This study introduces a readout system for 3He linear position-sensitive detectors (LPSDs), tailored for the Small Angle Neutron Scattering (SANS) spectrometer of the Compact Pulsed Hadron Source (CPHS) at Tsinghua University. Central to this system is the employment of a trapezoidal filter as the primary signal shaper, selected for its enhanced noise filtering capabilities and efficacy in mitigating ballistic deficit. Additionally, the integration of a digital CR filter aims to counteract baseline drift within trigger signals. This innovative architecture underwent validation via computer programs using experimental data, demonstrating superior performance in spatial resolution compared to conventional Gaussian filter-based approaches. Meanwhile, the improvement in spatial resolution comes with a narrower pulse width, promising a higher throughput at high count rates. When applied to a 16-tube detector module, the system achieved an average position resolution of 3.63 mm (FWHM) at the central region and 4.03 mm at the end regions. Furthermore, with a pusle width of 0.6 μs, the 96-tube detector array is promised to sustain a count rate over 1 Mcps.