Spectral Signal Processing Suite
v1.0

## signal.lib Class chebyshevPolynomial

```java.lang.Object
|
+--signal.lib.chebyshevPolynomial
```

public final class chebyshevPolynomial
extends java.lang.Object

Implements methods associated with the Chebyshev Polynomials, Tk(x).

 Constructor Summary `chebyshevPolynomial()`

 Method Summary `static void` ```chebyCoef(double[] u, double[] ak, int N)```           Given discrete function values u, the method returns the first N+1 discrete Chebyshev coefficients, ak `static double` ```chebySeries(double[] coef, double x)```           Evaluates the Chebyshev partial sum u += aN[k]*T(x,k) by Clenshaw's recurrence relation `static double` ```CJ(int m, int N)```           weights and normalizing factors, 1/Cj `static double` ```T(double x, double N)```           Returns the Chebyshev Polynomial of degree N `static double` ```Tp(double x, double N)```           Returns the derivative of the Chebyshev Polynomial of degree N `static double` ```xGL(int i, int N)```           Returns CGL points in the order order order -1,...,1 `static double` ```xGLr(int i, int N)```           Returns CGL points in the order order 1,...,-1

 Methods inherited from class java.lang.Object `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

 Constructor Detail

### chebyshevPolynomial

`public chebyshevPolynomial()`
 Method Detail

### xGLr

```public static double xGLr(int i,
int N)```
Returns CGL points in the order order 1,...,-1

### xGL

```public static double xGL(int i,
int N)```
Returns CGL points in the order order order -1,...,1

### CJ

```public static double CJ(int m,
int N)```
weights and normalizing factors, 1/Cj

### T

```public static double T(double x,
double N)```
Returns the Chebyshev Polynomial of degree N

### Tp

```public static double Tp(double x,
double N)```
Returns the derivative of the Chebyshev Polynomial of degree N

### chebyCoef

```public static final void chebyCoef(double[] u,
double[] ak,
int N)```
Given discrete function values u, the method returns the first N+1 discrete Chebyshev coefficients, ak

### chebySeries

```public static double chebySeries(double[] coef,
double x)```
Evaluates the Chebyshev partial sum u += aN[k]*T(x,k) by Clenshaw's recurrence relation

Spectral Signal Processing Suite
v1.0