Click here to go to the applet.
This applet is a demonstration of
digital filters. You should
hear a noise waveform when the applet starts up.
The applet starts up with a low-pass filter. It shows the frequency
response of the filter, the spectrum of the filtered waveform being
played, the waveform itself, and the impulse response of the filter.
Click on the response curve to change the cutoff frequency.
The freqency response graph shows the filter response (shown
vertically, in dB, with lines at 10 dB intervals) versus the frequency
(shown horizontally, with vertical lines marking off octaves). The
spectrum graph shows the spectrum of the sound output.
The Input popup menu allows you to select an input waveform.
The choices are:
- Noise
- Sine Wave - select the frequency by clicking on the spectrum.
- Sawtooth Wave
- Triangle Wave
- Square Wave
- Periodic Noise - select the frequency by clicking on the spectrum.
- Sweep - a sine wave that sweeps across the frequency spectrum at
an adjustable rate.
- Impulses
- Various mp3 files (you can add your own by downloading the applet
and then editing the index.html file)
The Filter popup menu allows you to select a filter. See
this site for technical
details about the filter types.
The choices are:
- FIR Low-pass - filters out high frequencies (everything below the
cutoff frequency, which is adjustable by clicking on the response graph
with the mouse).
- FIR High-pass - filters out low frequencies.
- FIR Band-pass - filters out everything except a range of frequencies. Use
the Center Frequency and Passband Width sliders to
adjust the range.
- FIR Band-stop - filters out a range of frequencies.
Here are some adjustable parameters that affect the quality of the
FIR filters: the number of points,
which you can adjust with the Order slider (more points is
better); and the window,
which you select with the Window popup. An FIR filter is
defined by its impulse response, which you can view near the bottom
of the window. To view the window function, select FIR Low-pass,
set the cutoff frequency near zero and look at the impulse response.
- Custom FIR - draw on the frequency response graph to specify your
own filter. The actual response, shown in red, is affected by the
Order slider and Window popup.
- None - no filtering
- Butterworth Low-pass - a flat filter that filters out high frequencies
- Butterworth High-pass - a flat filter that filters out low frequencies
- Butterworth Band-pass - a flat filter that filters out frequencies
outside of a certain band
- Butterworth Band-stop - a flat filter that filters out frequencies
inside of a certain band
- Chebyshev Low-pass - a low-pass filter with an adjustable amount
of ripple in the passband
- Chebyshev High-pass, Band-pass, Band-stop
- Inv Cheby Low-pass - inverse Chebyshev (also known as Chebyshev
type II), a low-pass filter with a flat passband, but an adjustable amount
of ripple in the stopband
- Inv Cheby High-pass, Band-pass, Band-stop
- Elliptic Low-pass -
(also known as Cauer) a low-pass filter with an adjustable amount
of ripple in the passband and stopband. Adjusting the Transition
Band Width will change the stopband attenuation.
- Elliptic High-pass, Band-pass, Band-stop
- Comb (+) - this filter (used on noise) sounds like someone blowing
into a tube.
- Comb (-) - this is a tube with one end covered.
- Delay - an echo filter (the same as a comb filter, but with longer delays)
- Plucked-String Filter - when the Input popup is set to
"Impulses", this sounds like a string being plucked.
- Inverse Comb
- Reson - resonates at one frequency
- Reson w/ Zeros - a reson filter with zeros added at 0 and half the
sampling rate
- Notch - filters out a narrow range of frequencies
- Moving Average - a simple FIR attempt at a low-pass filter. This filter
(when used on noise) reminds me of an Atari 2600.
- Triangle
- Allpass - passes all frequencies equally, but with different phase delay.
Use the Phase Response item in the View menu to view
the phase response. For low frequencies, this filter acts as a
fractional delay (a delay of less than one sample).
- Gaussian - the impulse response and
frequency response are both gaussian-shaped
- Random
- Custom IIR - drag the poles and zeros around to change the filter.
The Sampling Rate popup allows you to view or change the
sampling rate. You can't change the rate if the input is an MP3.
The View menu allows you to turn on or off the various views.
The Log Frequency Scale item which shows the
frequency response using a logarithmic plot instead of linear.
The Show Entire Waveform item will compress the waveform
segments horizontally so that each one fits in the window; this way, all of the waveform
will be displayed, but the window usually won't be wide enough to show
each sample separately. The Ferris Plot item
will display a
Ferris Plot
of the transfer function.
When displaying the frequency response, the applet only shows the
portion of the spectrum from 0 to the Nyquist
frequency (π). The rest of the response up to 2π is just a mirror image of this,
and then the response
repeats every 2π. For example, here is a frequency response as
displayed in the applet (up to π):
Here is the response up to 4π:
Good books about digital filters:
-
Steiglitz
(great intro to DSP; has info on comb filters, resons, plucked-string)
- Smith (downloadable)
-
Winder
-
Mitra
Click here to go to the applet.
java@falstad.com
A far higher place must be assigned to Judaism among the competitors for the allegiance of Europe. The cosmopolitan importance at one time assumed by this religion has been considerably obscured, owing to the subsequent devolution of its part to Christianity. It is, however, by no means impossible that, but for the diversion created by the Gospel, and the disastrous consequences of their revolt against Rome, the Jews might have won the world to a purified form of their own monotheism. A few significant circumstances are recorded showing how much influence they had acquired, even in Rome, before the first preaching of Christianity. The first of these is to be found in Cicero’s defence of Flaccus. The latter was accused of appropriating part of the annual contributions sent to the temple at Jerusalem; and, in dealing with this charge, Cicero speaks of the Jews, who were naturally prejudiced against his client, as a powerful faction the hostility of which he is anxious not to provoke.330 Some twenty years later, a great advance has been made. Not only must the material interests of the Jews be respected, but a certain conformity to their religious prescriptions is considered a mark of good breeding, In one of his most amusing satires, Horace tells us how, being anxious to shake off a bore, he appeals for help to his friend Aristius Fuscus, and reminds him of217 some private business which they had to discuss together. Fuscus sees his object, and being mischievously determined to defeat it, answers: ‘Yes, I remember perfectly, but we must wait for some better opportunity; this is the thirtieth Sabbath, do you wish to insult the circumcised Jews?’ ‘I have no scruples on that point,‘ replies the impatient poet. ‘But I have,’ rejoins Fuscus,—‘a little weak-minded, one of the many, you know—excuse me, another time.‘331 Nor were the Jews content with the countenance thus freely accorded them. The same poet elsewhere intimates that whenever they found themselves in a majority, they took advantage of their superior strength to make proselytes by force.’332 And they pursued the good work to such purpose that a couple of generations later we find Seneca bitterly complaining that the vanquished had given laws to the victors, and that the customs of this abominable race were established over the whole earth.333 Evidence to the same effect is given by Philo Judaeus and Josephus, who inform us that the Jewish laws and customs were admired, imitated, and obeyed over the whole earth.334 Such assertions might be suspected of exaggeration, were they not, to a certain extent, confirmed by the references already quoted, to which others of the same kind may be added from later writers showing that it was a common practice among the Romans to abstain from work on the Sabbath, and even to celebrate it by praying, fasting, and lighting lamps, to visit the synagogues, to study the law of Moses, and to pay the yearly contribution of two drachmas to the temple at Jerusalem.335 Jeff’s hand was quietly coming down. “What happened to you?” begged Sandy. “Something new has come up, sir. I was waiting there by my ship a good while back, and I heard another one cruising and spiraling, shooting the field, I guess, because he came in and set down. My crate, just the way you ordered, was down by the grove, not in plain sight in the middle of the course. But Jeff set his ship down, left the engine running, and went off. I stayed hid to see what would happen, but when he didn’t come back, I thought I’d better go and find you—and see if it meant anything to you.” She stood alone, with the sticky, wet knife in her hand, catching her breath, coming out of the madness. Then she stooped, and pushing the branches aside felt about for her pistol. It lay at the root of a tree, and[Pg 80] when she had picked it up and put it back in the holster, there occurred to her for the first time the thought that the shot in the dead stillness must have roused the camp. And now she was sincerely frightened. If she were found here, it would be more than disagreeable for Landor. They must not find her. She started at a swift, long-limbed run, making a wide detour, to avoid the sentries, bending low, and flying silently among the bushes and across the shadowy sands. The year 1756 opened with menaces to England of the most serious nature. The imbecility of the Ministry was beginning to tell in the neglect of its colonies and its defences. France threatened to invade us, and a navy of fifty thousand men was suddenly voted, and an army of thirty-four thousand two hundred and sixty-three of native troops; but as these were not ready, it was agreed to bring over eight thousand Hessians and Hanoverians. To pay for all this it was necessary to grant excessive supplies, and lay on new duties and taxes. In presenting the money bills in the month of May, Speaker Onslow could not avoid remarking that there were two circumstances which tended to create alarm—foreign subsidies and foreign troops introduced, and nothing but their confidence in his Majesty could allay their fears, or give them confidence that their burdens would be soon reduced. There was, in fact, no chance for any such reduction, for wars, troubles, and disgraces were gathering around from various quarters. The first reverse came from the Mediterranean. MUCH to their amazement, the boys waked up the next morning in Nashville, and found that they had passed through the "dark and bloody ground" of Kentucky absolutely without adventure. After drawing and dividing the rations and cartridges. Si gave the boys the necessary instruction about having their things ready so that they could get them in the dark the next morning, and ordered them to disregard the bonfires and mirth-making, and lie down to get all the sleep they could, in preparation for the hard work of the next day. Then, like the rest of the experienced men, who saw that the campaign was at length really on, and this would be the last opportunity for an indefinite while to write, he sat down to write short letters to his mother and to Annabel. "Bully for the Wild Wanderers of the Wabash," Shorty joined in. "They're the boss regiment in the army o' the Cumberland, and the Army o' the Cumberland's the boss army on earth. Hooray for US Co. Le's have a speech. Where's Monty Scruggs?" "Bring a light, do—I can't abide this dark." Albert suddenly began to look uneasy. After all he was not really drunk, only a little fuddled. He walked straight, and his roll was natural to him, while though he was exceedingly cheerful, and often burst into song, his words were not jumbled, and he generally seemed to have a fair idea of what he was saying. "But I heard what the doctor said to you." "A purty accident—wud them stacks no more dry than a ditch. 'Twas a clear case of 'bustion—fireman said so to me; as wicked and tedious a bit o' wark as ever I met in my life." Calverley stept from the shadow of the cliff, and beheld a meteor in the sky, brightening and expanding, as the clouds opened, until it assumed the appearance of a brilliant star, of astonishing magnitude, encircled by dazzling rays, which, in a singular manner, were all inclined in one direction, and pointing to that part of the horizon where lay the rival of England—France. The foreman's face assumed a deeper hue than usual: he looked fiercely at the galleyman, but there was a determination in the weather-beaten face that made him pause ere he spoke. "Galleyman," he at length said, "you knew the business before you came: if you be so fond of saving old witches' lives, why didn't you say so, that I might not now be in this dilemma?" "No, no, not the boy," replied Merritt, rather impatiently.