This paper proposes a new noise-robust spectral estimation method for speech recognition. The new method, called PHASOR, is characterized by inside-frame processing. The speech spectrum is estimated from a single impulse response obtained by summing multiple pitch periods in a frame with synchronizing the phase. PHASOR improves the spectral estimation accuracy and suppresses the additive noise because of the inside-frame processing. These improvement is more effective when the pitch fluctuates or changes in the frame. Speaker-dependent and speaker-independent phoneme recognition experiments demonstrate that the PHASOR greatly reduces the recognition error rate for speech data contaminated by noise. It also outperforms conventional noise reduction methods, cepstral mean normalization and spectral subtraction.