# Packages

• package

High level Smile operators in Scala.

High level Smile operators in Scala.

Definition Classes
root
• package
Definition Classes
root
• package

A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero.

A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero. Like the fast Fourier transform (FFT), the discrete wavelet transform (DWT) is a fast, linear operation that operates on a data vector whose length is an integer power of 2, transforming it into a numerically different vector of the same length. The wavelet transform is invertible and in fact orthogonal. Both FFT and DWT can be viewed as a rotation in function space.

Definition Classes
smile
• Operators
t

# Operators 

#### trait Operators extends AnyRef

Discrete wavelet transform (DWT).

Linear Supertypes
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### Value Members

1. final def !=(arg0: Any): Boolean
Definition Classes
AnyRef → Any
2. final def ##(): Int
Definition Classes
AnyRef → Any
3. def +(other: String): String
Implicit
This member is added by an implicit conversion from Operators to any2stringadd[Operators] performed by method any2stringadd in scala.Predef.
Definition Classes
4. def ->[B](y: B): (Operators, B)
Implicit
This member is added by an implicit conversion from Operators to ArrowAssoc[Operators] performed by method ArrowAssoc in scala.Predef.
Definition Classes
ArrowAssoc
Annotations
@inline()
5. final def ==(arg0: Any): Boolean
Definition Classes
AnyRef → Any
6. final def asInstanceOf[T0]: T0
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Any
7. def clone(): AnyRef
Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
8. def dwt(t: Array[Double], filter: String): Unit

Discrete wavelet transform.

Discrete wavelet transform.

t

the time series array. The size should be a power of 2. For time series of size no power of 2, 0 padding can be applied.

filter

wavelet filter.

9. def ensuring(cond: (Operators) ⇒ Boolean, msg: ⇒ Any)
Implicit
This member is added by an implicit conversion from Operators to Ensuring[Operators] performed by method Ensuring in scala.Predef.
Definition Classes
Ensuring
10. def ensuring(cond: (Operators) ⇒ Boolean)
Implicit
This member is added by an implicit conversion from Operators to Ensuring[Operators] performed by method Ensuring in scala.Predef.
Definition Classes
Ensuring
11. def ensuring(cond: Boolean, msg: ⇒ Any)
Implicit
This member is added by an implicit conversion from Operators to Ensuring[Operators] performed by method Ensuring in scala.Predef.
Definition Classes
Ensuring
12. def ensuring(cond: Boolean)
Implicit
This member is added by an implicit conversion from Operators to Ensuring[Operators] performed by method Ensuring in scala.Predef.
Definition Classes
Ensuring
13. final def eq(arg0: AnyRef): Boolean
Definition Classes
AnyRef
14. def equals(arg0: Any): Boolean
Definition Classes
AnyRef → Any
15. def finalize(): Unit
Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
16. def formatted(fmtstr: String): String
Implicit
This member is added by an implicit conversion from Operators to StringFormat[Operators] performed by method StringFormat in scala.Predef.
Definition Classes
StringFormat
Annotations
@inline()
17. final def getClass(): Class[_]
Definition Classes
AnyRef → Any
18. def hashCode(): Int
Definition Classes
AnyRef → Any
19. def idwt(wt: Array[Double], filter: String): Unit

Inverse discrete wavelet transform.

Inverse discrete wavelet transform.

wt

the wavelet coefficients. The size should be a power of 2. For time series of size no power of 2, 0 padding can be applied.

filter

wavelet filter.

20. final def isInstanceOf[T0]: Boolean
Definition Classes
Any
21. final def ne(arg0: AnyRef): Boolean
Definition Classes
AnyRef
22. final def notify(): Unit
Definition Classes
AnyRef
23. final def notifyAll(): Unit
Definition Classes
AnyRef
24. final def synchronized[T0](arg0: ⇒ T0): T0
Definition Classes
AnyRef
25. def toString(): String
Definition Classes
AnyRef → Any
26. final def wait(): Unit
Definition Classes
AnyRef
Annotations
@throws( ... )
27. final def wait(arg0: Long, arg1: Int): Unit
Definition Classes
AnyRef
Annotations
@throws( ... )
28. final def wait(arg0: Long): Unit
Definition Classes
AnyRef
Annotations
@throws( ... )
29. def wavelet(filter: String): Wavelet

Returns the wavelet filter.

Returns the wavelet filter. The filter name is derived from one of four classes of wavelet transform filters: Daubechies, Least Asymetric, Best Localized and Coiflet. The prefixes for filters of these classes are d, la, bl and c, respectively. Following the prefix, the filter name consists of an integer indicating length. Supported lengths are as follows:

Daubechies 4,6,8,10,12,14,16,18,20.

Least Asymetric 8,10,12,14,16,18,20.

Best Localized 14,18,20.

Coiflet 6,12,18,24,30.

Additionally "haar" is supported for Haar wavelet.

Besides, "d4", the simplest and most localized wavelet, uses a different centering method from other Daubechies wavelet.

filter

filter name

30. def wsdenoise(t: Array[Double], filter: String, soft: Boolean = false): Unit

The wavelet shrinkage is a signal denoising technique based on the idea of thresholding the wavelet coefficients.

The wavelet shrinkage is a signal denoising technique based on the idea of thresholding the wavelet coefficients. Wavelet coefficients having small absolute value are considered to encode mostly noise and very fine details of the signal. In contrast, the important information is encoded by the coefficients having large absolute value. Removing the small absolute value coefficients and then reconstructing the signal should produce signal with lesser amount of noise. The wavelet shrinkage approach can be summarized as follows:

• Apply the wavelet transform to the signal.
• Estimate a threshold value.
• The so-called hard thresholding method zeros the coefficients that are smaller than the threshold and leaves the other ones unchanged. In contrast, the soft thresholding scales the remaining coefficients in order to form a continuous distribution of the coefficients centered on zero.
• Reconstruct the signal (apply the inverse wavelet transform).

The biggest challenge in the wavelet shrinkage approach is finding an appropriate threshold value. In this method, we use the universal threshold T = σ sqrt(2*log(N)), where N is the length of time series and σ is the estimate of standard deviation of the noise by the so-called scaled median absolute deviation (MAD) computed from the high-pass wavelet coefficients of the first level of the transform.

t

the time series array. The size should be a power of 2. For time series of size no power of 2, 0 padding can be applied.

filter

the wavelet filter to transform the time series.

soft

true if apply soft thresholding.

31. def [B](y: B): (Operators, B)
Implicit
This member is added by an implicit conversion from Operators to ArrowAssoc[Operators] performed by method ArrowAssoc in scala.Predef.
Definition Classes
ArrowAssoc