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Filter

Foreign code F110003619
File No. A221-14WO
Posted date Jun 30, 2011
Country EPO
Application number 09762379
Gazette No. 2315353
Gazette No. 2315353
Date of filing Jun 1, 2009
Gazette Date Apr 27, 2011
Gazette Date Jul 29, 2020
International application number JP2009059953
International publication number WO2009150949
Date of international filing Jun 1, 2009
Date of international publication Dec 17, 2009
Priority data
  • P2008-151982 (Jun 10, 2008) JP
  • P2008-200907 (Aug 4, 2008) JP
  • 2009JP59953 (Jun 1, 2009) WO
Title Filter
Abstract Provided is an FIR filter capable of obtaining predetermined characteristics with a small number of input taps, delay circuits, and multipliers and achieving an improved response and low cost. In a low-pass filter, a band-pass filter, and a high-pass filter based on an FIR filter, a basic filter is configured that gives a basic impulse response function and has a filter coefficient determined from the impulse response function. Filters having different frequency characteristics are configured by changing the time scale or frequency scale of the basic filter. These filters having different frequency characteristics are combined in a cascade form or a step form, thereby constructing an FIR filter having a small number of taps.
Outline of related art and contending technology Background Art
With recent digitalization of multimedia information, the importance of arithmetic processing algorithms and arithmetic processing circuits that implement digital signal processing has been increasing. Especially, digital filters are used to eliminate noise, adjust frequency characteristics, separate signals, and so on. FIR filters having finite impulse response ensure stability always against bounded input. If the impulse response is symmetrical, the FIR filters can implement perfect linear phases. The linear phases are important characteristics in waveform transmission, measurement, sound reproduction, and so on. However, because of the trade-off between precision required in the frequency characteristics of the filter and the scale of the filter, high-order transfer characteristics are required to obtain steeper attenuation characteristics, and the circuit requires a large number of multipliers and delay elements. To create a passband filter with a very narrow band, for example, a very high degree of transfer characteristics is required, and a large number of multipliers are required accordingly.
In that context, many propositions have been made. Non-patent literature 1 describes the Remez method as a conventional method that has been used usually. Non-patent literature 2 describes a method of configuring a low-sensitivity linear-phase FIR filter by cascade connection, and the cascade connection allows the number of multipliers to be reduced. Patent literature 1 describes an FIR filter provided to vary the delay of the filter output signal.
Moreover, FIR filters for various uses such as filters for separating acoustic signal bands and filters for eliminating noise in image have been studied.
There are more conventional technologies. For example, non-patent literature 3 discloses the design and implementation of oversampled filter banks for multilevel FIR filters with low aliasing.
Non-patent literature 4 discloses a filter bank with desired frequency response and low aliasing noise.
Non-patent literature 5 discloses a realization of oversampled cosine modulated filter banks with perfect reconstruction.
Patent literature 2 discloses a filter bank and filtering method that can efficiently implement critically sampled filter banks for real-value signals and especially a cosine modulated filter bank.
Nakamura et al: "Design of FIR filter with small number of coefficients based on compactly supported fluency sampling function" (2003 IEEE Pacific Rim Conference on Communications, computers and signal processing) discloses the general concept of upsampling a basic low-pass and high-pass filter having an impulse response function configured by a piecewise polynomial with a finite support and using a value of the impulse response function at a connection point between the polynomials as a filter coefficient.
EP 1 533 898 A1 discloses low-pass and high-pass filter units with a common center frequency designed on the basis of a basic unit filter having a predetermined basic numeric string as a filter coefficient. The low-pass and high-pass filter units are connected in cascade in order to design a band pass filter.
Scope of claims [claim1]
1. A filter having desired passband characteristics, in particular a desired cut-off frequency (f1), a desired passband attenuation degree (A) and a desired frequency width Δfb(M) of the passband, comprising
-) a basic low-pass filter (L0) with passband width Δfb(0) and having an impulse response function (ψ) configured by a piecewise polynomial with a finite support and using values of the impulse response function (ψ) at connection points between the polynomials as filter coefficients c(k),
-) a basic high-pass filter (H0) with passband width Δfb(0) and having filter coefficients b(k) obtained by inverting the sign of the filter coefficients c(k) alternately, and
-) upsampled low-pass filters (Lp) and upsampled high-pass filters (Hq) combined in a cascade connection, characterized in that
-) the upsampled low-pass filters (Lp) are formed by upsampling the basic low-pass filter (L0) by all values of p (p=1,2,...P-1), with p being an upsampling factor in the time domain and P-1 being smaller than M, and
-) the upsampled high-pass filters (Hq) are formed by upsampling the basic high-pass filter (H0) by all values of q (q=1,2,... Q-1), with q being an upsampling factor in the time domain and Q-1 being smaller than M, with the maximum upsampling factor M+1 being determined by the ratio of the passband width Δfb(0) of the basic filter to the desired passband width Δfb(M).

[claim2]
2. A filter according to claim 1, characterized in that the upsampling factor P is the minimum value of p that satisfies the following equation:
f3p=f30/1+p<f3
with f3(p) being the cut-off frequency of the upsampled low-pass filter (LP) defined by a passband attenuation degree of -3dB, f3(0) being the cut-off frequency of the basic low-pass filter (L0) defined by a passband attenuation degree of -3dB and f3 being the desired cut-off frequency (f1) of the cascade connection stage defined by a desired passband attenuation degree (A) of -3dB.

[claim3]
3. A method for configuring an FIR filter to provide desired passband characteristics, in particular a desired passband width Δfb(M), the filter comprising a cascade connection of
-) a basic low-pass filter (L0) with a passband width Δfb(0) and having an impulse response function (ψ) configured by a piecewise polynomial with a finite support and using a value of the impulse response function (ψ) at a connection point between the polynomials as filter coefficients c(k),
-) a basic high-pass filter (H0) with a passband width Δfb(0) and having filter coefficients b(k) obtained by inverting the sign of the filter coefficients c(k) alternately, and
-) upsampled low-pass filters (Lp) and upsampled high-pass filters (Hq), the method comprising the step of inputting a desired center frequency (fc), a desired cut-off frequency (f1), a desired stopband frequency (f2), a desired passband attenuation degree (A) at the cut-off frequency (f1), a desired stopband attenuation degree (Ad) at the stopband frequency (f2), and a sampling frequency (fs), characterized in that the method further comprises the steps of
-) calculating the desired passband width Δfb(M) as (f1-fC)∗2 and obtaining the maximum upsampling factor M+1 by calculating the ratio of the passband width Δfb(0) of the basic filter to the desired passband width Δfb(M),
-) sequentially selecting a number of αp (αp =0,1,2,...) of the upsampled low-pass filters (Lp) formed by upsampling the basic low-pass filter (L0) by all values of p (p=1,2,...P-1), with p being an upsampling factor in the time domain and P-1 being smaller than M,
-) and sequentially selecting a number of βq (βq =0,1,2,...) of the upsampled high-pass filters (Hq) formed by upsampling the basic high-pass filter (H0) by all values of q (q=1,2,... Q-1), with q being an upsampling factor in the time domain and Q-1 being smaller than M, and
-) determining whether a cascade connection of the selected upsampled low-pass filters (Lp) and upsampled high-pass filters (Hq) conforms to the desired passband attenuation degree (A) at the cut-off frequency (f1) and to the desired stopband attenuation degree (Ad) at the stopband frequency (f2).

[claim4]
4. A method according to claim 3, characterized in that the selection of upsampled low-pass filters (Lp) and upsampled high-pass filters (Hq) is made depending on whether the attenuation degree at the stopband frequency (f2) is lower than or equal to the desired stopband attenuation degree (Ad).

[claim5]
5. A method according to claim 3 or 4, characterized in that the selection of upsampled low-pass filters (Lp) and upsampled high-pass filters (Hq) is made depending on whether the attenuation degree at the cut-off frequency (f1) is higher than or equal to a predetermined permissible level below the desired passband attenuation degree (A).

[claim6]
6. A method according to one of the claims 3 to 5, characterized in that an optimum combination of p, q, αp, and βq is selected by selecting αp and βq in descending order from stored maximum values and selecting p and q in descending order from the maximum upsampling factor M.

[claim7]
7. A method according to one of the claims 3 to 6, characterized in that αp and βq are increased, if this causes a filter gain at the desired stopband frequency (f2) of the filter to decrease.
  • Applicant
  • JAPAN SCIENCE AND TECHNOLOGY AGENCY
  • Inventor
  • KAWASAKI SHUJI
  • TORAICHI KAZUO
IPC(International Patent Classification)
Specified countries Contracting States: AT BE BG CH CY CZ DE DK EE ES FI FR GB GR HR HU IE IS IT LI LT LU LV MC MK MT NL NO PL PT RO SE SI SK TR
Reference ( R and D project ) CREST New High-Performance Information Processing Technology Supporting Information-Oriented Society - Aiming at the Creation of New High-Speed, Large-Capacity Computing Technology Based on Quantum Effects, Molecular Functions, Parallel Processing, etc.- AREA
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