Digital Filter

In signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is typically an electronic circuit operating on continuous-time analog signals.

A general finite impulse response filter with n stages, each with an independent delay, d_i, and amplification gain, a_i.

A digital filter system usually consists of an analog-to-digital converter (ADC) to sample the input signal, followed by a microprocessor and some peripheral components such as memory to store data and filter coefficients etc. Program Instructions (software) running on the microprocessor implement the digital filter by performing the necessary mathematical operations on the numbers received from the ADC. In some high performance applications, an FPGA or ASIC is used instead of a general purpose microprocessor, or a specialized digital signal processor (DSP) with specific paralleled architecture for expediting operations such as filtering.

Digital filters may be more expensive than an equivalent analog filter due to their increased complexity, but they make practical many designs that are impractical or impossible as analog filters. Digital filters can often be made very high order, and are often finite impulse response filters, which allows for linear phase response. When used in the context of real-time analog systems, digital filters sometimes have problematic latency (the difference in time between the input and the response) due to the associated analog-to-digital and digital-to-analog conversions and anti-aliasing filters, or due to other delays in their implementation.

Digital filters are commonplace and an essential element of everyday electronics such as radios, cellphones, and AV receivers.

Learning Tasks

• (Colors) Consider a color images and convert the image into greyscale. Explain, how color images are stored e.g. as an RGB image and explain how the color information are converted in brightness.
• (Loss of Information) Explain why a filter processes remove specific information and how the loss of information has e.g. an impact on the file size.
• (Audio-Video-Compression) Look at principles for the compression of digital audio and video files. What are the benefits of those compression algorithms? Why is the loss of information acceptable for the eye or ear according to the video and audio signal?

Submodules

• Characterization

See also

• Bessel filter
• Bilinear transform
• Biq­ filter
• Butterworth filter
• Chebyshev filter
• Electronic filter
• Elliptical filter (Cauer filter)
• Filter design
• High-pass filter, Low-pass filter
• Infinite impulse response, Finite impulse response
• Linkwitz–Riley filter
• Matched filter
• Sample (signal)
• Savitzky–Golay filter
• Two-dimensional filter

Further reading

• J. O. Smith III, Introduction to Digital Filters with Audio Applications, Center for Computer Research in Music and Acoustics (CCRMA), Stanford University, September 2007 Edition.
• Mitra, S. K. (1998). Digital Signal Processing: A Computer-Based Approach. New York, NY: McGraw-Hill. https://archive.org/details/digitalsignalpro0000mitr. 
• Oppenheim, A. V.; Schafer, R. W. (1999). Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice-Hall. https://archive.org/details/discretetimesign00alan. 
• Kaiser, J .F. (1974). Nonrecursive Digital Filter Design Using the Io-sinh Window Function. Proc. 1974 IEEE Int. Symp. Circuit Theory. pp. 20–23.
• Bergen, S. W. A.; Antoniou, A. (2005). "Design of Nonrecursive Digital Filters Using the Ultraspherical Window Function". EURASIP Journal on Applied Signal Processing 2005 (12): 1910–1922. doi:10.1155/ASP.2005.1910. 
• Parks, T. W.; McClellan, J. H. (March 1972). "Chebyshev Approximation for Nonrecursive Digital Filters with Linear Phase". IEEE Trans. Circuit Theory CT-19 (2): 189–194. doi:10.1109/TCT.1972.1083419. 
• Rabiner, L. R.; McClellan, J. H.; Parks, T. W. (April 1975). "FIR Digital Filter Design Techniques Using Weighted Chebyshev Approximation". Proc. IEEE 63 (4): 595–610. doi:10.1109/PROC.1975.9794. 
• Deczky, A. G. (October 1972). "Synthesis of Recursive Digital Filters Using the Minimum p-Error Criterion". IEEE Trans. Audio Electroacoustics AU-20 (4): 257–263. doi:10.1109/TAU.1972.1162392. 

Page Information

This page was based on the following Wikipedia source page:

• Digital filter https://en.wikipedia.org/wiki/Digital%20filter
• Date: 5/6/2021 - Source History Wikipedia
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