Digital Filters

Digital filters use digital signal processing (DSP) to perform numerical calculations on sampled values of a signal. They are used to separate signals that have been combined, and to restore signals that have been distorted. Signal separation is required to remove contamination from noise, interference, or other signals. Signal restoration is needed when a signal such as an audio recording or digital image has been distorted. Although low-cost analog filters can be used for these same tasks, digital filters provide far better performance. Whereas analog filters target the limitations of the electronics, digital filters emphasize the limitations of the signals themselves.

Digital filters have an impulse response, a step response and a frequency response. Each of these responses contains complete information about the digital filter, but in different form. The input response is the output of a system when the input is an impulse. The step response is the output of a system when the input is a step or edge (edge response). Because the step is the integral of the impulse, the step response is the integral of the impulse response. The frequency response can be found by using the fast Fourier transform (FFT) algorithm to take the discrete Fourier transform (DFT) of the impulse response.

There are three basic types of digital filters: time domain, frequency domain, and custom. Time domain filters are used when the shape of the signal’s waveform encodes the data. Digital filters with time domain filtering are used in applications such as direct current (DC) removal, smoothing, and waveform shaping. Frequency domain filters are used the information is encoded in the amplitude, phase, and frequency of the sinusoids. Digital filters with frequency domain filtering are designed to separate one band of frequencies from another. Custom filtering is used when a response (such as convolution) is required instead of high-pass, low-pass, band-pass or band-reject.

Filter frequency response is an important specification to consider when selecting digital filters. Choices include Bessel, Butterworth, Cauer, Chebyshev, and linear phase. Bessel filters have a relatively flat passband and slow roll-off. The stopband is fairly monotonic or ripple-free. Butterworth filters are digital filters that provide a very flat response and almost no attenuation in the passband. The roll-off rate is somewhat slower than other filters. Cauer filters or elliptic filters provide the fastest roll-off for a given order (number of poles). Typically, the pass band and stop band have ripples. Chebyshev filters provide a very fast roll-off, but at the expense of a rippled pass band. Linear phase response filters preserve the phase characteristics of a signal by time-delaying the signal components equally.

• Implementing IIR Digital Filters
  This application note describes the implementation of various digital filters using the PIC17C42, the first member of Microchip?s 2nd generation of 8-bit microcontrollers. The PIC17C42 is a very high...
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• What are Digital Filters?
  Digital filters that incorporate digital-signal-processing (DSP) techniques have received a great deal of attention in technical literature in recent years. Although they rarely serve as anti-aliasing...
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• Digital Filters Design for Signal and Image Processing
  Digital Filters Design for Signal and Image Processing Providing a preliminary step for the analog-to-digital filter conversion, this manual addresses the theoretical background for z-transform,...
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Part Numbers for Digital Filters