New PDF release: Power Systems Analysis - Solutions Manual

By John J. Grainger, William D. Stevenson Jr.

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Extra info for Power Systems Analysis - Solutions Manual

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This is constructive interference. At the other extreme, when the delay causes the two signals to be perfectly out of phase, they cancel each other out: an increase in one signal is precisely balanced by a decrease in the other, so they will sum to zero. This is destructive interference. Typical audio signals contain energy at a large number of frequencies. For any given delay value, some frequencies will add destructively and cancel out (notches in the frequency response) and others will add constructively (peaks).

Unlike other delay effects, the input signal x[n] is not mixed into the output. Delay alone does not introduce a pitch shift. Suppose the length M[n] of the delay line does not change. Then at every sampling period n, exactly one sample x[n] goes in and one sample y[n – M] comes out. The sound will be delayed but otherwise identical to the original. 16) In other words, the playback rate from the buffer is (1 + Δm) times the input rate. Correspondingly, the frequencies in the input signal x[n] will all be scaled upwards by a factor of (1 + Δm).

The studio technician Ken Townsend later said that “they would relate what sounds they wanted and we then had to go away and come back with a solution … they often liked to double-track their vocals, but it’s quite a laborious process and they soon got fed up with it. ” What Townsend devised was not the modern flanging, but the closely related chorus effect, or artificial double tracking (ADT). But it is implemented using the same approach, slowing down and speeding up a tape machine. The seemingly random variations in speed (and hence also pitch) mimic the effect of a singer trying to harmonize with the original.

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Power Systems Analysis - Solutions Manual by John J. Grainger, William D. Stevenson Jr.

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