of Microprocessors

500 MUSICAL ApPLICATIONS OF MICROPROCESSORS
increases such that the delay introduces a 180 0 phase shift, the delayed
signal cancels the undelayed signal in the mixer producing zero output.
Higher frequencies are passed in varying amounts until the phase shift
through the" delay reaches 3 X 180 0 which produces another cancellation
and so forth. The filter in Fig. 14-13B works the same way except that the
first notch is at zero frequency.
If the delay time is slowly varied while filtering a broadband signal
source, the distinctive sound of flanging is produced. In a digital synthesis
system, the delay is very easily produced with a small memory buffer, the
size of which determines the delay. Such a technique can only give delays
that are a multiple of the sample period, which results in some choppiness in
the flanging effect. This may be overcome, at some sacrifice in noise level, by
interpolating between adjacent samples at the end of the simulated delay line
to provide essentially continuous delay variation.
Filters with an Arbitrary Response
One of the advantages of digital signal processing is that any filter
response can be obtained in a straightforward manner. Furthermore, the
response may be changed as often and as much as desired concurrent with the
filtering action.
In the previous chapter, one method of arbitrary filtering was mentioned.
In use, one first ·takes the Fourier ttansform of the signal to be
filtered. Next the spectrum is modified according to the filter characteristic
desired. The modification involves multiplying the amplitude of each spectral
component by the filter's amplitude response value at the corresponding
frequency. If phase is important, the phase of each spectral component is
added to the filter's phase response value at the corresponding frequency. The
modified spectrum is then converted into the filtered signal via inverse
transformation.
Of course, with the FFT, the continuous stream of samples to be
filtered must be broken into records, processed, and the results spliced
together again. This indeed can be accomplished without the distortions that
were encountered in direct FFT synthesis, but the process is complex and can
be time consuming. Another method that works continuously, sample by
sample, is called direct convolution. With this method, one can write a subroutine
that accepts a table of numbers describing the filter's time domain
response along with indi1 1 idual input samples to produce individual output
samples. The routine is exceedingly simple and can be quite efficient when
written in assembly language or implemented in hardware.
Before describing the algorithm, it is necessary to become familiar with
a filter's impulse response because that is the table of numbers used by the tilter
subroutine. The transient response of high-fidelity components is usually
characterized by noting their response to square waves. If the square-wave