Interpolation of digital signals using signal sample replication

A filtering technique that results in improved performance of interpolating filters. The improved filter and technique replicates samples of the digital input signal instead of inserting zeroes before smoothing to eliminate undesired images of the sampled input signal. The filter includes a digital equivalent of a sample and hold for sampling the digital input signal at the input sample rate and for replicating the sampled digital input signal a predetermined number of times to increase the sample rate by an integer multiple and produce replicated samples of the input signal. A smoothing filter is coupled to the digital sample and hold for smoothing the replicated samples. The smoothing filter has a shape having a high frequency enhancement followed by a sharp cutoff that compensates for the replicated samples of the input signal. Interpolated digital output signals are provided therefrom that are at a sample rate higher than the input sample rate.

BACKGROUND 
The present invention relates to interpolating filters, and more 
particularly, to an interpolating filter and filtering technique that uses 
signal sample replication in lieu of zero insertion to achieve 
interpolation of digital signals. 
The traditional technique of interpolating digital signals is to increase 
the sample rate of the digital signals by inserting zero-valued samples 
between the samples of the signal, then filtering the resulting signal 
with an interpolating filter. Prior art relating to the present invention 
is disclosed in the following patents. U.S. Pat. No. 4,109,110 issued to 
Gingell entitled "Digital-to-Analog Converter" teaches multiplying the 
sampling rate of a digital signal by repeating the sampled signal the 
required number of times, with reference to FIG. 6 and the description at 
col. 4, lines 12-22. The Gingell patent teaches the use of an interpolator 
as part of a process of increasing the data rate by a large factor for 
reproducing music from a compact disk, for example. The interpolator can 
be a simple sample and hold in the digital world according to the patent. 
There is no suggestion that a smoothing filter to remove the sample and 
hold artifacts be employed. Gingell does suggest that perhaps a simply 
constructed linear interpolator be used as being a little better than a 
sample and hold. The technique of Gingell follows the interpolator by 
other processing steps that increase the sample rate still farther. The 
digital to analog converter and the following analog filter are very 
simple as a result. The use of a filter as part of the interpolator that 
corrects the sample and hold frequency distortion is not suggested. Since 
there is no such filter, there is no consideration of the number of bits 
used in the quantization of the filter coefficients. 
U.S. Pat. No. 4,270,026 issued to Shenoi et al. entitled "Interpolator 
apparatus for Increasing the Word Rate of a Digital Signal of the Type 
Employed in Digital Telephone Systems". This patent suggests using the 
traditional inserting of zero value samples to perform the increase in 
data rate for the digital signal. A recursive digital filter is used as 
the interpolator. The two pole recursive filter that is suggested will 
have very much less performance than the finite impulse response filter of 
the present invention. The present digital filter corrects for the digital 
sample and hold that I use while achieving the very sharp cutoff. Since 
this technique does not use a digital sample and hold, but a simple zero 
insert, there is no need to correct for the distortion, but the following 
filtering must use more accurate arithmetic. The subject of the Shenoi 
patent is a technique for implementing the recursive filter easily. 
U.S. Pat. No. 5,075,880 issued to Moses et al. entitled "Method and 
Apparatus for Time Domain Interpolation of Digital Audio Signals" uses a 
traditional zero insertion technique to increase the sample rate. The 
filtering is performed by using Lagrangian or spline interpolation from a 
mathematical technique for interpolation. The patent argues that there is 
no need to worry about the frequency response of the result, a simple 
mathematical interpolation operation is good enough. Since there is no 
filter, there is no consideration of the accuracy of the filter 
coefficients required to implement the filters. 
U.S. Pat. No. 4,209,771 issued to Miyata et at. entitled "Code Converting 
Method and System" implements a scheme for conversion to a high rate 
differential pulse code system using .+-.1 values. The conversion uses the 
usual DPCM approach of a linearly rising value at a high rate that can 
reach the value of the digital samples at the sample times. The result is 
an approximation to a carefully interpolated signal that may be acceptable 
in some applications. The distortions that occur are well known. As long 
as the signal changes slowly, the DPCM can keep up with it. When the 
signal changes rapidly with a large swing, the DPCM approximation will 
depart from the input signal, causing distortions in the signal and 
generating spurious frequencies that can cause interchannel interference 
when there is more than one signal in the bandwidth of the digital 
samples. 
U.S. Pat. No. 5,126,737 issued to Torii entitled "Method for Converting a 
Digital Signal into Another Digital Signal Having a Different Sampling 
Frequency" uses interpolating to produce an output sample rate that is 
nearly the same as the input sample rate. The technique proposed by Torii 
is to increase the sample rate by a large factor, then downsample to the 
required rate. The fact that the output samples can drift between the 
samples even at the very high rate is accounted for by a linear 
interpolator at the very high rate. The patent suggests using a simple 
linear interpolation between the two nearest samples. A phase-locked loop 
is used to determine how far between the two samples the output sample is 
supposed to occur. The step up to the high sample rate includes the 
possibility of using a sample and hold. Any technique for producing the 
high sample rate is acceptable for the purposes of this patent. There is 
no consideration of the accuracy of the arithmetic involved. There is no 
consideration of the possibility of correcting for the sample and hold in 
the filtering process. 
U.S. Pat. No. 4,630,034 issued to Takahashi entitled "Sampling Frequency 
Converting Apparatus" provides a description of a way to change television 
signals from one format to another. The technique uses a buffering scheme 
to collect "M" samples of the input, then uses standard digital filtering 
techniques to produce "N" output samples. The ratio of M/N provides the 
conversion. The filtering uses large number of sets of coefficients to 
generate filters that are equivalent to upsampling using zero insertion by 
a large factor, filtering, then downsampling. 
U.S. Pat. No. 4,460,890 issued to Busby entitled "Direct Digital to Digital 
Sampling Rate Conversion, Method and Apparatus" teaches something similar 
to Torii and to Moses above. The filters used are simple finite impulse 
response falters applied to signals whose sample rate is increased by 
effectively inserting zeroes. The Busby patent suggests interpolating the 
high sample rate signal with a polynomial interpolator instead of a spline 
or Lagrangian interpolation. Busby does suggest calculating only those 
higher rate samples needed in the interpolation of the output points. 
There is no consideration of the accuracy of the arithmetic used. 
U.S. Pat. No. 4,903,019 issued to Ito entitled "Sampling Frequency 
converter for Converting a Lower Sampling Frequency to a Higher Sampling 
Frequency and a Method Therefor: suggests using a nearly traditional 
interpolation technique. Instead of inserting zeroes between samples, this 
patent suggests inserting zeroes in a block at the end of a group of input 
samples. The number of zeroes inserted will be those required to pad a 
block of samples from M samples in the input block to N samples for the 
output block. The falter uses different sets of coefficients for each of 
the output points. The patent does not suggest any particular filters, 
just those that are well known in the industry. The patent does not 
consider the arithmetic accuracy. The scheme is equivalent to the scheme 
of inserting zeroes to upsample, then filtering to downsample to the new 
rate. 
Thus, from the above, several of the schemes discloses in the prior art 
patents use the traditional insert zeroes technique for upsampling before 
filtering. Others suggest a digital sample and hold that is similar to one 
used in the present invention. Further, none of the above patents are 
concerned with a finite impulse response filter with a limited number of 
bits for coefficients. The accuracy of the arithmetic in the recursive 
interpolating filter is addressed in the present invention and is not in 
the prior art patents. The prior art techniques that build a DPCM signal 
reduce the output to a very low number of bits at a high frequency, but do 
not consider the accuracy of the arithmetic in interpolating filters that 
are used in intermediate steps. 
Therefore, it is an objective of the present invention to provide for an 
improved filtering technique that uses signal sample replication with a 
correction filter in lieu of zero insertion to achieve interpolation of 
digital signals. 
SUMMARY OF THE INVENTION 
In order to meet the above and other objectives, the present invention 
provides for an improved interpolating filter and digital signal 
interpolation technique that replicates a digital signal a certain number 
of times, then uses a filter shaped to compensate for the additional 
samples of the signal. The result is a simpler filter to construct, and an 
interpolator with improved performance. The present interpolating filter 
suppresses unwanted images of the interpolated signal more effectively 
when the filter is implemented with integer arithmetic, and allows a 
simpler implementation of the interpolating filter with improved 
performance. The present invention improves upon the ideas outlined in the 
above-cited prior art patents by tailoring the interpolating filter to 
correct for frequency roll-off of the digital sample and hold. 
More particularly, the present invention is a filtering technique that 
results in improved performance of interpolating filters. The improved 
filter and technique replicates samples of the digital input signal 
instead of inserting zeroes before smoothing to eliminate undesired images 
of the sampled input signal. The filter includes a digital equivalent of a 
sample and hold for sampling the digital input signal at the input sample 
rate and for replicating the sampled digital input signal a predetermined 
number of times to increase the sample rate by an integer multiple and 
produce replicated samples of the input signal. A smoothing filter is 
coupled to the sample and hold for smoothing the replicated samples. The 
smoothing filter has a shape having a high frequency enhancement followed 
by a sharp cutoff that compensates for the replicated samples of the input 
signal. Interpolated digital output signals are provided therefrom that 
are at a sample rate higher than the input sample rate. 
The interpolation filter performs interpolation by replicating samples of 
the original signal a number of times that is required to increase the 
sample rate by an integer multiple. This technique is similar to sample 
and hold techniques that have been used in digital to analog converters, 
except the technique is applied in the digital domain before converting to 
the digital signals to analog signals. In the analog domain a smoothing 
filter follows the sample and hold. It is well known that the smoothing 
filter must correct for the frequency distortion of the sample and hold by 
having a frequency characteristic that counterbalances the effective low 
pass filtering effect of the sample and hold. The smoothing filter 
employed in the present invention has the required compensating shape, 
comprising a high frequency enhancement followed by a sharp cutoff. There 
is an interesting effect in using this technique. Filter coefficients in 
the digital smoothing filter can be implemented with much less accurate 
arithmetic. In particular, the filter coefficients can be quantized to 
eight bits and can achieve the same filtering performance as a traditional 
interpolation filter using twelve bit filter coefficients when the sample 
rate is increased by a large amount. 
The present invention improves upon the ideas outlined in the prior art 
patents by tailoring the interpolating filter to correct for frequency 
roll-off of the sample and hold. Further, the finite impulse response 
filter is implemented with a limited number of bits for coefficients. The 
prior art techniques that build a DPCM signal reduce the output to a very 
low number of bits at a high frequency, but do not consider the accuracy 
of the arithmetic in interpolating filters that are used in intermediate 
steps. 
The present invention is implemented using large scale integration 
processing chips that include circuits that are organized for filtering. 
Typically, these chips have a large number of multipliers. A chip from LSI 
Logic that is used in a reduced to practice embodiment of the present 
invention has 64 multipliers with associated adders that are used to 
implement the filter. With 64 multipliers, inserting zeroes wastes the 
multiplication performed by associated multipliers. In the present filter, 
all multipliers are used. Further, the integrated circuit chip is 
organized with limited coefficient accuracy of eight bits. To achieve more 
accuracy requires coupling of several chips together. Thus, the present 
invention uses resources of the filter chip most effectively in building a 
high performance filter for interpolating to a higher sample rate. In 
particular, side-lobes of the filter are reduced three dB for every 
doubling the number of times the samples are replicated in the digital 
sample and hold. Very flat filters with sharp cutoffs and low out-of-band 
frequency response are achieved using the present invention. 
This disclosure proposes an interpolating filter which changes the sampling 
rate of a digital signal by repeating the previous sampled signal the 
required number of times. The disclosure contrasts its approach to the 
prior art procedure of increasing the sampling rate by inserting the 
required number of "zeroes".

DETAILED DESCRIPTION 
Referring to the drawing figures, and by way of introduction, the classical 
technique of increasing the sample rate of a digital signal by an integer 
multiple is to insert a number of zeroes after each sample of the signal. 
The approach is shown in FIGS. 1a and 1b. For example, if the signal 
sample rate is to be increased by a factor of two, one zero is inserted 
after each sample. The resulting signal spectrum has images of the signal 
spaced in frequency at distances equal to the original sample rate. Since 
the new sample rate is at a multiple of the original sample rate, the 
images constitute unwanted signals in the signal spectrum. 
FIGS. 2a and 2b show a typical spectrum of an upsampled signal with images. 
FIG. 3 shows the bandpass characteristic of a filter that will remove the 
images of the signal shown in FIG. 2b. FIG. 4 shows the spectrum of the 
filtered signal with the images removed. The effect of the filter in the 
time domain is shown in FIG. 5. The filter calculates values for 
intermediate samples between the samples of the original signal, filling 
in the zeroes of the upsampled signal. 
When a interpolating filter is implemented in hardware that performs 
integer arithmetic, several problems arise. Limited capabilities of the 
arithmetic results in inaccuracies in computations of the filter outputs, 
and consequently of the interpolated signal. The digitized signal is 
represented by a set of integer values depending on the accuracy of the 
original analog-to-digital converter. Typically the signal is quantized 
with eight bits, ten bits, or twelve bits. Some video converters, for 
example, use as few as six bits. The signal values that can be represented 
will depend on the number of bits in the signal. For example, an eight bit 
signal will have values between -128 and +127. A ten bit signal will have 
values between -512 and +511. A typical representation of the signal value 
will be a "2s complement" integer. 
As a concrete example of an interpolating filter application, consider a 
telephone voice signal with a passband from 300 to 3700 Hz. These signals 
are traditionally sampled at 8000 Hz. If it is desired to increase the 
sample rate to 32000 Hz, a filter is required to eliminate the images 
between 4 kHz and 28 kHz. FIG. 6 shows the impulse response of a suitable 
filter that has a flat frequency response over the range from zero to 3700 
Hz. The frequency response of this filter is shown in FIG. 7. The impulse 
response has values that are integers at the sample points and that may be 
represented as eight bit numbers. 
When the integer value of the signal is multiplied by the integer value of 
the filter coefficient, a number is formed that has a number of bits that 
is equal to the sum of the number of bits in the number and the number of 
bits in the coefficient. In order to establish the gain of the system at a 
selected value, typically 1.0, the numbers are divided by a selected 
integer and the fractional part is discarded by rounding the result. 
Rounding of the coefficients to form integers for the filter 
implementation limits the performance of the filter. 
As shall be described below with reference to the present invention, 
performance is improved when interpolation is performed by replicating 
each sample instead of inserting zeroes. A different filter is required to 
compensate for the different implementation of the interpolation process. 
As an additional advantage, the replication of samples using the present 
invention is easier to perform compared to inserting zeroes. 
Given the above background, an improved interpolating filter 10 in 
accordance with the present invention will now be described. FIG. 8 shows 
a schematic diagram of the interpolating filter 10. FIGS. 8a and 8b 
illustrate the technique that is used to increase the sample rate in 
accordance with the principles of the present invention. The interpolating 
filter 10 is used to interpolate to a sample rate that is higher than an 
input sample rate of the digital input signal. The interpolating filter 10 
includes replicating means 11 comprising a sample and hold circuit 11 for 
sampling the digital input signal and replicating it digitally a 
predetermined number of times to increase the sample rate by an integer. 
This produces replicated samples of the input signal. A smoothing filter 
12 is coupled to the replicating means 11 (sample and hold circuit 11) for 
receiving the replicated samples. The smoothing filter 12 has a shape with 
a high frequency enhancement followed by a sharp cutoff that compensates 
for the replicated samples of the signal. The smoothing filter 12 
providing interpolated digital output signals therefrom that are at a 
sample rate higher than the input sample rate. 
Each sample of the digital input signal is replicated a requisite number of 
times, instead of inserting zeroes. This has the effect of producing a 
digital "sample and hold" of the signal. The sampled signal changes in 
steps instead of comprising a collection of pulses. In filtering theory, 
it is known that a sample and hold or boxcar filter has a sin(x/x) 
frequency response. The response rolls off at higher frequencies, 
distorting the shape of the signal. 
In accordance with the present invention, by building the interpolating 
filter 10 with a response that increases in frequency before the cut-off 
frequency is reached, the roll-off of the sin x/x filter may be corrected. 
This produces a frequency response for the entire interpolation process 
that is flat through the passband of the filter 10. The same performance 
in the passband may be achieved as for the conventional filter that 
processes the signal with inserted zero value samples. As is described 
below, the performance of the filter 10 in the stop band is considerably 
improved. In addition, the present filter 10 with replicated samples is 
easier to build, since the circuits that perform the sample and hold 
operation are much simpler than circuits that insert zeroes. 
By way of example, FIG. 9 shows the impulse response of a filter 10 that 
may be used to interpolate a signal to increase the sample rate by a 
factor of four. The frequency response of the filter 10 of FIG. 9 is shown 
in FIG. 10. In this example, the sample rate is 8000 samples per second. 
The new sample rate is 8000*4=32000 samples per second. In this example, 
the signal is a telephone voice signal with a passband from 300 to 3700 Hz 
with the signal down by 40 dB at 4000 Hz, suitable for digitization at 
8000 samples per second. The interpolating filter 10 is a low pass filter 
that is flat +0.2 dB to 3700 Hz. The filter rolls off to more than 40 dB 
down by 4300 Hz for the interpolated signal in order to eliminate the 
image that appears at 4300 Hz. 
The effect of replicating the Samples four times instead of inserting three 
zeroes is to increase the energy in the signal that is filtered by a 
factor of four. A factor of four provides a total of 12 dB greater 
effective signal power. At the same time, the sidelobe level of the filter 
has not changed. The result is that the present filtering technique has 
increased the image rejection power of the filter 10 by 12 dB over an 
implementation that uses inserted zeroes. 
The interpolation filter 10 may be generated using well-known techniques 
available from several sources. The filters 10 used as examples herein 
were generated using techniques described in a book by T. W. Parks and C. 
S. Burrus, entitled "Digital Filter Design", John Wiley and Sons, Inc. New 
York, 1987. The filters described in the present specification are low 
pass filters 10, but the present technique is equally applicable to 
bandpass filters 10, or to filters 10 of any arbitrary shape. The filters 
10 need only be tilted up at the high frequency end of the spectrum to 
account for the roll-off due to the replication of the samples. 
The present interpolating filter 10 and technique is useful in the 
implementation of a system where signals at a number of different sample 
frequencies are to be resampled at a single frequency for output through a 
digital-to-analog converter. It is useful, but not required, for the 
sample frequency (rate) to be a power of two different from the output 
sample frequency (rate). Any integer ratio between the input sample 
frequency and the output sample frequency may be used. As is traditionally 
done in the digital signal domain, an artificial sample frequency may be 
used that is an integer multiple of both the input sample rate and the 
output sample rate. In this situation, the output samples are calculated 
only at the samples of the output sample rate, eliminating the samples at 
the artificial sample rate that are not needed at the output. In this 
manner, a signal may be upsampled to a sample rate that is not a simple 
integer multiple of the input sample rate. 
Thus, an interpolating filter and filtering technique that uses signal 
sample replication in lieu of zero insertion to achieve interpolation of 
digital signals have been described. The improved filter replicates 
samples instead of inserting zeroes before filtering to eliminate 
undesired images of the signal. It is to be understood that the 
above-described embodiments are merely illustrative of some of the many 
specific embodiments which represent applications of the principles of the 
present invention. Clearly, numerous and other arrangements can be readily 
devised by those skilled in the art without departing from the scope of 
the invention.