Model VR240 Audio Logging Recorder
January 2000
4-3
recorder is also directly proportional to tape speed. The Nyquist Sampling Theorem states that
the sampling rate must be greater than twice the highest frequency you want to process.
4-6.
SAMPLING RATE IN THE VR240.
In the VR240, the recording time of a tape depends on the “sampling rate” chosen via the front
panel. We chose the term “sampling rate” because it is more obviously related to digital audio
than “transcoding rate”, which is a more accurate term. When you select a “sampling rate”, the
actual sample rate does not change, and neither does the frequency response. What does
change when you change the “sampling rate” from the front panel is actually the
data rate
, or
the amount of digital information per channel that is stored on tape.
The input signals are sampled at 8000 times per second, and each sample occupies 8 bits.
When you select 32kbps, you are selecting 8000 samples per second times 4 bits per sample.
Likewise, at 16kbps you are selecting 2 bits per sample. The VR240 doesn’t simply throw away
bits to get the lower data rates. Various DSP operations are performed to eliminate redundant
information in the audio signal.
4-7.
DYNAMIC RANGE, SNR, AND THD+N.
Dynamic range is the ratio in dB of the largest undistorted signal to the smallest signal that can
be heard above the noise. For analog tape recorders, the largest signal is limited by tape
saturation and the smallest signal is limited by tape hiss. For digital systems, dynamic range is
determined by the largest number that a sample can be, which depends on the number of bits in
each sample.
Various tricks can be played to increase dynamic range. For analog signals, dynamic range
expander circuits can make loud signals louder and soft signals softer. Similar tricks are
possible with digital signals, which we play with numbers instead of voltages. The VR240 uses
8-bit samples, but these samples are
nonlinear
. The 8-bit samples used in the VR240 actually
have a dynamic range equivalent to 13-bit linear samples, but the 13-bit values are especially
coded into 8-bit quantities.
Signal-to-noise ratio is the ratio of the largest undistorted signal to the noise level with no signal
present. This is not the same as dynamic range. There may be 2mV of noise voltage in an
analog system, but it may be possible for a human to detect a 1mV audio signal even with the
noise there; in this case the dynamic range would be 6dB greater than the SNR. The situation
is even stranger for digital signals. Each sample is an approximation of an analog voltage. The
more bits per sample, the better the approximation, but there is always some error, which is
perceived as a combination of noise and distortion. You can measure the noise level in a digital
audio system with no signal present, and this can be very quiet indeed, but to properly state the
SNR of a digital audio system you must take the average sampling error into account. A 4-bit
system may be nearly silent with no input signal, but as soon as there is a signal you’ll hear
quite a bit of noise.
THD+N is measured by applying a pure sine wave to the input of the system under test and
subtracting a pure sine wave from the output; whatever is left over is the distortion plus noise.
