A speech processing system (10) incorporates an analogue to digital converter (16) to digitize input speech signals for Fourier transformation to produce short-term spectral cross-sections. These cross-sections are compared with one hundred and fifty reference patterns in a store (34), the patterns having respective stored sets of formant frequencies assigned thereto by a human expert. Six stored patterns most closely matching each input cross-section are selected for further processing by dynamic programming, which indicates the pattern which is a best match to the input cross-section by using frequency-scale warping to achieve alignment. The stores formant frequencies of the best matching pattern are modified by the frequency warping, and the results are used as formant frequency estimates for the input cross-section. The frequencies are further refined on the basis of the shape of the input cross-section near to the chosen formants. Formant amplitudes are produced from input cross-section amplitudes at estimated formant frequencies. The formant frequencies and amplitudes are used with a computer (25) to provide speech indications or with a Hidden Markov Model word matcher (24) to provide word recognition.