Math

Data Structures
struct	complex
	a complex number has a real and imaginary part More...

Macros
#define	PI   3.14159265358979323846264338327950288
	PI is ratio of circumference to diameter of a circle.

Typedefs
typedef struct complex	complex_t

Functions
void	fft (complex_t *v, int n, complex_t *tmp)
	fft More...
void	ifft (complex_t *v, int n, complex_t *tmp)
	Inverse fft. More...
int16_t	fixed_sin (int32_t theta)
	decimal fixed-point sin More...
int16_t	fixed_cos (int32_t theta)
	decimal fixed-point cos More...
int32_t	fixed_sin2 (int32_t theta)
	binary fixed-point sin More...
int32_t	fixed_cos2 (int32_t theta)
	binary fixed-point cos More...
int32_t	sin540 (int32_t theta)
	binary fixed-point sin More...
int32_t	cos540 (int32_t theta)
	binary fixed-point cos More...

Variables
float	Real
float	Imag

Detailed Description

Function Documentation

cos540()

int32_t cos540

(

int32_t

theta

)

binary fixed-point cos

binaryfixed-point cos****************

Parameters

theta

0 to 539, angle is in units 2*pi/540 = 0.011635528 radians (0 to 2pi)

Returns

-65536 to +65536, fixed point resolution 1/65536

Note

input theta=4096 means 90 degrees (pi/2 radians)

fft()

void fft	(	complex_t *	v,
		int	n,
		complex_t *	tmp
	)

fft

discrete Fast Fourier Transform, Converts time to frequency domain
Assume the input is real data sampled at fs
Place n measurements into the real part of array v
Set the imaginary part of array v to 0
Call fft() and the results are returned back in array v
If the input is real only, then the transform will contain
Index 0 <= k < n/2 complex components of frequency f=k/fs
E.g., k=0 represents the DC component of the input
Index n/2 <= k < n are complex conjugates of the first half

Parameters

v	array of input data in complex form
n	size of the two arrays 2, 4, 8, ..., 2048
tmp	temporary array of data in complex form

Returns

none

Note

n is a power of two from 2 to 2048

fixed_cos()

int16_t fixed_cos

(

int32_t

theta

)

decimal fixed-point cos

decimal fixed-point cos****************

Parameters

theta

-3142 to 3142, angle is in units radians/1000

Returns

-10000 to +10000, fixed point resolution 1/10000

Note

input theta=-1571 means 90 degrees (pi/2 radians)

fixed_cos2()

int32_t fixed_cos2

(

int32_t

theta

)

binary fixed-point cos

binaryfixed-point cos****************

Parameters

theta

-8192 to 8191, angle is in units 2*pi/16384 radians (-pi to +pi)

Returns

-65536 to +65536, fixed point resolution 1/65536

Note

input theta=4096 means 90 degrees (pi/2 radians)

fixed_sin()

int16_t fixed_sin

(

int32_t

theta

)

decimal fixed-point sin

decimal fixed-point sin****************

Parameters

theta

-3142 to 3142, angle is in units radians/1000

Returns

-10000 to +10000, fixed point resolution 1/10000

Note

input theta=1571 means 90 degrees (pi/2 radians)

fixed_sin2()

int32_t fixed_sin2

(

int32_t

theta

)

binary fixed-point sin

binary fixed-point sin****************

Parameters

theta

-8192 to 8191, angle is in units 2*pi/16384 radians (-pi to +pi)

Returns

-65536 to +65536, fixed point resolution 1/65536

Note

input theta=-4096 means -90 degrees (pi/2 radians)

ifft()

void ifft	(	complex_t *	v,
		int	n,
		complex_t *	tmp
	)

Inverse fft.

discrete Inverse Fast Fourier Transform, Converts frequency to time domain
Assume the input is complex data with components k=0 to n-1
Index 0 <= k < n-1 complex components of frequency f=k/fs
E.g., k=0 represents the DC component of the input
Place n complex values into the array v
Typically the index n/2 <= k < n are complex conjugates of the first half
Call ifft() and the results are returned back in array v
If the input is real only, then the transform will contain

Parameters

v	array of input data in complex form
n	size of the two arrays 2, 4, 8, ..., 2048
tmp	temporary array of data in complex form

Returns

none

Note

n is a power of two from 2 to 2048

sin540()

int32_t sin540

(

int32_t

theta

)

binary fixed-point sin

binary fixed-point sin****************
e.g., 359.3degrees (2pi radians) theta=539 sin540(539) = -763 (-0.0116)
e.g., 270 degrees (3pi/4 radians) theta=405 sin540(405) = -65536 (-1)
e.g., 180 degrees (pi radians) theta=270 sin540(270) = 0 (0)
e.g., 90 degrees (pi/2 radians) theta=135 sin540(135) = 65536 (+1)
e.g., 45 degrees (pi/4 radians) theta= 67 sin540(67) = 46071 (sqrt(2)/2)
e.g., 0 degrees (0 radians) theta= 0 sin540(0) = 0 (0)

Parameters

theta

0 to 539, angle is in units 2*pi/540 = 0.011635528 radians (0 to 2pi)

Returns

-65536 to +65536, fixed point resolution 1/65536