Compensation of dispersion distortions of broadband signals in an ionospheric channel is investigated. Due to different phase delays, the spectral components of the signal arrive at the receiver with different group delays, resulting in a nonlinear dependence of delay on frequency. A polynomial model is used to describe the phase response. A frequency sampling method for finite impulse response (FIR) compensating filter synthesis with quadratic approximation of the response is proposed. The Gibbs effect is investigated, and the minimum number of FIR compensating filter coefficients is determined for different channel parameters, signal bandwidths, and sampling frequencies.