Digital Signal Processing
Digital signal
processing can be summarized very briefly as follows. You take the ordinary
analog audio signal from an electronic organ or other musical instrument,
convert it to a bunch of numbers, manipulate the numbers somehow, and turn
that back to an analog signal and send it off to a speaker so you can hear
the results of that manipulation. Sounds pretty simple, right? Unfortunately,
the implementation of the above is anything but simple. The theory however
is that it's a lot easier to manipulate a bunch of numbers than it is to do
the same thing with an analog signal, but in the studios of the major recording
companies, most of what we do today by simple, small digital signal processors
was indeed done by analog means for many years previous to the advent of digital
signal processing. The big plus about digital signal processing is that in
spite of the complexity of the machinery and the process, the hardware that
performs digital signal processing is small, not too expensive and getting
easier to use than it was previously.
Years ago, one of the best ways to get really
natural sounding reverberation was to use a real echo chamber, a reasonably
large room with hard reflecting surfaces for walls, floor and ceiling. In
one part of the room there was a very high quality speaker, and at the other
end was a high quality microphone. Sounds from the studio or the electronic
organ or whatever was being played went to the high quality speaker and got
converted to sound. The sound bounced around in this special room creating
very good reverberation. Then the microphone picked up the reverberated sound
and it went back to the recording control room to be mixed in with the actual
recording of the musical instrument.
Today, via DSP, you need only a small unit,
perhaps 18 inches long, 5 inches deep and two inches high, or some special
software installed in a computer and you will end up with really high
quality reverberation.
If the early echo chamber created a reverb
that was too long, the recording engineer would move large baffles into
the room which were covered with acoustical material to absorb some of
the sound and make the reverb decay time shorter. With a modern digital
signal processor, you need make only a few tweaks of some controls or
enter a command on a computer keyboard, and you can shorten the reverb
time if you'd like. Here, in a brief summary with a few simple diagrams
is the basic outline of the process.
It all starts out in the ADC or analog-to-digital
converter. Here, an audio AC waveform gets sampled thousands of times
per second and the values of that signal at each sampling instance get
converted to a specific numerical value. Figure one.
 |
Figure 1. Here are small sam-pled sections of two AC audio waveforms; the left and right channels of a stereo signal. As you look at them you can see the overall shape of the waveforms but you can also see the in-dividual "steps" or samples. This is a greatly magnified view. The sampling frequency is 44,100 Hz which is much higher than even the highest audio frequency waveform that might exist. See "Nyquist Theory" explanation for this below.
As
the picture above shows, it's easy to see the general shape of the waveform,
and yet you can also see the individual samples or steps. The audio frequency
band consists of fre-quencies from 20 Hz to 20,000 Hz. This is the typical
band of frequencies or pitches that people can hear, from the lowest to
the highest. Above 20,000 [20 kHz] it's not necessary to sample because
we can't hear it anyhow! In fact most adults' hearing begins to cut out
around 15 kHz and for some people, the cutoff frequency is lower than
that.
The sampling frequency must, however be
higher than the highest frequency that we would want to reproduce accurately.
The Nyquist theory states that the sampling frequency must be at least
twice as high as the highest frequency that we wish to convert for accurate
reproduction. In most music digital signal applications, the sampling
frequency therefore is 44.1 kHz. This is a little higher than twice the
20 kHz which is the top limit that we need to be concerned with. 20 kHz
is the upper limit for audio CDs and we all know how good they sound.
Unless we are making music for bats, there is no need for humans to worry
about any audio frequencies above 20 kHz because that's our top limit
of hearing. It is possible, however, that some musical instrument sounds
may contain frequencies that are higher than 22.05 kHz. High notes on
a loudly played trumpet, for example, will produce harmonics whose frequencies
exceed 20 kHz. The same is true of harmonics of high violin notes and
even some of the sibilance noises in speech.
If these were to enter the analog to digital
converter, they would be higher than the Nyquist limit. If this were to
happen, the analog to digital converter would get loused up and generate
so-called "alias" frequencies which would lie in the audible
range and result in severe distortion in the final result. Therefore,
the very first thing that happens when a musical signal enters a digital
signal processor is that it must run through a low pass filter that will
eliminate all of these ultrasonic frequencies above 20 kHz.
In reality, filters such as these are not
that sudden, in that they don't immediately cut off 100% just above the
selected cutoff value. Therefore, a filter which is designed to cut out
frequencies above 20 kHz will still let a little bit that is slightly
over 20 kHz get through. This is why designers of digital audio equipment
have standardized the frequency of 44.1 kHz as a sampling frequency. They
figure that if a low pass filter should cut out frequencies above 20 kHz,
by the time the frequency is up to 22.05 kHz, now a 20 kHz filter will
be cutting the signal out completely.
So the first step is to low-pass filter
the signal to eliminate anything over 20 kHz and then sample the result
at a much higher rate, typically 44,100 times a second and then get discrete
values for each sample. At this point, the values are binary numbers,
that is all zeros and ones according to the binary system. From here on
the process becomes considerably more complicated. There is a great deal
on the Internet about the subsequent aspects of the process so rather
than for me to fill pages and pages with some really technical stuff which
you can easily look up if you wish, I will summarize briefly on the following
pages what happens in a typical digital signal processor [often called
an effects processor] and then follow it up with a few pictures and sound
clips that demonstrate particular effects.
It remains to be said that at the other
end of the process, after the DSP has done its magic to the digitally
sampled signal, this has to be converted back to an analog signal so that
it can be amplified and ultimately sent to a speaker. Essentially the
waveform is reconstructed, and then another filtering circuit eliminates
the 44.1 kHz component from the resulting waveform. As you look at the
above picture, it's very easy to see the shape of the waveform. We just
need to filter out the individual little steps so that the result looks
like this, below.
 |
Figure 2. After the sampling frequency is removed, we are left with a regular smooth analog waveform virtually identical to the initial input waveform, unless of course that the digital signal processor had made some changes while the signal was in digital form and being pro-cessed.
