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COREFIR-AR Datasheet(PDF) 3 Page - Actel Corporation |
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COREFIR-AR Datasheet(HTML) 3 Page - Actel Corporation |
3 / 14 page CoreFIR v3.0 3 FIR Filter Using Distributed Arithmetic Algorithm Distributed Arithmetic Algorithm Overview FIR filters are used in applications that require exact linear phase response. Typical applications for a FIR filter include: image processing, digital audio, digital communication, and biomedical signal processing. A FIR filter is defined in EQ 1: EQ 1 where: c[n] = h[ntaps - n -1] and h is the impulse response. The term ntaps is short for number of taps. In summary, the direct computation for one point of FIR requires: ntaps multiplications + (ntaps-1) additions. Distributed Arithmetic (DA) is a well-known method for eliminating resources in multiply-and-accumulate structures (MACs) implementing digital signal processing (DSP) functions. DA trades memory for combinatory elements, resulting in an efficient implementation in FPGAs. Another feature of DA is its easy serialization of the input, which further reduces the cost of operation when FIR data rate is low compared to the system clock, a common scenario in FIR applications. The input of a FIR can be expressed in the composition of its bits, as shown in EQ 2: EQ 2 where x[n][b] is the bth bit of x[n] and nbits_in is the number of bits of input. The resulting output of the FIR filter is shown in EQ 3: EQ 3 Changing the summation order gives the results shown in EQ 4: EQ 4 Table 2 • Test Configurations Configuration nbits_input nbits_coef ntaps fpga_family coef_fixed 18 16 8 All 1 216 16 16 All 1 312 15 32 All 1 412 15 32 AX, RTAX-S, APA 0 516 15 64 All 1 6 16 16 128 AX, RTAX-S, APA 0 y[n] c[n] x[n] × 0 ntaps 1 – ∑ = xn [] x[n][b]2 b × 0 nbits_in 1 – ∑ = y[n] c[n] 0 ntaps 1 – ∑ x[n] c[n] x[n][b]2 b 0 nbits_in 1 – ∑ 0 ntaps 1 – ∑ == y[n]2 b c[n] x[n][b]2 b T(X[b]) 0 nbits_in 1 – ∑ = 0 ntaps 1 – ∑ 0 nbits_in 1 – ∑ = |
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