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MISCELLANEOUS, Continued:FILTERS for NOISE REJECTION:Simple filters can often be made of nothing more than a resistor and capacitor. A highpass filter could be placed just before the input of a preamplifier, and a lowpass on its output. Here's how to make a simple highpass filter:
..  C . Preamp   `' Input R Output  ^This filter has a "cutoff" frequency of F = 1 / (2 × pi × R × C).Any input component at this frequency will have its amplitude reduced by half. Higher frequencies are passed (that's why we call it "highpass") with less amplitude reduction as the frequency rises. Lower frequencies have their amplitudes strongly reduced: For every halving of frequency below the cutoff, the output will be further cut in half. Let's say you want to build a 300 Hz highpass filter. You probably want to pick R somewhere in the 10000 Ohm (10k) to 100000 Ohm (100k) range. (Too small may load down the signal source, and too large may encourage the circuit to act like an antenna and pick up 60 Hz power line noise from the surroundings, as well as not allow the preamp to operate properly.) So let's start with 33k, which is the geometric middle of that range. (10k / 33k is about the same as 33k / 100k.) Rearranging our formula we find C = 1 / (2 × pi × R × F) = (2 × 3.1415 × 33000 × 300) = 1.6 × 10^8 Farads (16 nF, or 0.016 uF)If you happen to have this value on hand, you are done. However, since resistors are readily available in many more values than capacitors, you may need to use the nearest value of C that you have, then solve for a new value of R. Note that the input impedance of the preamp is in parallel with the resistor, and will need to be considered unless it is many times larger. Usually, the impedance is either high enough to ignore (over 1 Megohm), or low due to a simple fixed resistance across the input of the circuit. If you know that this impedance is a simple resistor you can select your filter resistor such that the parallel combination gives the correct value. Otherwise, if you only know a general ballpark range for the input impedance, you will probably want to select the filter resistor to be around one tenth of this or less.
LOWPASS FILTER:Similarly, you can make a lowpass filter to remove unwanted high frequency components:
..  Preamp  R . `'  Input C Output  ^This is just the mirror of the highpass filter, and it uses the same formula. Here again input signals at the cutoff frequency have their amplitudes reduced by half, but now higher frequency components are cut in half for every doubling of frequency. The formula assumes that the output impedance of the preamp is much lower than filter resistor, which is usually a safe assumption with modern equipment. Otherwise, its value must be added to the resistor value to get the effective R for the filter calculation. Note that input impedance of whatever follows the output of this filter will tend to reduce the signal level by causing a voltage divider effect. You may want to compensate for losses by using the UvUser Units / Volt factor for critical work. You can easily use both highpass and lowpass filters on opposite ends of the same preamp. If these don't reduce unwanted frequencies enough, there are more elaborate filters available. However, these are NOT made by just cascading multiple simple filters, and they will require operating power as well. One source for more information about filters is The Active Filter Cookbook by Don Lancaster. There is one potential problem with using filters to reduce noise: They often change the appearance of the waveform beyond removing the unwanted components. The desired signal will typically have its different frequency components shifted in time by different amounts, so that what started as a sharp pulse or step may become smeared out or even show transient oscillations. More elaborate filters can help this, but these can be expensive.
GRID:The grid display may be toggled off and on via the Gkey. This is sometimes useful to resolve fine details in the trace that are near a grid dot, especially if the trace Line0 style is set to show only separate data points with a monochrome VGA monitor. This may also be useful before printing the screen.
LAPTOP HINTS:
LAPTOP SLOW DISPLAY RESPONSE:Many laptop displays have slow response times. This means that very active or "busy" signals can be hard to see, since the trace is not in the same place long enough for the slow LCD display to actually show them.Exponential averaging can make signals much easier to see on these displays, since it essentially "slows down" the activity of the signal. Of course, it also adds a smoothing and noise reduction that may not always be desired. In such cases, use Pause or Single Sweep to "freeze" the changing signal instead of slowing it down.
TRACE LINE STYLE (Line0, Line1, Line2):The unshifted Lkey steps between three basic trace line styles on successive hits of the key:
Line0 = POINTS ONLY:Only actual data points are shown. This can make it harder to interpret complex traces, but it is occasionally useful to see the raw data apart from any interpolation, especially when Xpand has been used to stretch the trace. This is also the fastest type of trace for Daqarta to draw, so if you are running on a slow machine this can give you a little extra speed.This mode is also useful for learning about sampling and aliasing. Try setting the Virtual Source sine wave frequency to submultiples of the sampling frequency. At half the sample rate (the Nyquist frequency), all the data points form a horizontal line... the source makes one full cycle between samples, ending up at exactly the same point in the cycle each time. Make the frequency a little higher or lower and observe what happens. Now try one forth of the sample rate, and so on. At intermediate frequencies you will see interesting crisscrossing sine waves appear in the point alignments, as the sine wave phase advances just the right amount between samples to make points from adjacent cycles seem to line up at a much lower frequency. The technical term for what you are doing is "messing around", but besides being fun it is also building an intuitive feel for what happens during the sampling process... so enjoy!
Line1 = SOLID LINES:Straight lines connect data points. This is the default line style for waveforms.
Line2 = VERTICAL BARS:A vertical line extends from the bottom of the trace up to each data point, like a high resolution bargraph. This is the default FFT line style. This shows you each data point without any interpolation connecting the points as for Line1 mode, but each point still shows up clearly, unlike Line0 mode if adjacent samples have widely different values. This is the slowest line style for Daqarta to draw because it may have to put a lot of points on the screen, so you should avoid this if display update speed is an issue.
STANDARD MUSICAL NOTE FREQUENCIES:The equaltempered scale of western music is based upon an octave (frequency doubling) that contains 12 notes, or "semitones", each of which is 1.059463 (the 12th root of 2) times the one below it.The standard musical tone frequencies of the equaltempered piano keyboard are tabulated below, but you can find others by extending the series. To find the same note letter in the next higher octave, just multiply by 2. To go down one octave, divide by 2. For example, C0 = C1 / 2 = 32.703 / 2 = 16.352 Hz.
Notes that correspond to the black keys on a standard piano keyboard are shown in boldface: Note Hz A0 27.500 A#0 29.135 B0 30.868 C1 32.703 C#1 34.648 D1 36.708 D#1 38.891 E1 41.203 F1 43.654 F#1 46.249 G1 48.999 G#1 51.913 A1 55.000 A#1 58.270 B1 61.735 C2 65.406 C#2 69.296 D2 73.416 D#2 77.782 E2 82.407 F2 87.307 F#2 92.499 G2 97.999 G#2 103.826 A2 110.000 A#2 116.541 B2 123.471 C3 130.813 C#3 138.591 D3 146.832 D#3 155.563 E3 164.814 F3 174.614 F#3 184.997 G3 195.998 G#3 207.652 A3 220.000 A#3 233.082 B3 246.942 C4 261.626 MIDDLE C C#4 277.183 D4 293.665 D#4 311.127 E4 329.628 F4 349.228 F#4 369.994 G4 391.995 G#4 415.305 A4 440.000 Concert A A#4 466.164 B4 493.883 C5 523.251 C#5 554.365 D5 587.330 D#5 622.254 E5 659.255 F5 698.456 F#5 739.989 G5 783.991 G#5 830.609 A5 880.000 A#5 932.328 B5 987.767 C6 1046.502 C#6 1108.731 D6 1174.659 D#6 1244.508 E6 1318.510 F6 1396.913 F#6 1479.978 G6 1567.982 G#6 1661.219 A6 1760.000 A#6 1864.655 B6 1975.533 C7 2093.005 C#7 2217.461 D7 2349.318 D#7 2489.016 E7 2637.020 F7 2793.826 F#7 2959.955 G7 3135.963 G#7 3322.438 A7 3520.000 A#7 3729.310 B7 3951.066 C8 4186.009


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