Digital filters difference equations

If you ve had enough of digital filters, difference equations, the z-plane, and all that for now, you can skip the next sections and go on to Chapter 4. However, if you just can t get enough of this stuff, read on for some notes about implementing digital filters. 

The first-order digital filter is the simplest filter and its input-output relationship is described by a first-order linear difference equation,... 

The most general digital filter operates on both its inputs and outputs, and its difference equation is written ... 

Digital LTI Filters are often described in terms of their time domain difference equation, which relates input samples to output samples. The finite impulse response or FIR filter has the difference equation ... 

A digital filter with impulse response having infinite length is called an infinite impulse response (HR) filter. An important class of HR filters can be described by the difference equation... 

Then, a moving difference digital filter (equation 3) was applied to the time series of the relative ehanges of RinP/o. 

Figure 2 shows that the frequency ache is normalized. For the comparison of the results must be considered that 71=1 . To compare the practical results with theoretical values, different sinus signals with different frequencies are conveyed over the digital filter on the board. Consequently the attenuation of the signals on the output is measured. The logarithm output attenuation is given with the following equation. 

For solution by digital simulation, the depth of filter cake is divided into nine segments, each of which has an equivalent dimensionless thickness Ax. For any element n, the form of the resulting difference differential equation is given by... 

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