In this work, a harmonic-canceling synthesizer for Built-In Self-Test (BIST) applications is presented. The main contribution is the implementation of the required irrational tap coefficients by using integer numbers in a recursive approach without any calibration scheme. A coefficient generator that exploits properties of skew-circulant matrices and relaxes the trade-off between output linearity and coefficients mismatch is proposed. The cascade of Harmonic-Canceling Filters (HCFs) allows to filter out up to the 47th harmonic of the input square-wave. Also, a band-pass HCF that enables the selection of its input’s 1st or 5th harmonic is presented. The system is fabricated in 180nm CMOS technology. Measurement results show a maximum 66 dBc Spurious-Free Dynamic Range (SFDR) and output frequencies ranging from 0.8 MHz to 100 MHz.