So far, on our quest for converting analog audio signals to digital ones, we have only
been looking at one aspect of the signal - its timing.
Sampling, as we found out, is just the process of selecting a regular time interval at which
we make our measurements.
So at a sampling rate of 44.1kHz, we’ve evenly split our signal along the time axis
into 44,100 points every second.
And at these points we can measure the signal amplitude.
All the rest of the points in between are skipped.
But throughout this entire process, we never really gave much thought on how we’re going
to measure and store the signal amplitude.
We just assumed that at every sample point, we’d get an accurate measure of what the
analog signal is.
But this is a faulty assumption, for the very same reason that we needed to sample the signal
in the first place.
An analog signal is a continuous signal.
There are infinitely many points between 2 time intervals where the signal can be measured.
So to have any chance of representing analog signals in the digital domain, we sample the
signal at discrete points in time, and ignore the rest.
Similarly, each point on the amplitude scale can have a theoretically infinite resolution,
with an unending number of digits.
So we really need to put our foot down and draw a line to represent the maximum resolution
that we are willing to maintain.
You can think about it as the accuracy of measurement.
If the resolution is really small, the accuracy of measurement drops as well.
And if you have a large enough resolution, the measurements become super accurate, but
you have to deal with the technical task of having to measure with such high accuracy
consistently, and fast enough before the next sampling interval arrives.
You need top of the line hardware.
Another consideration with high resolution and accuracy is the storage capacity needed
to represent and save all the sampled points and the bandwidth required to transmit large
amounts of data associated with highly precise representation.
So like any discipline of engineering, finding the right resolution is a balancing act.
Unlike the sampling rate, governed by the sampling theorem, which pretty much guarantees
lossless conversion beyond a certain rate, the determination of resolution is not quite
so lossless.
But what real world effect does it have on sound?
We saw that sampling along the time axis determines the maximum frequency you can represent.
The higher the sampling rate, higher is the capacity for frequency representation within
the digitized signal.
And what about sample resolution then?
The size of the sampling interval along the amplitude axis or the y-axis in this case
determines the maximum dynamic range that the digital signal can represent.
Dynamic range is the range between the highest and lowest amplitude moments of the sound.
If you’re new to digital audio, this might not have been the answer you were expecting.
Possibly because I’ve been describing the audio sample points in terms of resolution.
A common analogy you would draw when hearing the term resolution, is the resolution of
an image.
The higher the number of pixels or resolution, the better the quality and sharpness and clarity
of the image.
Decreasing the resolution, would pixelate the image and reduce the overall quality.
But you cannot apply this analogy in relation to music.
When I talk about resolution, I mean the accuracy of values of sample points being maintained,
the decimal point or floating point accuracy if you will, and nothing to do with the quality
of the sound.
The resolution only impacts the amount of noise present in the digitized signal.
This noise affects the overall dynamic range that is available.
Let’s demonstrate this, with a simple yet impractical example.
Let’s take an arbitrary signal, which is sampled along the time axis.
And let’s say that we split the amplitude scale into 8 discrete levels.
At every sampled point, our measurements have to stick to one of these discrete levels.
The 8 levels are regarded as the resolution of the digitization process.
Also, the process of mapping the analog signal values to a limited range of discrete values
like this, is called quantization.
You can think about quantization as a latch, which either pulls or pushes a sample value
to the nearest discrete measure.
As you can see, with 8 discrete points, the resolution is quite poor.
This is infact a 3 bit resolution, but more about bits and bit depth later.
You could, at this point of time, plot a graph, with the y-axis as the difference between
the original analog signal value, and discrete digital value that the signal is constrained
to.
You’d get something like this, which represents the quantization error within our digital
signal when compared to the original analog signal.
This error causes unintended noise to permeate into the digital signal due to the low number
of discrete points.
And the dynamic range of the digitized signal is just the difference between the highest
discrete point the signal is represented on, on the upper end, to the amplitude of the
quantization error itself, since any audio representation below this noise floor is just
masked by the noise or error signal.
In all but the worst circumstances, quantization and bit depth isn’t something that you need
to worry about.
Choosing a default bit depth anywhere between 16bits to 24bits on your audio converters
or programs, should do you perfectly well in most situations.
Modern advances in digital technology can let you get away with bit depths as low as
8bits and still offer better dynamic range than an analog medium like the cassette tape.
So, is it worth studying about it?
Certain musical applications will require the highest dynamic range possible, like the
audio in film played in cinemas and theatres.
You’d want to hear the whispers between characters, against the quiet and acoustically
treated backdrop of a good movie theater, while not hearing any digital noise.
And on the other end of the loudness spectrum, you’d want to hear the deafening sounds
of a stuka dive bomber descending.
A wide dynamic range in this case is really important to tell the right story.
On the other hand, certain genres of music, like dance music, electronica or metal, don't
require a wide dynamic range, since the music is generally loud all the time.
A listening environment makes a lot of difference as well, listening to songs on a car stereo
system while driving drops the overall dynamic range that’s available to us.
That’s because the road, wind and traffic noise all act to reinforce the noise floor,
lower than which our music from the stereo is just not heard.
More importantly, our study on bit depth and quantization will inadvertently lead us to
explore several other concepts like the noise floor, the signal to noise ratio, headroom,
dynamic range, the bitwise representation of digital audio, binary arithmetic, dithering
and noise shaping.
So if you fancy any of that, do carry on.
See you in the next one!