Digital filter
In
electronics, a digital filter is any
electronic filter that works by performing digital mathematical operations on an intermediate form of a signal. This is in contrast to older analog filters which work entirely in the analog realm and must rely on physical networks of electronic components to achieve the desired filtering effect.
Digital filters can achieve virtually any filtering effect that can be expressed as a mathematical function or
algorithm. The two primary limitations of digital filters are their
speed , and their
cost. However as the cost of
integrated circuits has continued to drop over time, digital filters have become increasingly commonplace and are now an essential element of many everyday objects such as
radios,
cellphones, and
stereo receivers.
Encyclopedia
In
electronics, a
digital filter is any
electronic filter that works by performing digital mathematical operations on an intermediate form of a signal. This is in contrast to older analog filters which work entirely in the analog realm and must rely on physical networks of electronic components to achieve the desired filtering effect.
Digital filters can achieve virtually any filtering effect that can be expressed as a mathematical function or
algorithm. The two primary limitations of digital filters are their
speed , and their
cost. However as the cost of
integrated circuits has continued to drop over time, digital filters have become increasingly commonplace and are now an essential element of many everyday objects such as
radios,
cellphones, and
stereo receivers.
Digital filter advantages
Digital filters can easily realise performance characterisics far beyond what are possible with analog filters. It is not particularly difficult, for example, to create a 1000Hz
low-pass filter which can achieve near-perfect transmission of a 999Hz input while entirely blocking a 1001Hz signal. Analog filters cannot discriminate between such closely spaced signals.
Also, for complex multi-stage filtering operations, digital filters have the potential to attain much better
signal to noise ratios than analog filters. This is because whereas at each intermediate stage the analog filter adds more noise to the signal, the digital filter performs noiseless mathematical operations at each intermediate step in the transform. The primary source of noise in a digital filter is to be found in the initial AtoD - analog to digital conversion step, where in addition to any circuit noise introduced, the signal is subject to an unavoidable quantization error which is due to the finite resolution of the digital representation of the signal.
Note also that digital filters will become confounded if presented with an input signal which contains any substantial subcomponent with a frequency exceeding half the sampling rate of the filter . Thus a small
anti-aliasing filter is always placed ahead of the analog to digital conversion circuitry to prevent these high-frequency components from interfering with the sampling.
Types of digital filters
Many digital filters are based on the Fast Fourier transform, a mathematical algorithm that quickly extracts the
frequency spectrum of a signal, allowing the spectrum to be manipulated before converting the modified spectrum back into a time-series signal.
Another form of a typical linear digital filter, expressed as a transform in the Z-domain, is
where
M is the order of the filter.
See Z-transform#LCCD equation for further discussion of this transfer function.This form is for an
infinite impulse response filter, but if the
denominator is unity then this is the form for a
finite impulse response filter.
Another form of a digital filter is that of a state space model.
A well used state-space filter is the
Kalman filter published by
Rudolf Kalman in 1960.
References
- A. Antoniou, Digital Filters: Analysis, Design, and Applications, New York, NY: McGraw-Hill, 1993.
- S.K. Mitra, Digital Signal Processing: A Computer-Based Approach, New York, NY: McGraw-Hill, 1998.
- A.V. Oppenheim and R.W. Schafer, Discrete-Time Signal Processing, Upper Saddle River, NJ: Prentice-Hall, 1999.
- J.F. Kaiser, Nonrecursive Digital Filter Design Using the Io-sinh Window Function, Proc. 1974 IEEE Int. Symp. Circuit Theory, pp. 20-23, 1974.
- S.W.A. Bergen and A. Antoniou, Design of Nonrecursive Digital Filters Using the Ultraspherical Window Function, EURASIP Journal on Applied Signal Processing, vol. 2005, no. 12, pp. 1910-1922, 2005.
- T.W. Parks and J.H. McClellan, Chebyshev Approximation for Nonrecursive Digital Filters with Linear Phase, IEEE Trans. Circuit Theory, vol. CT-19, pp. 189-194, Mar. 1972.
- L. R. Rabiner, J.H. McClellan, and T.W. Parks, FIR Digital Filter Design Techniques Using Weighted Chebyshev Approximation, Proc. IEEE, vol. 63, pp. 595-610, Apr. 1975.
- A.G. Deczky, Synthesis of Recursive Digital Filters Using the Minimum p-Error Criterion, IEEE Trans. Audio Electroacoust., vol. AU-20, pp. 257-263, Oct. 1972.
See also
External links
- – Free filter design software
- – Free filter design software
- - Floating and fixed-point design with LabVIEW or ANSI C autocode generation
