Peripheral nerve interfaces are designed to record neural activity from residual nerves in amputees. Reliable detection of neural events from these recordings dictate the performance of neuroprosthetic device control. Extraction of neural events from peripheral nerve recordings is challenging because of low signal to noise ratio (SNR), sparse spiking pattern and the presence of electromyographic signal contamination from the surrounding muscles. In this study, we developed a spike detection algorithm based on Short-time Fourier Transform (STFT) and compared its performance to simple thresholding technique using synthesized nerve recordings. To mimic peripheral nerve recordings and produce ground-truth for validation, a quasi-simulation framework is proposed to incrementally synthesize signals from physiological recordings. A detection threshold was optimized on the spectral features of simulated signals and performance evaluation was done using an independent simulated data set. Results show that the STFT based technique, compared to the simple thresholding, reduces the false detection rate even in recordings with moderately low SNR.