BANDWIDTH EXTENSION OF TELEPHONY SPEECH - Adaptive Signal Processing: Next Generation Solutions - page 353

in [20] the first experiments were conducted in 1933 using a nonlinear (quadratic)
characteristic. Later on the British Broadcasting Corporation (BBC) was interested in
increasing the bandwidth during telephone contributions [6]. Mainly these are two
different nonmodel based algorithms. In the following wewill discuss these (historical)
methods briefly as some of these ideas will be touched upon again in later sections.
7.3.1 Oversampling with Imaging
This method makes use of the spectral components that occur when upsampling
(inserting zeros) a signal either without any anti-imaging filter at all or with a filter
H AI ( e jV ) showing only some slow decay above half of the desired sampling frequency
(see Fig. 7.4). This upsampling process results in a spectrum that is mirrored at half of
the original sampling frequency. This method profits from the noise-like nature of the
excitation signal concerning unvoiced utterances. Unvoiced utterances result in a spec-
trum which has most of its energy in the higher frequency regions and therefore
exactly these portions are mirrored. The temporal behavior of unvoiced components
below the cutoff frequency correlates strongly with those above the cut-off frequency
which is preserved by applying this mirroring.
A drawback of this method concerning telephony speech is that the lower frequency
part of the spectrum is not extended at all. Furthermore if a signal that is bandlimited
according to the frequency response of an analog telephone system with 8 kHz
sampling rate is upsampled a spectral gap is produced around 4 kHz. A rather costly
alternative would be to first downsample the signal to a sampling rate that is equal
to twice that of the maximum signal bandwidth (e.g. 2 3600 Hz) before upsampling
once again. An example is depicted in Figure 7.5. The upper plot shows a time-
frequency analysis of the incoming bandlimited telephone signal ˜ tel ( n ). After insert-
ing zeros in between neighboring samples of the input signal (upsampling with r ¼ 2)
and filtering with an antiimaging filter that has its 3 dB cutoff frequency at about
7 kHz (instead of 4 kHz) a wideband signal s ext ( n ) as depicted in the lower diagram
of Figure 7.5 is generated.
The results crucially depend on the effective bandwidth of the original signal and
the upsampling ratio. For increasing the bandwidth of signals that are bandlimited to
8 kHz up to 12 kHz, for example, this method works surprisingly well, but in the case
of telephony speech this method produces poor results [5, 8].
7.3.2 Application of Nonlinear Characteristics
The application of nonlinear characteristics to periodic signals produces harmonics as
we will see in more detail in Section 7.5.1. This can be exploited for increasing the
Figure 7.4 Bandwidth extension based on oversampling and imaging.