Modern vector processors support a wide variety of instructions for fixed-point digital signal processing. These instructions support a proliferation of rounding, saturating, and type conversion modes, and are often fused combinations of more primitive operations. While these are common idioms in fixed-point signal processing, it is difficult to use these operations in portable code. It is challenging for programmers to write down portable integer arithmetic in a C-like language that corresponds exactly to one of these instructions, and even more challenging for compilers to recognize when the instructions can be used. Our system, Pitchfork, defines a portable fixed-point intermediate representation, FPIR, that captures these idioms. FPIR can be used directly by programmers experienced with fixed-point, or Pitchfork can automatically lift from integer operations into FPIR using a term-rewriting system (TRS) composed of verified manual and automatically-synthesized rules. Pitchfork then lowers from FPIR into target-specific fixed-point instructions using a set of target-specific TRSs. We show that this approach improves run-time performance of portably-written fixed-point signal processing code in Halide, across a range of benchmarks, by geomean 1.31x on x86 with AVX2, 1.82x on ARM Neon, and 2.46x on Hexagon HVX compared to a standard LLVM-based compiler flow, while maintaining or improving existing compile times.