Representation of Audio Signals 493of samples with a low-pass fi lter set to remove the components between the top of the
audio band and the lower sideband of the 4 Fs component.
The process effectively transfers the antialias fi lter from the analogue to the digital
domain with the attendant advantages of digital operation. These include a near ideal
transfer function, low ripple in the audio band, low group delay distortion, wide dynamic
range, exactly repeatable manufacture, and freedom from a wide range of analogue
component and design compromises. The four times upsampling process spreads the
(^0) fs 2 fs 3 fs 4 fs
0 fs 2 fs 3 fs 4 fs
(^0) fs 2 fs 3 fs 4 fs
Interpolation filter
rejection band
Digital signal band-limited by interpolation, low-pass filter
spectral replications now occur at 4fs
Spectrum of digital signal using Nyquist sampling
Spectrum of digital signal with insertion of zero samples (no change!)
Figure 15.31(b) : At the new sample rate (shown here as 4 F (^) s ). The spectrum of the signal
now extends to 4 F (^) s , although there is only audio content up to F (^) s /2. Thus when the
signal is passed to the DAC element (an element that will have to be able to work at the
required oversampling speed) the resulting audio spectrum can be fi ltered simply from the
nearest interfering frequency component, which will be at 4 F (^) s. Note that the process of
interpolation does not add information. If the oversampling is being carried out in the ADC
direction, the analogue audio signal itself will be sampled and quantized at the higher rate.
The next stage requires the reduction of the sequence of data by a factor of four. First data
are fi ltered in order to remove components in the band between the top of the required
audio band and the lower of the 4 F (^) s sideband and then the data sequence can be simply
subsampled (only one data word out of each four is retained).