Audio Engineering

476 Chapter 15

15.9 Other Binary Operations .......................................................................................

One useful area of digital activity is related to fi ltering, and its activity can be described
by similar algebra. The technique uses a shift register whose output is fed back and

Missing sample value replaced by average of

adjacent values

Sample

value

Missing or

corroneous

sample value

t

(a)

Figure 15.18 : (a) Interpolation involves guessing the value of the missing sample. The fastest

guess uses the average of the two adjacent good sample values, but an average based on

many more sample values might provide a better answer. The use of a simple rectangular

window for including the values to be sampled will not lead to as accurate a replacement

value. The effect is similar to that caused by examining the spectrum of a continuous signal

that has been selected using a simple rectangular window. The sharp edges of the window

function will have frequency components that cannot be separated from the wanted signal.

(b) A more intelligent interpolation uses a shaped window that can be implemented as an

FIR, or transversal, fi lter with a number of delay stages, each contributing a specifi c fraction

of the sample value of the output sum. This kind of fi lter is less likely than the simple linear

average process to create audible transitory aliases as it fi lls in damaged sample values.

Error when simple

average is used

t

(b)