optmm

Smooth the multiplier matrix using a two dimensional convolution.

Usage

optmm(mflag, a, w)

mflag

selects the method used to modify the multiplier matrix; currently only the method mflag=0 is implemented

a

The multiplier matrix. Each row a[i] contains one linear filter spectrum to be applied to a signal.

w

The smoothing matrix, containg a two dimensional a smoothing function.

Description

• nrow(w) = 2M+1 and nrow(a) >> M
• ncol(w) = 2N+1 and ncol(w) = ncol(a)
• The matrix w contains the weighting function, with the maximum at w[M,N] and which should be symetrical in both dimensions.

w[M-i,N-j]=w[M-i,N+j]=w[M+i,N-j]=w[M+i,N+j]; with: i=1..M, j=1..N

• The smoothed output is computed as follows:

r [ i ] = ∑ j = − M M ∑ k = − N N a [ i + j , N + k ] . w [ M + j , N + k ] {\displaystyle r[i]=\sum _{j=-M}^{M}\sum _{k=-N}^{N}a[i+j,N+k].w[M+j,N+k]} $r[i]=\sum _{j=-M}^{M}\sum _{k=-N}^{N}a[i+j,N+k].w[M+j,N+k]$

with: i=0..nrow(a)-1; a[i+j]=0 if i+j<0 or i+j>=nrow(a)

Result

The vector r with the length nrow(a), containing the smoothed filter spectrum.

See also

hcomb, cvphase, script application MulAc

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