## SVD noise reduction (SVDNR)

Purpose

Description

Macro Synopsis

Modules

Related Functions

References

### Purpose

Noise reduction by singular value decomposition in phase space

### Description

This function performs noise reduction by singular value decomposition of local sets of state vectors in phase space and projection of the state vectors onto the submanifold of the principal components.

Parameters are:
- delay
`tau` (no. of samples) for phase space reconstruction,
- embedding dimension m,
- dimension
`md` of the manifold onto which the state vectors are to be projected,
- minimum number M of neighbors of a point in the embedding space used for the singlular value decomposition,
- minimum relative radius r of phase space environments, which will be increased automatically if the initial neighbourhood contains less neighbours than specified in M,
- the precision (iteration) p, either
- a "Single loop" (0), where the neighbourhoods and centre of mass for the neighbourhood of each point in the embedding space are computed, or
- a "Double loop" (1), where the centres of mass are corrected additionally.

Note that since this function operates on a 'pure' time series, the scale and the shift of the given signal do not affect the result.

### Macro Synopsis

`y = SVDNR(x,tau,m,md,M,r,p);`

signal x,y;

int tau,m,md,M;

float r;

option p;

### Modules

Nonlinear

### Related Functions

Median filter, Schreiber noise reduction.

### References

Grassberger et al. [58], [59]