For channel estimation in a spectrally shaped wireless communication system, an initial frequency response estimate is obtained for a first set of P uniformly spaced subbands (1) based on pilot symbols received on a second set of subbands used for pilot transmission and (2) using extrapolation and/or interpolation, where P is a power of two. A channel impulse response estimate is obtained by performing a P-point IFFT on the initial frequency response estimate. A final frequency response estimate for N total subbands is derived by (1) setting low quality taps for the channel impulse response estimate to zero, (2) zero-padding the channel impulse response estimate to length N, and (3) performing an N-point FFT on the zero-padded channel impulse response estimate. The channel frequency/impulse response estimate may be filtered to obtain a higher quality channel estimate.