analysis: Compute the Analysis Operator for a Graph Signal

View source: R/analysis.R

analysisR Documentation

Compute the Analysis Operator for a Graph Signal


analysis computes the transform coefficients of a given graph signal using the provided frame coefficients.


analysis(y, tf)



Numeric vector or matrix representing the graph signal to analyze.


Numeric matrix of frame coefficients.


The analysis operator uses the frame coefficients to transform a given graph signal into its representation in the transform domain. It is defined by the linear map T_{\mathfrak F} : \mathbb R^V \rightarrow \mathbb R^I. Given a function f \in \mathbb R^V, the analysis operation is defined as:

T_{\mathfrak F}f=(\langle f,r_i \rangle)_{i \in I}

where r_i are the frame coefficients.

The transform is computed as:

coef = tf \times y


coef Numeric vector or matrix of transform coefficients of the graph signal.

See Also

synthesis, tight_frame


## Not run: 
# Extract the adjacency matrix from the grid1 and compute the Laplacian
L <- laplacian_mat(grid1$sA)

# Compute the spectral decomposition of L
decomp <- eigensort(L)

# Generate the tight frame coefficients using the tight_frame function
tf <- tight_frame(decomp$evalues, decomp$evectors)

# Create a random graph signal.
f <- rnorm(nrow(L))

# Compute the transform coefficients using the analysis operator
coef <- analysis(f, tf)

## End(Not run)

gasper documentation built on Oct. 27, 2023, 1:07 a.m.