Mean Filter

In single-scale filtering, basis functions are of a fixed resolution and all basis functions have the same localization in the time-frequency domain. For example, frequency domain filtering relies on basis functions localized in frequency but global in time, as shown in Fig. 7b. Other popular filters, such as those based on a windowed Fourier transform, mean filtering, and exponential smoothing, are localized in both time and frequency, but their resolution is fixed, as shown in Fig. 7c. Single-scale filters are linear because the measured data or basis function coefficients are transformed as their linear sum over a time horizon. A finite time horizon results infinite impulse response (FIR) and an infinite time horizon creates infinite impulse response (HR) filters. A linear filter can be represented as... 

For a mean filter with a window width of T, the impulse response is given by... 

ER Davies. The relative effects of median and mean filters on noisy signals. J. Modern Optics, 39 103-113, 1992. 

The mean filter can also be thought of as a convolution of the measured signal with a vector of I constant coefficients, each equals l/I. A schematic diagram of the weights used by a mean filter of length I = 5 is shown in Fig. 3(a). 

Fig. 3 Filter used in (a) mean filtering and (b) exponential smoothing.

Fig. 14 (a) Bumps signal with mean shift and white noise oj varianee 0.5. (h) OLMS filtering using Haar (MSE = 0.1635J, (e) mean filtering (MSE = 0.2530J, (d) exponential smoothing (MSE - 0.2237). 

The principle of pressure filters differs from that of vacuum filters only in the fact that a positive rather than a negative pressure is used to force the filtrate through the filter membrane. On this account, pressures as high as feasible can be attained. Consequently, materials not filterable on vacuum filters may be handled by this means. Filter presses are of three general types those employing both plates and frames, those using recessed plates, and continuous rotary pressure filters. 

Since the main function of any filter is the removal and separation of impurities, and the filters are rated in many different ways, it is inevitable that many tests are available to substantiate these ratings. The tests include the bubble point test used to establish the mean filter rating and the multi-pass test which provides the beta ratio of the hydraulic and lubrication filters. 

One possibility is temporal averaging where several pictures of the same area are taken at different times. Hence the investigated flow has to be time independent. Another possibility to decrease the deviation of the hue values is local filtering of the image. Common filters for this purpose are mean filter, Gaussian filter, and median filters. Note that filtering always leads to loss of resolution. 

In image processing, local filtering is used to increase the quality of an image. As a desired result, the image is smoothed and noise is removed. T3q)ical local filters are mean filter, low-pass filter, Gaussian filter, and median filter. Local averaging causes loss of spatial information. 

Where successful cake filtration is obtained, the medium resistance will generally be a low percentage (< 10%) of the mean filter cake resistance. Another way of eTqiressing this principle is that the medium should represent an extra equivalent cake thickness in the range 0.02 < I. < 0.15. 

A special case was concerned with measurement of uranium aerosols generated when DU munitions penetrate armored vehicles (Parkhurst 2003). In this study, DU penetrators were fired at a tank and another armored vehicle and the aerosols were collected by different means (filter cassettes, cascade impactors, five-stage cyclone, and a moving filter). Wipe samples were also collected from surfaces and deposition trays. Analysis included particle size distribution, morphology, uranium oxide phases, and dissolution in vitro. The uranium mass was determined by different methods radioanalytical beta spectrometry for some filters and ICPMS, ICP-AES, and KPA for other samples. 

Seismic ground motions may be modeled as a zero-mean filtered Gaussian shot-noise random process with a Kanai-Tajimi spectrum... 

A mean filter rating is a measurement of the mean pore size of a filter element. It is far more meaningful than a nominal filter rating, and, in the case of filter elements... 

---