highest-quality time stretching. Frame-based approach In order to preserve an audio signal's pitch when stretching or compressing its duration, many time-scale modification (TSM) procedures follow a frame-based approach. Given an original discrete-time audio signal, this strategy's first step is to split the signal into short analysis frames of fixed length. The analysis frames are spaced by a fixed number of samples, called the analysis hopsize . To achieve the actual time-scale modification, the analysis frames are then temporally relocated to have a synthesis hopsize . This frame relocation results in a modification of the signal's duration by a stretching factor of . However, simply superimposing the unmodified analysis frames typically results in undesired artifacts such as phase discontinuities or amplitude fluctuations. To prevent these kinds of artifacts, the analysis frames are adapted to form synthesis frames, prior to the reconstruction of the time-scale modified output signal. The strategy of how to derive the synthesis frames from the analysis frames is a key difference among different TSM procedures. Speed hearing and speed talking For the specific case of speech, time stretching can be performed using PSOLA. Time-compressed speech is the representation of verbal text in compressed time. While one might expect speeding up to reduce comprehension, Herb Friedman says that "Experiments have shown that the brain works most efficiently if the information rate through the ears—via speech—is the 'average' reading rate, which is about 200–300 wpm (words per minute), yet the average rate of speech is in the neighborhood of 100–150 wpm." Listening to time-compressed speech is seen as the equivalent of speed reading. Pitch scaling These techniques can also be used to transpose an audio sample while holding speed or duration constant. This may be accomplished by time stretching and then resampling back to the original length. Alternatively, the frequency of the sinusoids in a sinusoidal model may be altered directly, and the signal reconstructed at the appropriate time scale. Transposing can be called frequency scaling or pitch shifting, depending on perspective. For example, one could move the pitch of every note up by a perfect fifth, keeping the tempo the same. One can view this transposition as "pitch shifting", "shifting" each note up 7 keys on a piano keyboard, or adding a fixed amount on the Mel scale, or adding a fixed amount in linear pitch space. One can view the same transposition as "frequency scaling", "scaling" (multiplying) the