Sites:

## 10.5 Constrained Deconvolution

Another concept of restoration is represented by constrained deconvolution. This method does not impose the requirement of minimising estimation errors but only requests that the original noise power in the restored signal be preserved. It comes from the general tendency of deconvolution methods to lead to a substantial degradation in signal-to-noise ratio and therefore it seeks an approximate approach which would correct the convolution distortion without increasing the noise level.

The method uses the notion of a discrete model of deterioration consisting in distortion caused by a discrete linear system with a finite impulse response { h n}, n = 0, 1, , J - 1, and additive noise { ? n},

 (10.47)

For a finite section { x n} of the input signal, M samples long, obviously n ÃŽ ?0, M + J - 2 ?, i ÃŽ ?0, M - 1 ?. The model equation can then be rewritten into vector form

 (10.48)

where the nonzero elements of the matrix are H n,i = h n - i, ( n - i) ÃŽ ?0, J - 1 ? so that it is a circulant matrix. The noise energy of the observed signal, that is before restoration, is

 (10.49)

If the noise is centred, its energy is given by the variance,

We shall define the residuum r as being the difference vector dependent...

##### Products & Services
Thermocouple Temperature Transmitters
Thermocouple temperature transmitters convert the small millivolt output of a thermocouple to a current signal (typically 4-20 mADC) that is immune to noise and voltage drops over a long distance.
Audio Analyzers
Audio analyzers measure the noise and audio spectrum of output from an amplifier or a stereo.
Noise Figure Meters
RF noise figure meters measure the noise contribution of an amplifier relative to a noise-free amplifier at a reference temperature. Usually expressed in dB for Ku-band amplifiers.
Frame Grabbers
Frame grabbers are image processing computer boards that capture and store image data for industrial applications such as quality control.
Audio Processor ICs
Audio processors IC are semiconductor devices used to detect, decode and process analog or digital audio.

##### Topics of Interest

10.6 Deconvolution via Impulse-Response Optimisation Another approach to deconvolution is represented by the method of optimising the shape of a specially defined impulse response. It is based on...

10.2 Plain Deconvolution and Pseudo-Inversion As far as the influence of the linear system (distortion) prevails in the deterioration according to models (10.1) or (10.2), the purpose of restoration...

10.7 Generalised Discrete Mean-Square-Error Minimisation The method that we shall introduce in this section is, in a sense a generalisation of Wiener filtering. The concept assumes that both the...

15.1 Useful Matrix Types A Toeplitz matrix A from a sequence a = [ a ? N +1, , a M ?1] of length M + N ? 1 is an M N matrix where A i, j = a i ? j, i = 0, , M ? 1, j = 0, , N ? 1, in...

10.8 Other Approaches to Signal Restoration We shall briefly mention two other approaches to restoration. The first of these is the method of maximum a posteriori probability (MAP). The concept of...

Product Announcements
Acromag, Inc.
Pyromation, Inc.
Conax Technologies