Digital filters - Computable efficient recursive filters

Abstract: In signal processing, the most widely used digital filter type is the Finite Impulse Response(FIR), mainly for its guaranteed stability. However, these filters requiring a higher order forthe same specification compared with its recursive correspondence, the Infinite ImpulseResponse (IIR) filter. The order can be seen as required number of adders, multipliers andmemory for the filter. In Application Specific Integrated Circuits (ASIC) and FieldProgrammable Gate Arrays (FPGA) applications, especially number of multipliers isdesirable to keep low due the extensive logic. Hence, signal processing with FIR filters willresult in a large amount of silicon or gates used. This thesis proposes two recursive filters, theCascaded Integrator Comb- (CIC) filter and the Wave Digital Filter (WDF), where the formeris used mainly for interpolation- or decimation. The CIC is a recursive moving average filterwhich is multiplier free, consisting only of two building blocks and has a linear phase. TheWDFs simulates an analog lossless network, such as the ladder- or the lattice structure byusing the bilinear transform and voltage waves as signal parameters. For fair comparison ofthe filters, methods for estimating the hardware cost are developed. A FIR halfband filter isalso included and may be seen as a reference in both hardware cost and performance. Forcomparing performance Error Vector Magnitude (EVM) and Adjacent Channel LeakageRatio is used, according the method described in 3GPP (3rd Generation Partnership Project).Moreover, interpolation and decimation is handled in a mathematical way to show theimportance of using good lowpass filters in multirate systems.