JPS61100015A - Digital filter for sampling frequency conversion - Google Patents

Abstract

PURPOSE:To obtain a sufficient band stop attenuation without increasing the filter order and the number of times of multiplication/addition by connecting digital filters having different prescribed characteristics in cascade. CONSTITUTION:After an input X having a sampling frequency fS is converted into an output Y having a sampling frequency 2fS at a filter DF1, the result is converted into an output Z having a sampling frequency 4fS. In the frequencies below the fS of the characteristic I, frequencies below fA give the pass band, frequencies over fS-fA provide the block band and frequencies between the fA and the fS-fA give a transition frequency band with a prescribed slope. In frequencies below 2fS of the characteristic II, the pass band cut-off frequency is between the fA and fS/2, the band stop frequency is between 3fS/2 and 2fS-fA, and the transition frequency band with a prescribed slope is attained between the pass band cut-off frequency and the stop band cut-off frequency. Thus, a sufficient stop band attenuation is obtained without increasing the filter order and the number of times of multiplication/addition.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a digital filter for sampling frequency conversion used in fields such as digital audio.

[Conventional technology]

Recent advances in digital old data processing technology and semi-sensitive integrated circuits have made it possible to perform digital recording and playback in place of conventional analog recording media. In particular, new systems such as the compact disc (CD) and digital audio technology (DAT) were developed in the field of order and f-o.

In the field of research, audio signals such as audio and music are sampled at a constant sampling frequency and quantized to a certain bit length using an 8-digit converter, and then converted to a digital binary code. It is recorded as a data string. Then, during these reproductions, the digital data string after digital No. 16 processing such as code correction is converted into an analog signal using a D-A 4i converter, and ζ et al.
The aliasing noise (unnecessary No. 15 component other than the analog original signal that occurs with sample 1) is removed by a low-pass filter, and the complete analog signal is input to a subsequent amplifier, etc. that reproduces the signal.

However, in the low frequency filter used to reproduce this digital signal, the sample frequency is 2 of the analog original.
If it is not more than twice as large, a low-pass filter with a salivary reduction property of 9 degrees is required. Sample 1 is analog 1H of 20 KHz or less, such as voice.
Frequency: 44.1KHz''T: For audio equipment such as CDs to be recorded, this low-pass filter is used as a 2C1x
A filter with steep reduction in the range from Hz to 24.1 KHz is required.

In recent years, analog filters have been replaced by finite impulse response digital films, which have no constant temperature change or change over time, and can easily be custom-made linearly. ing. The role of this digital filter is 1'J d. Using CD as an example, 9.
Sampling frequency 44. 2 KHz digital signal
The purpose is to convert the sample frequency into data with a higher frequency of 8A2KHz or 4 times 17&4KHz. Second, among the frequency spectra of digital signals, the analog original signal of 20 KHz or less remains at 1, but as it doubles or quadruples, the spectrum of aliasing noise becomes analog. This results in a distance of 7+' from the spectrum of the original signal.

This point has been explained in more detail based on the 9th to 12th kagu. Analog number 1g below frequency fA is 21
Figures 9 to 12 (a)' and (b) show the correspondence between the temporal signal sequence and the spectral distribution in the frequency domain when sampled at a sampling frequency fS of Å or more. 9th
Figures (a) and (b) show the outside of the waveform and spectral distribution of the analog input signal. Figure 10 (1), (b
) are each sampled at 7″l samples f and frequency f days and π1
The spectral distribution of the impulse sequence failure of No. G is shown. The spectral distribution S1 of the analog source H is shown to be different from the 91st element 1 (b) and the rJ 210 element (b) in the spectrum of the sample 1 signal frequency f8.
Then, the spectral component of one square meter is s2. s3. s-
...2'1 yo are added infinitely to form a π spectral distribution.

7? When the analog signal in Figure 9 (a) is converted into one vote at twice the sampling frequency 2fa, the distribution outside the impulse series and its spectrum can be obtained, Figure 11 (a), (b). Furthermore, the impulse sequence and spectral distribution of 1G- when the analog 1J of FIG. 'Figure 2 (2).

Shown in (b). As is clear from Figure 11(b) and Figure 12(b), the sampling frequency is doubled.

If you raise it to 4@, the spectral component of the folded spectrum will be affected. In the case of twice the amount, the spectrum has components s2. as shown in FIG. 10(b). s4... is missing, 2
There will be only aliasing components centered at frequencies that are multiples of fS, and in the case of 4 times, the spectral components 82, 83, 84, etc. in Fig. 10(b) will disappear, and there will be aliasing components centered at frequencies that are multiples of 4fS. Only the ingredients.

As explained above, the sampling frequency is 2.
As the height increases, such as 4 times or 4 times, the spectral components of the aliasing or the spectrum of the analog original signal become more distant. As a result, the custom-made attenuation of the low-pass filter after the D-A converter is
As the sampling frequency becomes higher, it becomes easier to use custom-made attenuation, and it becomes possible to implement it with a low-order analog filter (for example, an active filter), and it becomes possible to achieve 20KH.
Group delay distortion due to phase rotation in the band below z is improved to 1/2.

If high-quality audio can be reproduced using such a low-order analog filter, there will be great advantages such as a reduction in the number of parts that need to be used in the manufacture of CDs and the like, and a reduction in costs. If the f conversion of the sampling frequency is doubled or quadrupled as shown in the upper case, it becomes possible to configure a low V, tracing filter with a lower-order analog filter, which is more advantageous.

L'l"L filters, etc. Currently, there are no methods other than semi-U1 integrated circuits to realize such digital filters, which require multipliers and adders with high-speed VC operation. There is no way to do this.Furthermore, quadrupling frequency conversion has stricter requirements in terms of scale and speed of the fjIF circuit than do double sampling frequency conversion.

Therefore, with the conventional digital filter that performs four times the sampling frequency conversion described below, there is a limit to the speed of the multiplier and adder. However, it is not possible to sufficiently attenuate the analysis noise for commercial quality reproduction.

Figure 13 shows the configuration of a conventional 96th order finite impulse response digital filter for 4x sampling frequency conversion. This converts the sampling frequency at once to 4 fS, which is 4 times as much as 18 by one linear phase finite innopulse response digital filter, and as shown in Figure 10 (b), S 83 + 8
The folded spectrum components of 4fe are reduced to some extent, leaving only the analog original signal spectrum S1 and the folded spectrum centered at frequencies that are multiples of 4fe.

First, in Fig. 13(a), D5 to Ds are time tVIT
delay element, m s-m 5 and filter coefficients al~a9
A multiplier for g and an adder for As. filter coefficient a1
~ai16 is at:1g7-1 to make it a linear phase
(L=1~48) The relationship is 47c and 6%.

In the above configuration, input data of sampling frequency f8 is input every period 4 T=1/fS, and 96 delay elements transmit data at a period T==174,7's, which is 1/4 of this period. The output of each terminal in the column is multiplied by the corresponding filter coefficient, and each multiplication result is applied by the 7J1'F1 device A5. This output is obtained every period T, and the sampling frequency is 41S, which is a fourfold increase.

In this example, the input sampling frequency is fS, and the delay redoubts D5 to D5 transfer at four times the speed, which is 1/
8, so the delay required JD%, K is 4T = 1/fS, only one limb data is retained, and the other 5LgI are zero @
The π-th power of the filter coefficients al to a96, which is the positive 374, is wasted. The 131st is to solve this problem.
(b) For (b), D6 to DsU time 4T = 1/f
The delay element of S, [r16 to m6 multiplied by] lI, and A6 are adders. Filter coefficient a1 in multipliers m6 to m6
Divide ~a96 into 4 groups, and every period T = 174f days, 24 delayed data and 1 of the 4 groups.
It multiplies the filter coefficients of the group and outputs the result of the addition n. In this case as well, the output is increased to four times the sampling frequency of 4fa, and the number of delay elements is increased so that the multiplication circuit becomes 174 in the above example.

[Problem that the invention seeks to solve]

In order to realize a digital filter for four times the sampling frequency using the w1 configuration as described above, it is necessary to determine filter coefficients that will give the filter characteristics as shown in FIG. In other words, if we look at frequencies 2f[+ and below, frequencies below fA are passbands, and frequencies fA and ra (fll
-fA), it is attenuated at a constant slope, and ta 1>II stop band occurs at frequencies of 18 and above.

Currently, CDs and other devices that perform 16-pit linear quantization have a dynamic range of 90 dB or more, and to take advantage of these characteristics, the stop band attenuation can be reduced to 90 dB.
Although we would like to achieve dB or more, it is extremely difficult to do so using the conventional method described above. In other words, in the conventional 96th order digital filter, the sampling frequency fSi44. If the lKH2% trace passband ripple is ±(LldB, the stopband attenuation is approximately 55
dB and 70) obtained 1. There isn't.

Incidentally, one stage of digital filter increases the sampling frequency by four times,
The relationship between the filter number N and the stopband attenuation amount A when performing the a conversion is expressed by the following equation.

N2(-10ffoj ILI(ha・δ2)-15)/
14Δli+1...(1) Blocking, δ+U7 overband ripple (when ±li aB, δIIO20116)
, δ2 is the stopband one horn pull (-20RogIoδ2=
A), ΔFH relative transition bandwidth (MuF = Fa−Fp:
Fa and Fp are n and standard frequency (hiζ), respectively.
7 stopband cutoff frequency and trace band cutoff frequency)
Yes. FIG. 15 shows the relationship between the baydN of the filter and the stopband attenuation film A.

From the above formula, the order of the filter required to obtain a stopband attenuation of 9 (] dB or more using the conventional method is calculated as follows:
As shown in FIG. 15, 153 orders are required.

Digital audio devices such as CDs are usually stereo, and must play two channels at the same time.44. The recovery of π-th, multiplication, and addition 1L that performs two-channel filtering within a period of I K HZ will be doubled. However, it is difficult to obtain a sufficient amount of stopband attenuation by simply increasing the filter order.

In the present invention, the filter order and the number of multiplication and addition strokes are increasedζ
Sufficient stopband attenuation S' can be obtained without any interference.
The present invention provides a digital filter for double the sampling frequency.

[Meaning to solve problems]

As shown in FIG. 1, the present invention is based on a first digital filter DF having a characteristic of 1, and a second digital filter DF having a characteristic of The input X is passed through the first digital filter D
After the output is subjected to YK conversion at a sampling frequency of 2fS by F, the output is subjected to ZK conversion at a sampling frequency of 4fS through a second digital filter DF. Above characteristics 1. lI is shown as r in FIGS. 2(a) and (b), respectively. Special order I only has information on frequencies below f8. and the frequency J'
Below A, there is an off-shore passband, and above the frequency (fS - 1 person) there is a cutoff band.
Frequency fA This is the turning frequency a band with a constant gradient in the darkness of Katana et al. (fS-fA). Custom-made “Ni, Frequency 21
If we look only at s and below, as shown in Figure 2 (1)]
Mouth 1 pass/jutsu power cutoff frequency is frequency fA and frequency fS/2
and the stop band, the L-base cutoff frequency g, is the frequency u, 5f
Between a/2 and circumference σ (number (2fS-fA) &
There is a transition frequency band with a constant slope between the passband cutoff frequency and the lSu stopband cutoff frequency.

When each of the digital filters DFI and DF2 are connected in cascade, the total custom order of 1 becomes as shown in Figure 2 (0), and has the same four-vote frequency conversion function as in Figure 414. .

By configuring as described above, a sufficient excavated band i decay meter can be obtained without increasing the overall number of enkaku 2 times. The reason for this is that the first digital filter DF has a steep attenuation characteristic. However, in the second digital filter DF2, the digital filter LIF cannot remove w,
, 2fS, 6f8... Since it is only necessary to remove the aliasing components centered on the frequencies, the digital filter DF
, the filter with a much lower order is fj
'I can do this with the sword 1 and others.

[Implementation row]

1st: Runo, 1st. second digital filter DF,
.

A specific example of groove formation for DF2 is shown in Figure 3. In the direction 14, the first digital filter DFlp is 80th order, the second
In the first digital filter DF, which shows a sequence composed of digital filters DF2f16y)<, the sampling amount is
The data 69 delays between groups 4-J! ! Sori, the data in ~D1 is Shu 2・□Katana 4
T: Transferred at 1/fS. And each delay amount crab i, east! '? :':'5no+=m+ and addition;:i A
1, the filter is 'l + a3 +
a5...Outside the box that is multiplied and added to a'79, filter coefficient a2, "4 + '6..."
Multiplying with ago, :It(:E) has a period of 2T
==1 / 2 fS, alternating, IQ book (hi frequency piece
The output Y of fS is given as i4.

Next, in the second digital filter DF2, the above output Y becomes an input, and each data of 81 times qh 2 to D2 at time j:'d 2 T is transmitted at a period of 2T=V2fS. Each delayed output is filtered by the filter coefficient b1+b3 in the multiplier m2~machi and the adder A2Vc.
・b13. B15 and Kazu, Kure, and Noshimaai who are stored in PaJro,
Filter coefficient s, 2+ b4...b+4+b
16 and the case where the stop and stop are added) until 1 cut T = 1
/! 2 is allowed in rs, and an output Z with a frequency of 4fS is given. If the filter coefficients are 21st (a) and (b), the first and second digital filters are respectively 21st
) Special order 1. It is set to have if.

When using this method, a sample fS similar to cD is used.
~44.1 KHz, when applied to the convex liver of 20KH7 in j5 / number of sentences fA of one analog word, the ↑ digital filter has an OT function of 80th order and stopband attenuation of 90 dB, and the second digital filter has At the 16th order, 70 dB of 11-kun superior imperial desire is possible. That is, there are 96 orders in total, which is the same as the conventional method. this is,
This is also derived from the above equation (1), and the passband ripple in the first digital filter DFI is ±Q,
1 dB, the relationship between the filter order N of the first digital filter DF1 and the stopband attenuation, PA, is calculated based on the above formula (11K).
Sleep 1. From now on, the stopband attenuation is 9
It can be seen that the filter order needs to be 77th order or higher to achieve 0 dB! In the digital filter DF2 of fci2, when the i-range pull is ±0.01 dB,
Based on the above equation (1)K, the second digital filter D
When the relationship between the filter order N of F2 and the stop band attenuation amount A is calculated, it becomes K as shown by the straight line t2 in FIG. From this, it can be seen that the filter order needs to be 16th order or higher in order to set the stopband attenuation amount to 70 dB.

The fourth south straight line t3 also has a second digital filter of 90
This is an illustration in which the total number of filter orders in a digital filter of [1, $2] is considered as 4 when expressed as dB.

Here, the first digital filter DF1'i80th order,
The second digital filter DF2″f: 16° is shown in the ear 51A. This is 176.4
If the frequency is higher than 20 KHz, the frequency is 4.
'rW range, 24.1 KJ (z ~ 152.3
K Hz Jh stopband output. In this D blocking J area, ld
Below B and at 70 dB; there is 4'+i,
When actually using a digital filter, an analog filter with the characteristics shown in Figure 6 should be added to the D-A converter. If the attenuation exceeds 1) K1
Since the 6 & 2 KH2 to 11 G and 3 K11z portions also have a Kiet f of 90 dB or more, the second digital filter has a DF2 of 70 dB (4ζ).

When using an analog filter, as in No. 64, use a filter that does not impair the linearity of the phase time characteristic in the f range below 20 KHz; (When it comes to 1 power, the present invention has 4 times the original frequency!:!, the digital filter's 11-digit conversion phase is fully utilized, and there is no group delay distortion.
It is possible to achieve sufficient separation and noise attenuation of 7''L...D.

By the way, in the π3 diagram::';j Fl″i, is gl
The digital filter D F 1 and the second digital filter DF2 are both 1st and 1st type Nyquist condition (
The general K td is applied when the filter coefficient at the sampling point does not satisfy the following conditions: 0 and 9, and the code amount interference is 0.

However, the l attenuation/' characteristic is +! As shown in FIG. 7, the digital filter DF2 with a gentle value of $2 can have a filter coefficient that satisfies the Nyquist condition, and can be configured as shown in FIG. In this column, for the first digital filter DF, it is similar to the implementation column in Figure 3, and the time 4T
It consists of 39M1 delay elements D3 to D30, multipliers m3 to m3, and adder A3. The second digital filter DF2 consists of eight delay filters D4-D4 of time 2T, multipliers m4-m4, force multiplier aA4 and period τ=J
/4 f B and a switching circuit S.

In the above configuration, the output of each delay element D4 to D4 is multiplied and added by the filter coefficient i:l b + -bs.6. niL
- There is a method in which the output Z is obtained by switching the output z1 obtained t) and the data z2 taken out from the center of the delay element array at a cycle T=114 fS using a switching circuit S.

child,? 1 [, the number of multiplications in the second digital filter DF2 is eight, which is half of that in the previous embodiment.

The overall characteristics of this filter are shown in Figure 5 (see above)
It is similar to the first example.

In this example, since the second digital filter DF fully satisfies the first Nyquist condition, its temporality (2) is limited to the punctuality shown by the solid line fb) in FIG. 2. In other words, for only frequencies below 2fS,
The passband cutoff frequency is limited to 5fS/2.

However, in the case of +(-IJ in Figure 5), 1 overband cutoff frequency 1 frequency is between the frequency fA and the frequency rs/2, and the stopband cutoff frequency is between the frequency 6ta/2 and the frequency It is sufficient if it is between (2fS-fA).

Now, let's move on to the required multiplication circuits within 1.0 km of 44.1 KHz, and explain the completed construction, each embodiment of the present invention, and the gold ratio.
I tried writing it. First, in the conventional system, the relationship between the required number of multiplications and the rupture in the blocking area is shown by the straight line t4 in FIG. From this, if we require a damping gorge of 90 d13, then . In response to this, 1. In the implementation column of Figure 6, the first digital filter DF1 requires 80 multiplications and the second digital filter D F2 tefd 16X2 = 32 multiplications, which is 112 times multiplied by 3''J. However, compared to the conventional one, it is much less.

In the example of the 7th point, the second digital filter DF2Kt- can be applied 8 times, and the total number of needles is 9.
It only takes 6 times.

Straight lines 15 and 16 in FIG. 8 correspond to lines 15 and 16 in FIG. , and in the implementation sequence ζ of FIG. The required number of multiplications when the attenuation size of the second digital filter is the same,
Giai: This shows the theoretical 1st karate of greatness. For example, in the embodiment shown in FIG. 3, if the first and second digital filters are all 90 dBK, theoretically VC can be multiplied about 112 times, and in the embodiment shown in FIG.
You can understand Suukoshichi in the episode.

However, when actually commercializing the product, the above theoretical value and the number of deviations will increase because the design is designed with a margin.

Note that in the above explanation, fc is used in a CD playback device, but it is not limited to this, and it is not limited to this, but it is also used in cases where fc requires quadruple frequency conversion, or when it is sampled from digital data that has been sampled. This method is generally effective for devices that reproduce analog signals before they have been converted. In particular, in the field of Digimel audio, it can be widely used in playback devices for digital audio tapes, circular broadcasting, etc.

〔effect〕

KJ of the present invention: Re:Yo, the first and second digital filters of the linear limited impulse response type having twice the frequency conversion function of the Okumoto ratio are connected in cascade, and the first digital filter By making the attenuation characteristic of the digital filter relatively sharp, the first stopband attenuation can be made sufficiently large without increasing the order of the second digital filter, and the aliasing noise can be sufficiently attenuated.

[Brief explanation of the drawing]

Figure 1 is a block diagram showing the components of the present invention, Figure 2'9
+-1J I Figure 3 is a characteristic diagram showing each digital filter and a custom-made filter according to the present invention. Figure 3 is a fixed block diagram showing one residential row of the present invention. Figure 4 is a diagram showing the order and order of the filter according to the present invention. 9 is a characteristic diagram showing the relationship with the land band attenuation 1, 5th is a constant characteristic diagram showing the depreciation characteristic according to one embodiment of the present invention 4, and 6 is a characteristic diagram of analog filter 6 which is read directly to the rear part. A custom-made drawing showing a good example, Fig. 7 is a block diagram showing another Jitsuhata by Akira Motoyaku, Fig. 8 is a custom-made drawing showing the IA section of Urataka with multiplication lol number and attenuation 1,・Ear 9, evil (a),
(b) is an analog signal waveform diagram and spectral distribution diagram, respectively. Figures 10 (1) and (b) are O impulse sequence and its spectral distribution diagram at sample f frequency fS, respectively. Figure 11 (a), (b) is an impulse sequence and its spectral distribution diagram at a sampling frequency of 2f8, respectively; Figures 12 (a) and (b) are impulse sequences and its spectral distribution diagram at a sampling frequency of 4fEI; The figure is a block diagram showing a conventional 4-way sampling frequency conversion digital filter.
The figure shows the attenuation characteristics necessary for 4 times sample north wave number conversion, and FIG. 15 shows the relationship between the filter order and the attenuation amount due to the conventional groove bottom, and has a characteristic of 4. DFl...First digital filter DF2...Second digital filter D1%D1...Delay element
n111~ml... Multiplier Al... Adder
m2~m2... Multiplier A2... Adder
D3-D3...delay elements m3-m3...multiplier
A3...Adder D4-D4...Delay element m4
~m4... Multiplier A4... Adder S...
・More than switching circuits Japan Precision Circuits Co., Ltd. Fig. 2 (C) Fig. 3 Fig. 4 Blocking IFt failure reward tA (dB) Fig. 5 Fig. 7 Blocking 1 (d B) Figure 9 (a) (b) Figure 11 (Q) (b
) Fig. 18 (b) Fig. 14 Inhibition band acid 5) A (dB)'

Claims (1)

[Claims] An analog signal with a frequency f_A or lower is sampled at a sampling frequency f_S.
(However, if a binary code digital data string sampled at f_S>2f_A) is input, and if we look at custom filters only for frequencies below f_S, the pass band is below frequency f_A, and the stop band is above frequency (f_S - f_A). ,
a phase-linear finite impulse response type first digital filter having a double sampling frequency conversion function and having a filter coefficient having a transition frequency band with a constant slope between frequency f_A and frequency (f_S-f_A); When inputting the output of the first digital filter whose frequency is 2f_S and looking at the filter characteristics only for frequencies below 2f_S, the passband cutoff frequency is between the frequency f_A and the frequency f_S/2, and the stopband cutoff is The frequency is frequency 3f_S/2 and frequency (2f_S-f_
A) A phase-linear finite element having a double sampling frequency conversion function with a custom-made filter that has a transition frequency band with a constant slope between the passband cutoff frequency and the upperband cutoff frequency. 1. A digital filter for sampling frequency conversion, comprising a second digital filter of impulse response type, and characterized in that the first digital filter and the second digital filter are continuously connected.