473:
1527:
3443:
173:
3365:
27:
1292:
1225:
2079:
1522:{\displaystyle V_{\text{out}}(t)=\overbrace {C\,\left({\frac {\operatorname {d} V_{\text{in}}}{\operatorname {d} t}}-{\frac {\operatorname {d} V_{\text{out}}}{\operatorname {d} t}}\right)} ^{I(t)}\,R=RC\,\left({\frac {\operatorname {d} V_{\text{in}}}{\operatorname {d} t}}-{\frac {\operatorname {d} V_{\text{out}}}{\operatorname {d} t}}\right)}
1006:
1898:
3117:
and therefore a high corner frequency of the filter. Hence, this case corresponds to a high-pass filter with a very wide stopband. Because it requires large (i.e., fast) changes and tends to quickly forget its prior output values, it can only pass relatively high frequencies, as would be expected
984:
Discrete-time high-pass filters can also be designed. Discrete-time filter design is beyond the scope of this article; however, a simple example comes from the conversion of the continuous-time high-pass filter above to a discrete-time realization. That is, the continuous-time behavior can be
3356:
power. However, that model's basic design has been superseded by newer designs such as the Crown Macro-Tech series developed in the late 1980s which included 10 Hz high-pass filtering on the inputs and switchable 35 Hz high-pass filtering on the outputs. Another example is the
3036:
of the filter. Hence, this case corresponds to a high-pass filter with a very narrow stopband. Because it is excited by small changes and tends to hold its prior output values for a long time, it can pass relatively low frequencies. However, a constant input (i.e., an input with
2221:
3388:. Some models have fixed-slope, fixed-frequency high-pass filters at 80 or 100 Hz that can be engaged; other models have sweepable high-pass filters, filters of fixed slope that can be set within a specified frequency range, such as from 20 to 400 Hz on the
1884:
183:
A resistor and either a capacitor or an inductor can be configured as a first-order high-pass filter. The simple first-order capacitive high-pass filter shown in Figure 1 is implemented by placing an input voltage across the series combination of a
136:(time-varying voltage or current) applied to its input port. A high-pass filter attenuates frequency components below a certain frequency, called its cutoff frequency, allowing higher frequency components to pass through. This contrasts with a
3434:—a low-frequency boost for very close sources. This low-frequency boost commonly causes problems up to 200 or 300 Hz, but Main notes that he has seen microphones that benefit from a 500 Hz high-pass filter setting on the console.
1220:{\displaystyle {\begin{cases}V_{\text{out}}(t)=I(t)\,R&{\text{(V)}}\\Q_{c}(t)=C\,\left(V_{\text{in}}(t)-V_{\text{out}}(t)\right)&{\text{(Q)}}\\I(t)={\frac {\operatorname {d} Q_{c}}{\operatorname {d} t}}&{\text{(I)}}\end{cases}}}
3278:
616:
2074:{\displaystyle y_{i}=\overbrace {{\frac {RC}{RC+\Delta _{T}}}y_{i-1}} ^{\text{Decaying contribution from prior inputs}}+\overbrace {{\frac {RC}{RC+\Delta _{T}}}\left(x_{i}-x_{i-1}\right)} ^{\text{Contribution from change in input}}}
315:
956:
Filters of higher order have steeper slope in the stopband, such that the slope of n-order filters equals 20n dB per decade. Higher order filters can be achieved simply by cascading these first order filters. While
723:
2414:
418:
2712:
2640:
2090:
159:, which is inversely related to frequency, a high pass optical filter, which attenuates light frequencies below a cutoff frequency, is often called a short-pass filter; it attenuates longer wavelengths.
3352:
beginning in the 1960s, did not have high-pass filtering at all, and could be used to amplify the DC signal of a common 9-volt battery at the input to supply 18 volts DC in an emergency for
961:
and loading must be taken into account when chaining passive filters, active filters can be easily chained because the signal is restored by the output of the op amp at each stage. Various
2853:
1741:
1649:
2523:
2472:
3446:
Example of high-pass filter applied to the right half of a photograph. The left side is unmodified, Right side is with a high-pass filter applied (in this case, with a radius of 4.9).
3283:
An alternative, which provides good quality sound without inductors (which are prone to parasitic coupling, are expensive, and may have significant internal resistance) is to employ
1749:
3361:
PLX amplifier series which includes an internal 5 Hz high-pass filter which is applied to the inputs whenever the optional 50 and 30 Hz high-pass filters are turned off.
2256:
2791:
1676:
1584:
2983:
A large α implies that the output will decay very slowly but will also be strongly influenced by even small changes in input. By the relationship between parameter α and
2742:
2329:
1557:
1264:
2546:
2349:
2276:
3190:
938:
2573:
3139:
3115:
3092:
3062:
3030:
3007:
2814:
2765:
2302:
2944:
1284:
490:
3402:. Veteran systems engineer and live sound mixer Bruce Main recommends that high-pass filters be engaged for most mixer input sources, except for those such as
206:
1532:
This equation can be discretized. For simplicity, assume that samples of the input and output are taken at evenly spaced points in time separated by
2863:
The filter recurrence relation provides a way to determine the output samples in terms of the input samples and the preceding output. The following
82:
in the context of audio engineering. High-pass filters have many uses, such as blocking DC from circuitry sensitive to non-zero average voltages or
645:
3680:
3337:, for preventing the amplification of DC currents which may harm the amplifier, rob the amplifier of headroom, and generate waste heat at the
2357:
931:
3752:
347:
3430:
system and wrapping around to the stage. Main indicates that high-pass filters are commonly used for directional microphones which have a
2651:
2216:{\displaystyle y_{i}=\alpha y_{i-1}+\alpha (x_{i}-x_{i-1})\qquad {\text{where}}\qquad \alpha \triangleq {\frac {RC}{RC+\Delta _{T}}}}
3566:
924:
2581:
3187:, applied to a tweeter with a resistance of 10 Ω, will determine the capacitor value for a cut-off frequency of 5 kHz.
3690:
3183:(although very simple high-pass filters for tweeters can consist of a series capacitor and nothing else). As an example, the
3455:
3720:
2867:
algorithm will simulate the effect of a high-pass filter on a series of digital samples, assuming equally spaced samples:
3632:
3832:
3596:
144:, which allows a certain band of frequencies through and attenuates frequencies both higher and lower than the band.
3163:
while attenuating bass signals which could interfere with, or damage, the speaker. When such a filter is built into a
151:
a high pass filter is a transparent or translucent window of colored material that allows light longer than a certain
3542:
155:
to pass through and attenuates light of shorter wavelengths. Since light is often measured not by frequency but by
3745:
2819:
3466:, or sharpening, operation used in image editing software is a high-boost filter, a generalization of high-pass.
1681:
1589:
1286:. Substituting Equation (Q) into Equation (I) and then Equation (I) into Equation (V) gives:
47:
3723:, an intuitive explanation of the source of phase shift in a high-pass filter. Also verifies simple passive LPF
2477:
2426:
1879:{\displaystyle y_{i}=RC\,\left({\frac {x_{i}-x_{i-1}}{\Delta _{T}}}-{\frac {y_{i}-y_{i-1}}{\Delta _{T}}}\right)}
3714:
758:
3306:
Rumble filters are high-pass filters applied to the removal of unwanted sounds near to the lower end of the
3827:
849:
197:
71:
3738:
2229:
993:
3071:
is large) to cause the output to change much. By the relationship between parameter α and time constant
3067:
A small α implies that the output will decay quickly and will require large changes in the input (i.e.,
3761:
962:
118:
67:
43:
3454:
to perform image modifications, enhancements, noise reduction, etc., using designs done in either the
966:
866:
819:
814:
782:
2770:
1654:
1015:
3664:
Main, Bruce (February 16, 2010). "Cut 'Em Off At The Pass: Effective Uses Of High-Pass
Filtering".
3431:
1562:
480:
Figure 2 shows an active electronic implementation of a first-order high-pass filter using an
3822:
2721:
2307:
1535:
860:
729:
20:
3534:
105:
have the opposite meanings, with a "high-pass" filter (more commonly "short-pass") passing only
3418:
inputs) do not need high-pass filtering as they are not subject to modulation by low-frequency
3399:
3273:{\displaystyle C={\frac {1}{2\pi fR}}={\frac {1}{6.28\times 5000\times 10}}=3.18\times 10^{-6}}
872:
832:
2084:
That is, this discrete-time implementation of a simple continuous-time RC high-pass filter is
1233:
3334:
2531:
2334:
2261:
481:
109:
wavelengths (higher frequencies), and vice versa for "low-pass" (more commonly "long-pass").
3500:
2967:
However, the earlier form shows how the parameter α changes the impact of the prior output
2551:
97:
In the optical domain filters are often characterised by wavelength rather than frequency.
611:{\displaystyle {\frac {V_{\rm {out}}(s)}{V_{\rm {in}}(s)}}={\frac {-sR_{2}C}{1+sR_{1}C}}.}
8:
3574:
3349:
1890:
733:
3121:
3097:
3074:
3044:
3012:
2989:
2796:
2747:
2284:
3527:
3419:
3393:
3345:
3041:) will always decay to zero, as would be expected with a high-pass filter with a large
2929:
1269:
978:
958:
877:
789:
461:
125:
3803:
3724:
3686:
3538:
3319:
839:
771:
193:
2870:// Return RC high-pass filter output samples, given input samples, // time interval
472:
3792:
3787:
3480:
3459:
3451:
3300:
3284:
3033:
2947:
844:
794:
91:
55:
3782:
3772:
3463:
3410:
and piano, sources which will have useful low-frequency sounds. Main writes that
3172:
3156:
986:
809:
799:
464:
reaches -3dB referenced to the at an infinite frequency at the cutoff frequency.
310:{\displaystyle {\frac {V_{\rm {out}}(s)}{V_{\rm {in}}(s)}}={\frac {sRC}{1+sRC}}.}
141:
137:
87:
83:
3607:
3490:
3427:
3389:
3373:
3353:
3168:
762:
754:
176:
Figure 1: A passive, analog, first-order high-pass filter, realized by an
3816:
3639:
3385:
3311:
3307:
3288:
2984:
2279:
854:
804:
736:
passband gain. That is, high-frequency signals are inverted and amplified by
329:
3730:
19:
This article is about an electronic component. For the
Australian band, see
3442:
3717:, a short primer on the mathematical analysis of (electrical) LTI systems.
3495:
3407:
3338:
3330:
3292:
3164:
1743:
which correspond to the same points in time. Making these substitutions:
997:
910:
718:{\displaystyle f_{c}={\frac {1}{2\pi \tau }}={\frac {1}{2\pi R_{1}C}},\,}
63:
977:
For another method of conversion from continuous- to discrete-time, see
62:
signals with frequencies lower than the cutoff frequency. The amount of
3475:
3415:
3341:
3296:
2864:
2409:{\displaystyle RC=\Delta _{T}\left({\frac {\alpha }{1-\alpha }}\right)}
905:
900:
895:
449:
177:
156:
152:
3364:
3155:
High-pass filters have many applications. They are used as part of an
172:
140:, which attenuates frequencies higher than a certain frequency, and a
3423:
3403:
3380:
software. This high-pass filter has a slope of 18 dB per octave.
3358:
3315:
3310:
or below. For example, noises (e.g., footsteps, or motor noises from
413:{\displaystyle f_{c}={\frac {1}{2\pi \tau }}={\frac {1}{2\pi RC}},\,}
185:
129:
59:
51:
3709:
3485:
3180:
622:
189:
122:
26:
3291:
or active digital filters with separate power amplifiers for each
2707:{\displaystyle f_{c}={\frac {1-\alpha }{2\pi \alpha \Delta _{T}}}}
3411:
3160:
484:. The transfer function of this linear time-invariant system is:
3318:) may be removed because they are undesired or may overload the
3377:
3369:
3323:
3184:
3176:
441:
332:(τ); it is inversely proportional to the cutoff frequency
148:
133:
3682:
Computer processing of remotely sensed images: an introduction
66:
for each frequency depends on the filter design. A high-pass
457:
433:
2635:{\displaystyle \alpha ={\frac {1}{2\pi \Delta _{T}f_{c}+1}}}
192:
and using the voltage across the resistor as an output. The
3396:
1213:
3384:
Mixing consoles often include high-pass filtering at each
3564:
3368:
A 75 Hz "low cut" filter from an input channel of a
2816:
is significantly smaller than the sampling interval, and
3668:. Framingham, Massachusetts: ProSoundWeb, EH Publishing.
3450:
High-pass and low-pass filters are also used in digital
3565:
Andrews, Keith; posting as ssltech (January 11, 2010).
753:
All of these first-order high-pass filters are called
3193:
3124:
3100:
3077:
3047:
3015:
2992:
2932:
2822:
2799:
2773:
2750:
2724:
2654:
2584:
2554:
2534:
2480:
2429:
2360:
2337:
2310:
2287:
2264:
2232:
2093:
1901:
1752:
1684:
1657:
1592:
1565:
1538:
1295:
1272:
1236:
1009:
648:
493:
350:
209:
86:
devices. They can also be used in conjunction with a
3685:(3rd ed.). John Wiley and Sons. p. 181.
3526:
3272:
3133:
3109:
3086:
3056:
3024:
3001:
2938:
2847:
2808:
2785:
2759:
2736:
2706:
2634:
2567:
2540:
2517:
2466:
2408:
2343:
2323:
2296:
2270:
2250:
2215:
2073:
1878:
1735:
1670:
1643:
1578:
1551:
1521:
1278:
1258:
1219:
717:
610:
412:
309:
992:From the circuit in Figure 1 above, according to
3814:
3520:
3518:
3516:
2767:time constant equal to the sampling period. If
320:The product of the resistance and capacitance (
3678:
3392:Heritage 3000, or 20 to 20,000 Hz on the
1266:is the charge stored in the capacitor at time
3760:
3746:
2907:α := RC / (RC + dt) y := x
2858:
932:
3567:"Re: Running the board for a show this big?"
3513:
2919:n y := α × y + α × (x − x)
2848:{\displaystyle RC\approx \alpha \Delta _{T}}
972:
969:for higher orders exist, which ease design.
765:is well below the filter's cutoff frequency.
16:Type of electronic circuit or optical filter
1736:{\displaystyle (y_{1},y_{2},\ldots ,y_{n})}
1644:{\displaystyle (x_{1},x_{2},\ldots ,x_{n})}
162:
3753:
3739:
3715:ECE 209: Review of Circuits as LTI Systems
3558:
3179:and so often employs both a capacitor and
2518:{\displaystyle RC={\frac {1}{2\pi f_{c}}}}
2467:{\displaystyle f_{c}={\frac {1}{2\pi RC}}}
939:
925:
3524:
1772:
1439:
1426:
1325:
1092:
1052:
714:
476:Figure 2: An active high-pass filter
409:
30:Ideal high-pass filter frequency response
3441:
3363:
3094:above, a small α corresponds to a small
3009:above, a large α corresponds to a large
471:
171:
25:
3657:
3571:Recording, Engineering & Production
1976:Decaying contribution from prior inputs
3815:
3422:—low frequency sounds coming from the
2926:The loop which calculates each of the
167:
3734:
3118:with a high-pass filter with a small
467:
3663:
3633:"User Manual: PLX Series Amplifiers"
3329:High-pass filters are also used for
2964:n y := α × (y + x − x)
3727:by means of trigonometric identity.
3606:. Crown Audio. 2007. Archived from
3295:. Such low-current and low-voltage
2251:{\displaystyle 0\leq \alpha \leq 1}
13:
2836:
2692:
2604:
2371:
2312:
2201:
2008:
1940:
1860:
1812:
1540:
1502:
1484:
1466:
1448:
1388:
1370:
1352:
1334:
1191:
1173:
535:
532:
509:
506:
503:
251:
248:
225:
222:
219:
14:
3844:
3703:
3638:. QSC Audio. 1999. Archived from
2067:Contribution from change in input
3159:to direct high frequencies to a
2304:in terms of the sampling period
1889:And rearranging terms gives the
951:
3721:ECE 209: Sources of Phase Shift
3145:
2258:. The expression for parameter
2173:
2167:
1678:be represented by the sequence
1586:be represented by the sequence
621:In this case, the filter has a
3672:
3625:
3589:
2786:{\displaystyle \alpha \ll 0.5}
2164:
2132:
1730:
1685:
1671:{\displaystyle V_{\text{out}}}
1638:
1593:
1421:
1415:
1312:
1306:
1253:
1247:
1164:
1158:
1136:
1130:
1114:
1108:
1083:
1077:
1049:
1043:
1034:
1028:
639:and has a cutoff frequency of
547:
541:
521:
515:
263:
257:
237:
231:
112:
1:
3597:"Operation Manual: MA-5002VZ"
3573:. ProSoundWeb. Archived from
3529:The Art of Sound Reproduction
3506:
1579:{\displaystyle V_{\text{in}}}
815:Optimum "L" (Legendre) filter
198:linear time-invariant system
72:linear time-invariant system
7:
3469:
2737:{\displaystyle \alpha =0.5}
2324:{\displaystyle \Delta _{T}}
1552:{\displaystyle \Delta _{T}}
74:. It is sometimes called a
10:
3849:
2859:Algorithmic implementation
976:
18:
3833:Filter frequency response
3801:
3768:
3762:Signal-processing filters
3280:, or approx 3.2 μF.
3167:cabinet it is normally a
1559:time. Let the samples of
973:Discrete-time realization
967:network synthesis filters
867:Bridged T delay equaliser
783:Network synthesis filters
3710:Common Impulse Responses
3666:Live Sound International
3533:. Focal Press. pp.
3525:Watkinson, John (1998).
3437:
3150:
1259:{\displaystyle Q_{c}(t)}
163:Continuous-time circuits
70:is usually modeled as a
3679:Paul M. Mather (2004).
2541:{\displaystyle \alpha }
2344:{\displaystyle \alpha }
2271:{\displaystyle \alpha }
833:Image impedance filters
800:Elliptic (Cauer) filter
757:, because they perform
728:Because this filter is
21:High Pass Filter (band)
3778:High-pass filter (HPF)
3447:
3414:inputs (as opposed to
3400:digital mixing console
3381:
3335:audio power amplifiers
3333:at the inputs of many
3299:crossovers are called
3274:
3135:
3111:
3088:
3058:
3026:
3003:
2940:
2849:
2810:
2787:
2761:
2738:
2708:
2636:
2569:
2542:
2519:
2468:
2410:
2345:
2325:
2298:
2278:yields the equivalent
2272:
2252:
2217:
2075:
1880:
1737:
1672:
1645:
1580:
1553:
1523:
1280:
1260:
1221:
996:and the definition of
873:Composite image filter
719:
612:
477:
414:
311:
180:
54:higher than a certain
31:
3773:Low-pass filter (LPF)
3445:
3367:
3344:. One amplifier, the
3275:
3171:that also includes a
3136:
3112:
3089:
3059:
3027:
3004:
2950:into the equivalent:
2941:
2850:
2811:
2788:
2762:
2739:
2709:
2637:
2570:
2568:{\displaystyle f_{c}}
2543:
2520:
2469:
2411:
2346:
2326:
2299:
2273:
2253:
2218:
2076:
1881:
1738:
1673:
1646:
1581:
1554:
1524:
1281:
1261:
1222:
850:General image filters
820:Linkwitz–Riley filter
720:
613:
482:operational amplifier
475:
415:
312:
175:
29:
3501:Circular convolution
3348:model DC300 made by
3191:
3122:
3098:
3075:
3045:
3032:and therefore a low
3013:
2990:
2930:
2874:, and time constant
2820:
2797:
2771:
2748:
2722:
2652:
2582:
2552:
2532:
2478:
2427:
2358:
2335:
2308:
2285:
2262:
2230:
2091:
1899:
1750:
1682:
1655:
1590:
1563:
1536:
1293:
1270:
1234:
1007:
646:
491:
348:
207:
3828:Synthesiser modules
3645:on February 9, 2010
3350:Crown International
1891:recurrence relation
857:(constant R) filter
168:First-order passive
3613:on January 3, 2010
3448:
3382:
3346:professional audio
3270:
3134:{\displaystyle RC}
3131:
3110:{\displaystyle RC}
3107:
3087:{\displaystyle RC}
3084:
3057:{\displaystyle RC}
3054:
3025:{\displaystyle RC}
3022:
3002:{\displaystyle RC}
2999:
2936:
2845:
2809:{\displaystyle RC}
2806:
2783:
2760:{\displaystyle RC}
2757:
2734:
2704:
2632:
2565:
2538:
2515:
2464:
2406:
2341:
2321:
2297:{\displaystyle RC}
2294:
2268:
2248:
2213:
2071:
1876:
1733:
1668:
1641:
1576:
1549:
1519:
1276:
1256:
1217:
1212:
979:Bilinear transform
959:impedance matching
790:Butterworth filter
774:electronic filters
761:for signals whose
715:
608:
478:
468:First-order active
462:frequency response
410:
307:
181:
132:components from a
126:electronic circuit
117:In electronics, a
32:
3810:
3809:
3804:Electronic filter
3725:transfer function
3692:978-0-470-84919-4
3604:Macro-Tech Series
3320:RIAA equalization
3301:active crossovers
3289:active RC filters
3246:
3219:
2979:. In particular,
2939:{\displaystyle n}
2702:
2630:
2513:
2462:
2400:
2211:
2171:
2070:
2068:
2063:
2018:
1979:
1977:
1972:
1950:
1869:
1821:
1665:
1573:
1512:
1497:
1476:
1461:
1425:
1409:
1398:
1383:
1362:
1347:
1303:
1279:{\displaystyle t}
1208:
1201:
1149:
1127:
1105:
1061:
1025:
963:filter topologies
949:
948:
840:Constant k filter
709:
678:
603:
551:
404:
380:
302:
267:
194:transfer function
44:electronic filter
3840:
3793:Band-stop filter
3788:Band-pass filter
3755:
3748:
3741:
3732:
3731:
3697:
3696:
3676:
3670:
3669:
3661:
3655:
3654:
3652:
3650:
3644:
3637:
3629:
3623:
3622:
3620:
3618:
3612:
3601:
3593:
3587:
3586:
3584:
3582:
3562:
3556:
3555:
3553:
3551:
3532:
3522:
3481:Band-stop filter
3460:frequency domain
3452:image processing
3432:proximity effect
3285:bi-amplification
3279:
3277:
3276:
3271:
3269:
3268:
3247:
3245:
3225:
3220:
3218:
3201:
3140:
3138:
3137:
3132:
3116:
3114:
3113:
3108:
3093:
3091:
3090:
3085:
3070:
3063:
3061:
3060:
3055:
3040:
3034:corner frequency
3031:
3029:
3028:
3023:
3008:
3006:
3005:
3000:
2978:
2970:
2945:
2943:
2942:
2937:
2854:
2852:
2851:
2846:
2844:
2843:
2815:
2813:
2812:
2807:
2792:
2790:
2789:
2784:
2766:
2764:
2763:
2758:
2743:
2741:
2740:
2735:
2713:
2711:
2710:
2705:
2703:
2701:
2700:
2699:
2680:
2669:
2664:
2663:
2641:
2639:
2638:
2633:
2631:
2629:
2622:
2621:
2612:
2611:
2592:
2575:are related by:
2574:
2572:
2571:
2566:
2564:
2563:
2547:
2545:
2544:
2539:
2524:
2522:
2521:
2516:
2514:
2512:
2511:
2510:
2491:
2473:
2471:
2470:
2465:
2463:
2461:
2444:
2439:
2438:
2415:
2413:
2412:
2407:
2405:
2401:
2399:
2385:
2379:
2378:
2350:
2348:
2347:
2342:
2330:
2328:
2327:
2322:
2320:
2319:
2303:
2301:
2300:
2295:
2277:
2275:
2274:
2269:
2257:
2255:
2254:
2249:
2222:
2220:
2219:
2214:
2212:
2210:
2209:
2208:
2189:
2181:
2172:
2169:
2163:
2162:
2144:
2143:
2125:
2124:
2103:
2102:
2080:
2078:
2077:
2072:
2069:
2066:
2064:
2059:
2058:
2054:
2053:
2052:
2034:
2033:
2019:
2017:
2016:
2015:
1996:
1988:
1985:
1983:
1978:
1975:
1973:
1968:
1967:
1966:
1951:
1949:
1948:
1947:
1928:
1920:
1917:
1915:
1911:
1910:
1885:
1883:
1882:
1877:
1875:
1871:
1870:
1868:
1867:
1858:
1857:
1856:
1838:
1837:
1827:
1822:
1820:
1819:
1810:
1809:
1808:
1790:
1789:
1779:
1762:
1761:
1742:
1740:
1739:
1734:
1729:
1728:
1710:
1709:
1697:
1696:
1677:
1675:
1674:
1669:
1667:
1666:
1663:
1650:
1648:
1647:
1642:
1637:
1636:
1618:
1617:
1605:
1604:
1585:
1583:
1582:
1577:
1575:
1574:
1571:
1558:
1556:
1555:
1550:
1548:
1547:
1528:
1526:
1525:
1520:
1518:
1514:
1513:
1511:
1500:
1499:
1498:
1495:
1482:
1477:
1475:
1464:
1463:
1462:
1459:
1446:
1424:
1410:
1405:
1404:
1400:
1399:
1397:
1386:
1385:
1384:
1381:
1368:
1363:
1361:
1350:
1349:
1348:
1345:
1332:
1320:
1318:
1305:
1304:
1301:
1285:
1283:
1282:
1277:
1265:
1263:
1262:
1257:
1246:
1245:
1226:
1224:
1223:
1218:
1216:
1215:
1209:
1206:
1202:
1200:
1189:
1188:
1187:
1171:
1150:
1147:
1143:
1139:
1129:
1128:
1125:
1107:
1106:
1103:
1076:
1075:
1062:
1059:
1027:
1026:
1023:
994:Kirchhoff's Laws
941:
934:
927:
845:m-derived filter
795:Chebyshev filter
768:
767:
724:
722:
721:
716:
710:
708:
704:
703:
684:
679:
677:
663:
658:
657:
617:
615:
614:
609:
604:
602:
598:
597:
578:
574:
573:
557:
552:
550:
540:
539:
538:
524:
514:
513:
512:
495:
460:. The filter's
419:
417:
416:
411:
405:
403:
386:
381:
379:
365:
360:
359:
316:
314:
313:
308:
303:
301:
284:
273:
268:
266:
256:
255:
254:
240:
230:
229:
228:
211:
92:band-pass filter
56:cutoff frequency
36:high-pass filter
3848:
3847:
3843:
3842:
3841:
3839:
3838:
3837:
3813:
3812:
3811:
3806:
3797:
3783:All-pass filter
3764:
3759:
3706:
3701:
3700:
3693:
3677:
3673:
3662:
3658:
3648:
3646:
3642:
3635:
3631:
3630:
3626:
3616:
3614:
3610:
3599:
3595:
3594:
3590:
3580:
3578:
3577:on 15 July 2011
3563:
3559:
3549:
3547:
3545:
3523:
3514:
3509:
3472:
3464:unsharp masking
3440:
3376:as measured by
3322:circuit of the
3261:
3257:
3229:
3224:
3205:
3200:
3192:
3189:
3188:
3173:low-pass filter
3157:audio crossover
3153:
3148:
3123:
3120:
3119:
3099:
3096:
3095:
3076:
3073:
3072:
3068:
3046:
3043:
3042:
3038:
3014:
3011:
3010:
2991:
2988:
2987:
2976:
2968:
2965:
2946:outputs can be
2931:
2928:
2927:
2924:
2861:
2839:
2835:
2821:
2818:
2817:
2798:
2795:
2794:
2772:
2769:
2768:
2749:
2746:
2745:
2723:
2720:
2719:
2695:
2691:
2681:
2670:
2668:
2659:
2655:
2653:
2650:
2649:
2617:
2613:
2607:
2603:
2596:
2591:
2583:
2580:
2579:
2559:
2555:
2553:
2550:
2549:
2533:
2530:
2529:
2506:
2502:
2495:
2490:
2479:
2476:
2475:
2448:
2443:
2434:
2430:
2428:
2425:
2424:
2420:Recalling that
2389:
2384:
2380:
2374:
2370:
2359:
2356:
2355:
2336:
2333:
2332:
2315:
2311:
2309:
2306:
2305:
2286:
2283:
2282:
2263:
2260:
2259:
2231:
2228:
2227:
2226:By definition,
2204:
2200:
2190:
2182:
2180:
2168:
2152:
2148:
2139:
2135:
2114:
2110:
2098:
2094:
2092:
2089:
2088:
2065:
2042:
2038:
2029:
2025:
2024:
2020:
2011:
2007:
1997:
1989:
1987:
1986:
1984:
1974:
1956:
1952:
1943:
1939:
1929:
1921:
1919:
1918:
1916:
1906:
1902:
1900:
1897:
1896:
1863:
1859:
1846:
1842:
1833:
1829:
1828:
1826:
1815:
1811:
1798:
1794:
1785:
1781:
1780:
1778:
1777:
1773:
1757:
1753:
1751:
1748:
1747:
1724:
1720:
1705:
1701:
1692:
1688:
1683:
1680:
1679:
1662:
1658:
1656:
1653:
1652:
1632:
1628:
1613:
1609:
1600:
1596:
1591:
1588:
1587:
1570:
1566:
1564:
1561:
1560:
1543:
1539:
1537:
1534:
1533:
1501:
1494:
1490:
1483:
1481:
1465:
1458:
1454:
1447:
1445:
1444:
1440:
1411:
1387:
1380:
1376:
1369:
1367:
1351:
1344:
1340:
1333:
1331:
1330:
1326:
1321:
1319:
1300:
1296:
1294:
1291:
1290:
1271:
1268:
1267:
1241:
1237:
1235:
1232:
1231:
1211:
1210:
1205:
1203:
1190:
1183:
1179:
1172:
1170:
1152:
1151:
1146:
1144:
1124:
1120:
1102:
1098:
1097:
1093:
1071:
1067:
1064:
1063:
1058:
1056:
1022:
1018:
1011:
1010:
1008:
1005:
1004:
982:
975:
954:
945:
916:
915:
891:
883:
882:
878:mm'-type filter
835:
825:
824:
810:Gaussian filter
785:
773:
759:differentiation
755:differentiators
749:
742:
699:
695:
688:
683:
667:
662:
653:
649:
647:
644:
643:
638:
631:
593:
589:
579:
569:
565:
558:
556:
531:
530:
526:
525:
502:
501:
497:
496:
494:
492:
489:
488:
470:
431:
390:
385:
369:
364:
355:
351:
349:
346:
345:
340:
285:
274:
272:
247:
246:
242:
241:
218:
217:
213:
212:
210:
208:
205:
204:
170:
165:
142:bandpass filter
138:low-pass filter
115:
88:low-pass filter
84:radio frequency
80:bass-cut filter
24:
17:
12:
11:
5:
3846:
3836:
3835:
3830:
3825:
3823:Linear filters
3808:
3807:
3802:
3799:
3798:
3796:
3795:
3790:
3785:
3780:
3775:
3769:
3766:
3765:
3758:
3757:
3750:
3743:
3735:
3729:
3728:
3718:
3712:
3705:
3704:External links
3702:
3699:
3698:
3691:
3671:
3656:
3624:
3588:
3557:
3543:
3511:
3510:
3508:
3505:
3504:
3503:
3498:
3493:
3491:Differentiator
3488:
3483:
3478:
3471:
3468:
3456:spatial domain
3439:
3436:
3428:public address
3374:mixing console
3354:mixing console
3312:record players
3267:
3264:
3260:
3256:
3253:
3250:
3244:
3241:
3238:
3235:
3232:
3228:
3223:
3217:
3214:
3211:
3208:
3204:
3199:
3196:
3169:passive filter
3152:
3149:
3147:
3144:
3143:
3142:
3130:
3127:
3106:
3103:
3083:
3080:
3065:
3053:
3050:
3021:
3018:
2998:
2995:
2952:
2935:
2869:
2860:
2857:
2842:
2838:
2834:
2831:
2828:
2825:
2805:
2802:
2782:
2779:
2776:
2756:
2753:
2733:
2730:
2727:
2716:
2715:
2698:
2694:
2690:
2687:
2684:
2679:
2676:
2673:
2667:
2662:
2658:
2643:
2642:
2628:
2625:
2620:
2616:
2610:
2606:
2602:
2599:
2595:
2590:
2587:
2562:
2558:
2537:
2526:
2525:
2509:
2505:
2501:
2498:
2494:
2489:
2486:
2483:
2460:
2457:
2454:
2451:
2447:
2442:
2437:
2433:
2418:
2417:
2404:
2398:
2395:
2392:
2388:
2383:
2377:
2373:
2369:
2366:
2363:
2340:
2318:
2314:
2293:
2290:
2267:
2247:
2244:
2241:
2238:
2235:
2224:
2223:
2207:
2203:
2199:
2196:
2193:
2188:
2185:
2179:
2176:
2166:
2161:
2158:
2155:
2151:
2147:
2142:
2138:
2134:
2131:
2128:
2123:
2120:
2117:
2113:
2109:
2106:
2101:
2097:
2082:
2081:
2062:
2057:
2051:
2048:
2045:
2041:
2037:
2032:
2028:
2023:
2014:
2010:
2006:
2003:
2000:
1995:
1992:
1982:
1971:
1965:
1962:
1959:
1955:
1946:
1942:
1938:
1935:
1932:
1927:
1924:
1914:
1909:
1905:
1887:
1886:
1874:
1866:
1862:
1855:
1852:
1849:
1845:
1841:
1836:
1832:
1825:
1818:
1814:
1807:
1804:
1801:
1797:
1793:
1788:
1784:
1776:
1771:
1768:
1765:
1760:
1756:
1732:
1727:
1723:
1719:
1716:
1713:
1708:
1704:
1700:
1695:
1691:
1687:
1661:
1640:
1635:
1631:
1627:
1624:
1621:
1616:
1612:
1608:
1603:
1599:
1595:
1569:
1546:
1542:
1530:
1529:
1517:
1510:
1507:
1504:
1493:
1489:
1486:
1480:
1474:
1471:
1468:
1457:
1453:
1450:
1443:
1438:
1435:
1432:
1429:
1423:
1420:
1417:
1414:
1408:
1403:
1396:
1393:
1390:
1379:
1375:
1372:
1366:
1360:
1357:
1354:
1343:
1339:
1336:
1329:
1324:
1317:
1314:
1311:
1308:
1299:
1275:
1255:
1252:
1249:
1244:
1240:
1228:
1227:
1214:
1204:
1199:
1196:
1193:
1186:
1182:
1178:
1175:
1169:
1166:
1163:
1160:
1157:
1154:
1153:
1145:
1142:
1138:
1135:
1132:
1123:
1119:
1116:
1113:
1110:
1101:
1096:
1091:
1088:
1085:
1082:
1079:
1074:
1070:
1066:
1065:
1057:
1055:
1051:
1048:
1045:
1042:
1039:
1036:
1033:
1030:
1021:
1017:
1016:
1014:
974:
971:
953:
950:
947:
946:
944:
943:
936:
929:
921:
918:
917:
914:
913:
908:
903:
898:
892:
890:Simple filters
889:
888:
885:
884:
881:
880:
875:
870:
864:
861:Lattice filter
858:
852:
847:
842:
836:
831:
830:
827:
826:
823:
822:
817:
812:
807:
802:
797:
792:
786:
781:
780:
777:
776:
763:frequency band
747:
740:
732:, it may have
726:
725:
713:
707:
702:
698:
694:
691:
687:
682:
676:
673:
670:
666:
661:
656:
652:
636:
629:
619:
618:
607:
601:
596:
592:
588:
585:
582:
577:
572:
568:
564:
561:
555:
549:
546:
543:
537:
534:
529:
523:
520:
517:
511:
508:
505:
500:
469:
466:
427:
421:
420:
408:
402:
399:
396:
393:
389:
384:
378:
375:
372:
368:
363:
358:
354:
336:
318:
317:
306:
300:
297:
294:
291:
288:
283:
280:
277:
271:
265:
262:
259:
253:
250:
245:
239:
236:
233:
227:
224:
221:
216:
169:
166:
164:
161:
128:which removes
114:
111:
76:low-cut filter
15:
9:
6:
4:
3:
2:
3845:
3834:
3831:
3829:
3826:
3824:
3821:
3820:
3818:
3805:
3800:
3794:
3791:
3789:
3786:
3784:
3781:
3779:
3776:
3774:
3771:
3770:
3767:
3763:
3756:
3751:
3749:
3744:
3742:
3737:
3736:
3733:
3726:
3722:
3719:
3716:
3713:
3711:
3708:
3707:
3694:
3688:
3684:
3683:
3675:
3667:
3660:
3641:
3634:
3628:
3609:
3605:
3598:
3592:
3576:
3572:
3568:
3561:
3546:
3544:0-240-51512-9
3540:
3536:
3531:
3530:
3521:
3519:
3517:
3512:
3502:
3499:
3497:
3494:
3492:
3489:
3487:
3484:
3482:
3479:
3477:
3474:
3473:
3467:
3465:
3461:
3457:
3453:
3444:
3435:
3433:
3429:
3425:
3421:
3417:
3413:
3409:
3405:
3401:
3398:
3395:
3391:
3387:
3386:channel strip
3379:
3375:
3371:
3366:
3362:
3360:
3355:
3351:
3347:
3343:
3340:
3336:
3332:
3327:
3325:
3321:
3317:
3313:
3309:
3308:audible range
3304:
3302:
3298:
3294:
3290:
3286:
3281:
3265:
3262:
3258:
3254:
3251:
3248:
3242:
3239:
3236:
3233:
3230:
3226:
3221:
3215:
3212:
3209:
3206:
3202:
3197:
3194:
3186:
3185:formula above
3182:
3178:
3174:
3170:
3166:
3162:
3158:
3128:
3125:
3104:
3101:
3081:
3078:
3066:
3051:
3048:
3035:
3019:
3016:
2996:
2993:
2986:
2985:time constant
2982:
2981:
2980:
2974:
2963:
2959:
2955:
2951:
2949:
2933:
2922:
2918:
2914:
2910:
2906:
2903:
2899:
2896:
2892:
2888:
2884:
2880:
2877:
2873:
2868:
2866:
2856:
2840:
2832:
2829:
2826:
2823:
2803:
2800:
2780:
2777:
2774:
2754:
2751:
2731:
2728:
2725:
2696:
2688:
2685:
2682:
2677:
2674:
2671:
2665:
2660:
2656:
2648:
2647:
2646:
2626:
2623:
2618:
2614:
2608:
2600:
2597:
2593:
2588:
2585:
2578:
2577:
2576:
2560:
2556:
2535:
2507:
2503:
2499:
2496:
2492:
2487:
2484:
2481:
2458:
2455:
2452:
2449:
2445:
2440:
2435:
2431:
2423:
2422:
2421:
2402:
2396:
2393:
2390:
2386:
2381:
2375:
2367:
2364:
2361:
2354:
2353:
2352:
2338:
2316:
2291:
2288:
2281:
2280:time constant
2265:
2245:
2242:
2239:
2236:
2233:
2205:
2197:
2194:
2191:
2186:
2183:
2177:
2174:
2159:
2156:
2153:
2149:
2145:
2140:
2136:
2129:
2126:
2121:
2118:
2115:
2111:
2107:
2104:
2099:
2095:
2087:
2086:
2085:
2060:
2055:
2049:
2046:
2043:
2039:
2035:
2030:
2026:
2021:
2012:
2004:
2001:
1998:
1993:
1990:
1980:
1969:
1963:
1960:
1957:
1953:
1944:
1936:
1933:
1930:
1925:
1922:
1912:
1907:
1903:
1895:
1894:
1893:
1892:
1872:
1864:
1853:
1850:
1847:
1843:
1839:
1834:
1830:
1823:
1816:
1805:
1802:
1799:
1795:
1791:
1786:
1782:
1774:
1769:
1766:
1763:
1758:
1754:
1746:
1745:
1744:
1725:
1721:
1717:
1714:
1711:
1706:
1702:
1698:
1693:
1689:
1659:
1633:
1629:
1625:
1622:
1619:
1614:
1610:
1606:
1601:
1597:
1567:
1544:
1515:
1508:
1505:
1491:
1487:
1478:
1472:
1469:
1455:
1451:
1441:
1436:
1433:
1430:
1427:
1418:
1412:
1406:
1401:
1394:
1391:
1377:
1373:
1364:
1358:
1355:
1341:
1337:
1327:
1322:
1315:
1309:
1297:
1289:
1288:
1287:
1273:
1250:
1242:
1238:
1197:
1194:
1184:
1180:
1176:
1167:
1161:
1155:
1140:
1133:
1121:
1117:
1111:
1099:
1094:
1089:
1086:
1080:
1072:
1068:
1053:
1046:
1040:
1037:
1031:
1019:
1012:
1003:
1002:
1001:
999:
995:
990:
988:
980:
970:
968:
964:
960:
952:Higher orders
942:
937:
935:
930:
928:
923:
922:
920:
919:
912:
909:
907:
904:
902:
899:
897:
894:
893:
887:
886:
879:
876:
874:
871:
868:
865:
862:
859:
856:
855:Zobel network
853:
851:
848:
846:
843:
841:
838:
837:
834:
829:
828:
821:
818:
816:
813:
811:
808:
806:
805:Bessel filter
803:
801:
798:
796:
793:
791:
788:
787:
784:
779:
778:
775:
772:Linear analog
770:
769:
766:
764:
760:
756:
751:
746:
739:
735:
731:
711:
705:
700:
696:
692:
689:
685:
680:
674:
671:
668:
664:
659:
654:
650:
642:
641:
640:
635:
628:
624:
605:
599:
594:
590:
586:
583:
580:
575:
570:
566:
562:
559:
553:
544:
527:
518:
498:
487:
486:
485:
483:
474:
465:
463:
459:
455:
451:
447:
443:
439:
435:
430:
426:
406:
400:
397:
394:
391:
387:
382:
376:
373:
370:
366:
361:
356:
352:
344:
343:
342:
339:
335:
331:
330:time constant
327:
323:
304:
298:
295:
292:
289:
286:
281:
278:
275:
269:
260:
243:
234:
214:
203:
202:
201:
199:
195:
191:
187:
179:
174:
160:
158:
154:
150:
145:
143:
139:
135:
131:
127:
124:
120:
110:
108:
104:
100:
95:
93:
90:to produce a
89:
85:
81:
77:
73:
69:
65:
61:
57:
53:
49:
45:
41:
37:
28:
22:
3777:
3681:
3674:
3665:
3659:
3647:. Retrieved
3640:the original
3627:
3615:. Retrieved
3608:the original
3603:
3591:
3579:. Retrieved
3575:the original
3570:
3560:
3548:. Retrieved
3528:
3449:
3383:
3339:loudspeakers
3328:
3305:
3282:
3154:
3146:Applications
2972:
2971:and current
2966:
2961:
2957:
2953:
2925:
2920:
2916:
2912:
2908:
2904:
2901:
2897:
2894:
2890:
2886:
2882:
2878:
2875:
2871:
2862:
2717:
2644:
2527:
2419:
2225:
2083:
1888:
1531:
1229:
991:
983:
955:
752:
744:
737:
727:
633:
626:
620:
479:
453:
445:
437:
428:
424:
422:
337:
333:
325:
321:
319:
182:
146:
116:
106:
102:
98:
96:
79:
75:
46:that passes
39:
35:
33:
3496:Convolution
3408:bass guitar
3331:AC coupling
3293:loudspeaker
3165:loudspeaker
2744:, then the
998:capacitance
987:discretized
341:, that is,
113:Description
64:attenuation
3817:Categories
3507:References
3476:DSL filter
3424:subwoofers
3420:stage wash
3416:microphone
3342:voice coil
3316:tape decks
3297:line level
2948:refactored
2865:pseudocode
1651:, and let
911:RLC filter
869:(all-pass)
863:(all-pass)
178:RC circuit
157:wavelength
153:wavelength
60:attenuates
3404:kick drum
3359:QSC Audio
3263:−
3255:×
3240:×
3234:×
3210:π
2975:in input
2881:highpass(
2837:Δ
2833:α
2830:≈
2778:≪
2775:α
2726:α
2693:Δ
2689:α
2686:π
2678:α
2675:−
2605:Δ
2601:π
2586:α
2536:α
2500:π
2453:π
2397:α
2394:−
2387:α
2372:Δ
2339:α
2313:Δ
2266:α
2243:≤
2240:α
2237:≤
2202:Δ
2178:≜
2175:α
2157:−
2146:−
2130:α
2119:−
2108:α
2061:⏞
2047:−
2036:−
2009:Δ
1970:⏞
1961:−
1941:Δ
1861:Δ
1851:−
1840:−
1824:−
1813:Δ
1803:−
1792:−
1715:…
1623:…
1541:Δ
1506:
1488:
1479:−
1470:
1452:
1407:⏞
1392:
1374:
1365:−
1356:
1338:
1195:
1177:
1118:−
906:LC filter
901:RL filter
896:RC filter
734:non-unity
693:π
675:τ
672:π
625:gain of −
560:−
395:π
377:τ
374:π
328:) is the
186:capacitor
130:frequency
99:High-pass
52:frequency
3649:March 9,
3617:March 9,
3550:March 9,
3486:Bias tee
3470:See also
3181:inductor
3175:for the
2893:RC)
2879:function
623:passband
196:of this
190:resistor
123:two-port
103:low-pass
42:) is an
3581:9 March
3537:, 479.
3458:or the
3426:or the
3412:DI unit
3161:tweeter
3069:(x - x)
3039:{{{1}}}
2977:(x - x)
2793:, then
442:seconds
107:shorter
50:with a
48:signals
3689:
3541:
3462:. The
3394:Yamaha
3378:Smaart
3370:Mackie
3324:preamp
3177:woofer
2973:change
2921:return
2900:y
1230:where
730:active
458:farads
456:is in
452:, and
448:is in
440:is in
432:is in
423:where
324:×
188:and a
149:optics
134:signal
119:filter
68:filter
3643:(PDF)
3636:(PDF)
3611:(PDF)
3600:(PDF)
3438:Image
3390:Midas
3372:1402
3287:with
3151:Audio
2528:then
2170:where
434:hertz
121:is a
3687:ISBN
3651:2010
3619:2010
3583:2010
3552:2010
3539:ISBN
3397:M7CL
3314:and
3252:3.18
3237:5000
3231:6.28
2958:from
2913:from
2905:real
2898:real
2891:real
2889:dt,
2887:real
2883:real
2645:and
2548:and
2331:and
965:and
450:ohms
200:is:
101:and
58:and
3535:268
2954:for
2909:for
2902:var
2895:var
2885:x,
2781:0.5
2732:0.5
2718:If
2474:so
1664:out
1496:out
1382:out
1302:out
1207:(I)
1148:(Q)
1126:out
1060:(V)
1024:out
147:In
78:or
40:HPF
3819::
3602:.
3569:.
3515:^
3406:,
3326:.
3303:.
3259:10
3243:10
2962:to
2960:2
2956:i
2923:y
2917:to
2915:2
2911:i
2876:RC
2872:dt
2855:.
2351::
1572:in
1460:in
1346:in
1104:in
1000::
989:.
750:.
444:,
436:,
94:.
34:A
3754:e
3747:t
3740:v
3695:.
3653:.
3621:.
3585:.
3554:.
3266:6
3249:=
3227:1
3222:=
3216:R
3213:f
3207:2
3203:1
3198:=
3195:C
3141:.
3129:C
3126:R
3105:C
3102:R
3082:C
3079:R
3064:.
3052:C
3049:R
3020:C
3017:R
2997:C
2994:R
2969:y
2934:n
2841:T
2827:C
2824:R
2804:C
2801:R
2755:C
2752:R
2729:=
2714:.
2697:T
2683:2
2672:1
2666:=
2661:c
2657:f
2627:1
2624:+
2619:c
2615:f
2609:T
2598:2
2594:1
2589:=
2561:c
2557:f
2508:c
2504:f
2497:2
2493:1
2488:=
2485:C
2482:R
2459:C
2456:R
2450:2
2446:1
2441:=
2436:c
2432:f
2416:.
2403:)
2391:1
2382:(
2376:T
2368:=
2365:C
2362:R
2317:T
2292:C
2289:R
2246:1
2234:0
2206:T
2198:+
2195:C
2192:R
2187:C
2184:R
2165:)
2160:1
2154:i
2150:x
2141:i
2137:x
2133:(
2127:+
2122:1
2116:i
2112:y
2105:=
2100:i
2096:y
2056:)
2050:1
2044:i
2040:x
2031:i
2027:x
2022:(
2013:T
2005:+
2002:C
1999:R
1994:C
1991:R
1981:+
1964:1
1958:i
1954:y
1945:T
1937:+
1934:C
1931:R
1926:C
1923:R
1913:=
1908:i
1904:y
1873:)
1865:T
1854:1
1848:i
1844:y
1835:i
1831:y
1817:T
1806:1
1800:i
1796:x
1787:i
1783:x
1775:(
1770:C
1767:R
1764:=
1759:i
1755:y
1731:)
1726:n
1722:y
1718:,
1712:,
1707:2
1703:y
1699:,
1694:1
1690:y
1686:(
1660:V
1639:)
1634:n
1630:x
1626:,
1620:,
1615:2
1611:x
1607:,
1602:1
1598:x
1594:(
1568:V
1545:T
1516:)
1509:t
1503:d
1492:V
1485:d
1473:t
1467:d
1456:V
1449:d
1442:(
1437:C
1434:R
1431:=
1428:R
1422:)
1419:t
1416:(
1413:I
1402:)
1395:t
1389:d
1378:V
1371:d
1359:t
1353:d
1342:V
1335:d
1328:(
1323:C
1316:=
1313:)
1310:t
1307:(
1298:V
1274:t
1254:)
1251:t
1248:(
1243:c
1239:Q
1198:t
1192:d
1185:c
1181:Q
1174:d
1168:=
1165:)
1162:t
1159:(
1156:I
1141:)
1137:)
1134:t
1131:(
1122:V
1115:)
1112:t
1109:(
1100:V
1095:(
1090:C
1087:=
1084:)
1081:t
1078:(
1073:c
1069:Q
1054:R
1050:)
1047:t
1044:(
1041:I
1038:=
1035:)
1032:t
1029:(
1020:V
1013:{
981:.
940:e
933:t
926:v
748:1
745:R
743:/
741:2
738:R
712:,
706:C
701:1
697:R
690:2
686:1
681:=
669:2
665:1
660:=
655:c
651:f
637:1
634:R
632:/
630:2
627:R
606:.
600:C
595:1
591:R
587:s
584:+
581:1
576:C
571:2
567:R
563:s
554:=
548:)
545:s
542:(
536:n
533:i
528:V
522:)
519:s
516:(
510:t
507:u
504:o
499:V
454:C
446:R
438:τ
429:c
425:f
407:,
401:C
398:R
392:2
388:1
383:=
371:2
367:1
362:=
357:c
353:f
338:c
334:f
326:C
322:R
305:.
299:C
296:R
293:s
290:+
287:1
282:C
279:R
276:s
270:=
264:)
261:s
258:(
252:n
249:i
244:V
238:)
235:s
232:(
226:t
223:u
220:o
215:V
38:(
23:.
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