The Scientist and Engineer's Guide to Digital signal by Steven W. Smith

By Steven W. Smith

The publication offers the basics of DSP utilizing examples from universal technology and engineering challenge

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Short bursts of sound are transmitted from the ship, reflected from the ocean floor, and received at the surface as an echo. Sound waves travel at a relatively constant velocity in water, allowing the depth to be found from the elapsed time between the transmitted and received pulses. As with all empirical measurements, a certain amount of error exists between the measured and true values. This particular measurement could be affected by many factors: random noise in the electronics, waves on the ocean surface, plant growth on the ocean floor, variations in the water temperature causing the sound velocity to change, etc.

This equation provides the same result as Eq. 2-2, but with less roundoff noise and greater computational efficiency. The signal is expressed in terms of three accumulated parameters: N, the total number of samples; sum, the sum of these samples; and sum of squares, the sum of the squares of the samples. The mean and standard deviation are then calculated from these three accumulated parameters. F 2 ' 1 N& 1 j N&1 i' 0 2 xi & j xi N&1 1 N 2 i '0 or using a simpler notation, F2 ' 1 N& 1 sum of squares & sum 2 N While moving through the signal, a running tally is kept of three parameters: (1) the number of samples already processed, (2) the sum of these samples, and (3) the sum of the squares of the samples (that is, square the value of each sample and add the result to the accumulated value).

This makes the algorithm much faster than the previously described methods. Think a factor of ten for very long signals with the calculations being performed on a general purpose computer. The notion that the acquired signal is a noisy version of the underlying process is very important; so important that some of the concepts are given different names. The histogram is what is formed from an acquired signal. The corresponding curve for the underlying process is called the probability mass function (pmf).

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