == %f numerator ",oad);
+ //complex_print (n);
+ //printf("denominator ",oad);
+ //complex_print (d);
+
+
+ d.imaginary = - d.imaginary; // conjugate
+ ans = complex_mul ( n, d );
+ complex_scalar_mul ( oad, &ans);
+
+ //printf("ans ");
+ //complex_print (ans);
+ //printf("\n");
+ return ans;
+}
+
+main () {
+
+ COMPLEX x,x_num,x_den, x_ans_den, x_ans_num, ccc;
+ int i,j,k; // counters
+ double r; // angle in radians
+
+ for (k=0;k<10;k++) { // zero all the Z parameters
+ xz[k] = 0.0;
+ yp[k] = 0.0;
+ }
+
+ // simple lag filter
+ // xz[0] = 0.125;
+ // yp[0] = 1.0;
+ // yp[1] = -0.875;
+ //
+ //
+ //simple 7/8th lag filter squared
+ xz[0] = (0.125*0.125);
+ yp[0] = 1.0;
+ yp[1] = -(2.0*0.875);
+ yp[2] = (0.875*0.875);
+
+ for (i=0;i<NYQUIST;i++) {
+
+ r = (double)i/NYQUIST * PI;
+
+ x.real = cos(r);
+ x.imaginary = sin(r);
+
+ x_ans_num.real = x_ans_num.imaginary = 0.0;
+ x_ans_den.real = x_ans_den.imaginary = 0.0;
+
+ // now take all the z transforms to their powers and multiple by coeffecients
+ // to get the denominator and numerator for the frequency under inspection
+ for (j=0;j<10;j++) {
+
+ x_num = x;
+ complex_pow((double)-j,&x_num);
+ complex_scalar_mul(xz[j],&x_num);
+ complex_add ( &x_ans_num, x_num);
+
+ x_den = x;
+ complex_pow((double)-j,&x_den);
+ complex_scalar_mul(yp[j],&x_den);
+ complex_add ( &x_ans_den, x_den);
+
+ }
+
+ // OK now perform the division to obtain the frequency response
+ //
+ ccc = complex_div ( x_ans_num, x_ans_den) ;
+
+ //ccc = x;
+ //complex_pow(2.0,&ccc);
+ printf(" %d arg = %f mag %f maglog10 %f\n", i, arg(ccc), mag(ccc), log(mag(ccc))*10.0 );
+ }
+
+ //----------------------------------------------------------------------------------------------------------
+ // Test pow and scalar multiply
+ /*
+ x.imaginary = 0.0;
+ x.real = 2.0;
+ complex_pow(3.0,&x);
+ printf(" x.r %f x.i %f\n", x.real, x.imaginary);
+ complex_scalar_mul(2.1,&x);
+ printf(" x.r %f x.i %f\n", x.real, x.imaginary);
+ printf(" after scalar * 2.1 x.r %f x.i %f\n", x.real, x.imaginary);
+
+ x.imaginary = 1.0;
+ x.real = 0.0;
+ complex_pow(3.0,&x);
+ printf(" x.r %f x.i %f\n", x.real, x.imaginary);
+ complex_scalar_mul(-2.1,&x);
+ printf(" after scalar * -2.1 x.r %f x.i %f\n", x.real, x.imaginary);
+ */
+ //----------------------------------------------------------------------------------------------------------
+ //
+ x_ans_num.real = 1.0; x_ans_num.imaginary = 10.0;
+ x_ans_den.real = 2.0; x_ans_den.imaginary = 80.0;
+ x = complex_div ( x_ans_num, x_ans_den );
+ printf(" after divide x.r %f x.i %f\n", x.real, x.imaginary);
+
+
+
+}
+