Abstract: Integrated circuits with wireless communications circuitry having digital predistortion (DPD) circuitry are provided. The digital predistortion circuitry may include a forward path filter, a time domain alignment (TDA) circuit, a frequency domain alignment (FDA) circuit, and an adaption circuit. The TDA circuit may receive power amplifier input signals and power amplifier output signals and may include a cross correlator, a peak detector, and a delay circuit for performing coarse time domain alignment (i.e., to align the power amplifier input and output signals). The FDA circuit may include a fast Fourier transform circuit, a matrix multiplier, and a matrix inverter for performing frequency domain alignment. The adaption circuit may analyze the aligned signals output from the FDA circuit to produce impulse response coefficients that are then used to control the forward path filter. The forward path filter may serve to predistort transmit signals prior to radio-frequency amplification.