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Daqarta for DOS
Data AcQuisition And Real-Time Analysis
Shareware for Legacy Systems

From the Daqarta for DOS Help system:

# MISCELLANEOUS, Continued:

## FILTERS for NOISE REJECTION:

Simple filters can often be made of nothing more than a resistor and capacitor. A high-pass filter could be placed just before the input of a preamplifier, and a low-pass on its output. Here's how to make a simple high-pass 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 "high-pass") 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 high-pass 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.

### LOW-PASS FILTER:

Similarly, you can make a low-pass filter to remove unwanted high frequency components:

```             .----------.
-----|  Preamp  |---- R ----.--------
`----------'           |
Input                          C      Output
|
----------------------------^--------

```
This is just the mirror of the high-pass 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 high-pass and low-pass 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 G-key. 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 L-key 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 sub-multiples 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 criss-crossing 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 bar-graph. 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 equal-tempered 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 equal-tempered 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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