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1、文献翻译外文：Digital filterIn electronics, computer science and mathematics, 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 anal
2、og filter, which is an electronic circuit operating on continuous-time analog signals. An analog signal may be processed by a digital filter by first being digitized and represented as a sequence of numbers, then manipulated mathematically, and then reconstructed as a new analog signal (see digital
3、signal processing). In an analog filter, the input signal is directly manipulated by the circuit.A digital filter system usually consists of an analog-to-digital converter to sample the input signal, followed by a microprocessor and some peripheral components such as memory to store data and filter
4、coefficients etc. Finally a digital-to-analog converter to complete the output stage. 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 applicat
5、ions, an FPGA or ASIC is used instead of a general purpose microprocessor, or a specialized 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 pr
6、actical many designs that are impractical or impossible as analog filters. Since digital filters use a sampling process and discrete-time processing, they experience latency (the difference in time between the input and the response), which is almost irrelevant in analog filters.Digital filters are
7、commonplace and an essential element of everyday electronics such as radios, cellphones, and stereo receivers.Characterization of digital filtersA digital filter is characterized by its transfer function, or equivalently, its difference equation. Mathematical analysis of the transfer function can de
8、scribe how it will respond to any input. As such, designing a filter consists of developing specifications appropriate to the problem (for example, a second-order low pass filter with a specific cut-off frequency), and then producing a transfer function which meets the specifications.The transfer fu
9、nction for a linear, time-invariant, digital filter can be expressed as a transfer function in the Z-domain; if it is causal, then it has the form: where the order of the filter is the greater of N or M. See Z-transforms LCCD equation for further discussion of this transfer function.This is the form
10、 for a recursive filter with both the inputs (Numerator) and outputs (Denominator), which typically leads to an IIR infinite impulse response behaviour, but if the denominator is made equal to unity i.e. no feedback, then this becomes an FIR or finite impulse response filter.Analysis techniquesA var
11、iety of mathematical techniques may be employed to analyze the behaviour of a given digital filter. Many of these analysis techniques may also be employed in designs, and often form the basis of a filter specification.Typically, one analyzes filters by calculating how the filter will respond to a si
12、mple input such as an impulse response. One can then extend this information to visualize the filters response to more complex signals. Riemann spheres have been used, together with digital video, for this purpose.Impulse responseThe impulse response, often denoted hk or hk, is a measurement of how
13、a filter will respond to the Kronecker delta function. For example, given a difference equation, one would set x0 = 1 and xk = 0 for and evaluate. The impulse response is a characterization of the filters behaviour. Digital filters are typically considered in two categories: infinite impulse respons
14、e (IIR) and finite impulse response (FIR). In the case of linear time-invariant FIR filters, the impulse response is exactly equal to the sequence of filter coefficients: IIR filters on the other hand are recursive, with the output depending on both current and previous inputs as well as previous ou
15、tputs. The general form of the an IIR filter is thus: Plotting the impulse response will reveal how a filter will respond to a sudden, momentary disturbance.Difference equationIn discrete-time systems, the digital filter is often implemented by converting the transfer function to a linear constant-c
16、oefficient difference equation (LCCD) via the Z-transform. The discrete frequency-domain transfer function is written as the ratio of two polynomials. For example: This is expanded: and divided by the highest order of z: The coefficients of the denominator, ak, are the feed-backward coefficients and the coefficients of the numerator are the feed-forward coefficients, bk. The resultant linear difference equation is: or, for the example above:rearranging terms: then
