In this paper, integrated silicon nitride edge filters are demonstrated to perform the function of frequency to amplitude (FM-to-AM) conversion of optical feedback interferometric (OFI) signals. Compared to existing OFI FM-to-AM conversion techniques employing optical edge filters based on gas cells, and free-space or fiber-based Mach Zehnder interferometers (MZIs), integrated photonic processing of OFI signals is found to offer greater compactness and design flexibility. In addition, higher resilience to parasitic mechanical vibrations and better temperature control of the photonic chip can potentially facilitate sensing system operation. Three different optical filters have been implemented to perform FM-to-AM conversion: two integrated MZIs with a 2- cm and 4- cm path-length imbalance, respectively, and one micro-ring resonator (MRR). The OFI FM-to-AM conversion factors are experimentally determined to be 0.37 GHz−1, 0.65 GHz−1 and, 1 GHz−1 for the 2- cm imbalanced MZI, the 4- cm imbalanced MZI and the MRR, respectively. The corresponding noise equivalent displacements (NEDs) with optical chip coupling are found to be approximately 25.4 nm, 11.5 nm and 4.9 nm, respectively, over a 1 kHz bandwidth. The results are compared to those obtained with a reference hydrogen cyanide gas cell exhibiting a sensitivity of approximately 0.25 GHz−1 and an NED of 5.6 nm.