# digital filter

(redirected from Digital filters)

## digital filter

[′dij·əd·əl ′fil·tər]
(electronics)
An electrical filter that responds to an input which has been quantified, usually as pulses.

## Digital filter

Any digital computing means that accepts as its input a set of one or more digital signals from which it generates as its output a second set of digital signals. While being strictly correct, this definition is too broad to be of any practical use, but it does demonstrate the possible extent of application of digital-filter concepts and terminology.

#### Capabilities

Digital filters can be used in any signal-manipulating application where analog or continuous filters can be used. Because of their utterly predictable performance, they can be used in exacting applications where analog filters fail because of time- or other parameter-dependent coefficient drift in continuous systems. Because of the ease and precision of setting the filter coefficients, adaptive and learning digital filters are comparatively simple and particularly effective to implement. As digital technology becomes more ubiquitous, digital filters are increasingly acknowledged as the most versatile and cost-effective solutions to filtering problems.

The number of functions that can be performed by a digital filter far exceeds that which can be performed by an analog, or continuous, filter. By controlling the accuracy of the calculations within the filter (that is, the arithmetic word length), it is possible to produce filters whose performance comes arbitrarily close to the performance expected of the perfect models. For example, theoretical designs that require perfect cancellation can be implemented with great fidelity by digital filters.

#### Linear difference equation

The digital filter accepts as its input signals numerical values called input samples and produces as its output signal numerical values called output samples. Each output sample at any particular sampling instant is a weighted sum of present and past input samples, and past output samples. If the sequence of input samples is xn, xn+1, xn+2, …, then the corresponding sequence of output samples would be yn, yn+1, yn+2,….

From this simple time-domain expression, a considerable number of definitions can be constructed. If the filter coefficients (the a's and the b's) are independent of the x's and y's, this digital filter is a linear filter. If the a's and b's are fixed, this is a linear time-invariant (LTI) filter. The order of the filter is given by the largest of the subscripts among the a's and b's, that is, the larger of M and N. If the b's are all zero (that is, if the output is the weighted sum of present and past input samples only), the digital filter is referred to as a nonrecursive (having no feedback) or finite impulse response (FIR) filter because the response of the filter to an impulse (actually a unit pulse) input is simply the sequence of the “a” coefficients. If any value of b is nonzero, the filter is recursive (having feedback) and is generally an infinite impulse response (IIR) filter.

If the digital filter under consideration is not a linear, time-invariant filter, the transfer function cannot be used.

#### Transfer functions

Although the time-domain difference equation is a useful description of a filter, as in the continuous-domain filter case, a powerful alternative form is the transfer function. The information content of the transfer function is the same as that of the difference equation as long as a linear, time-invariant system is under consideration. A difference equation is converted to transfer-function form by use of the z transform. The z transform is simply the Laplace transform adapted for sampled systems with some shorthand notation introduced.

So far only LTI filters have been discussed. An important class of variable-parameter filter change their coefficients to minimize an error criterion. These filters are called adaptive because they adapt their parameters in response to changes in the operating environment. An example is an FIR digital filter whose coefficients are continually adjusted so that the output will track a reference signal with minimum error. The performance criterion will be the minimization of some function of the error.

References in periodicals archive ?
The LTC2500-32 is a new and enabling approach for precision measurement applications, blending the high accuracy and speed of Linear Technology's proprietary SAR ADC architecture with flexible integrated digital filters to optimize system signal bandwidth and ease analog antialiasing filter requirements.
A method for improving the efficiency of digital filters using filter sharpening technique has been presented in [1].
Another possible approach is to adapt this structure for different types of digital filters like band-pass and high-pass.
Finally, "IET Signal Processing" will cover advances in single and multidimensional, linear and non-linear digital filters and filter banks, signal transformation techniques, spectral analysis, system modeling, the application of chaos theory, and neural network-based approaches to signal processing.
Which choice of analog or one of various digital filters you make depends upon your application, sampling requirements, and the type of signal you're measuring.
Methods used to convert lowpass FIB filter designs to bandpass and highpass digital filters are discussed and the Remez Exchange FIR filter design technique is described.
The book is not an exposition on digital signal processing (DSP) but rather a treatise on digital filters.
Milic (University of Belgrade) introduces digital filters in which the sampling rate of the input signal is changed in one or more intermediate points.
Using libraries and filter design tools, digital filters can replace analog filters to reduce noise.
Adaptive line enhancers are different from fixed digital filters because they can adjust their own impulse response.
The new solution, available free through a software "Component Pack" upgrade from Cypress, enables designers to quickly and easily design and customize digital filters with higher performance than any MCU solution.

Site: Follow: Share:
Open / Close