Audio Engineering

Representation of Audio Signals 469

contribution that each height makes to the average each time we calculate the average
of a 4-min period. Shaped windows are common in the fi eld of statistics and are used
in digital signal processing. The choice of window does affect the result, although as it
happens the effect is slight in the example given here.

One major practical problem with implementing practical fi nite impulse response (FIR)
fi lters for digital audio signals is that controlling the response accurately or at low

1 1.55

2 3 4 5 6 7 8 9

10

11

12

1.64

1.56

1.59

1.55

1.75

1.50

1.69

1.75

1.79

1.84

1.85

1.714

1.618

1.587

1.607

1.631

1.669

1.733

1.789

1.621

1.618

1.59

1.616

1.648

1.606

1.714

1.784

7/96

7/96

24/96

24/96

34/96

Weighting

factors

Unwindowed

average

Sample

number

Value Average

(b) (c) (d)

Figures 15.15(b)–15(d) : For a small portion of the curve, make measurements at each

interval. In the simplest averaging scheme we take a block of fi ve values, average them,

and then repeat the process with a fresh block of fi ve values. This yields a relatively coarse

stepped waveform. (c) The next approach carries out the averaging over a block of fi ve

samples but shifts the start of each block only one sample on at a time, still allowing each

of the fi ve sample values to contribute equally to the average each time. The result is a more

fi nely structured plot that could serve our purpose. (d) The fi nal frame in this sequence

repeats the operations of (c) except that the contribution that each sample value makes to

the averaging process is weighted, using a fi ve-element weighting fi lter or window for this

example whose weighting values are derived by a modifi ed form of least-squares averaging.

The values that it returns are naturally slightly different from those of (c).