SWHarden.com

The personal website of Scott W Harden

Field Day 2009

June 29, 2009
amateur radio

Last weekend was field day, a disaster simulation / competition for amateur radio operators. In a sentence, people are encouraged to make as many contacts as they can around the world (earning points) using emergency radio preparations (battery and solar powered radios, temporary antennas, etc) for a full 24 hours (2pm to 2pm). I spent the time with the UCF Amateur Radio Club who set up big antennas in a grassy field on campus. It was a fun experience, and the first time I ever got to see a HF rig in operation. A representative for the UCF newspaper showed up, took some interviews, and I ended-up being quoted in the article. I can also be seen in the photo, if you look close enough (yellow square).

Being that amateur radio was something I got into independently (I didn’t know anyone else with a license) I was (and still am) very isolated in the hobby. I’m really thankful I found the UCF ARC, even though it wasn’t until I’d already been going to UCF for 2 years and was already on my way out. Seeing (and actually get to use) a HF rig was an eye-opening experience for me, and one I’m a little regretful I participated in. Before yesterday, I had already come to terms with my situation (going to dental school in a few weeks and virtually dropping all of my hobbies) and was content with my summer accomplishments so far. My summer goal was to get into radio, and before yesterday I felt I had. I studied for my exam, got my license, learned how to use repeaters on VHF to easily make local contacts, and I was satisfied. I knew HF was out there, and that it allowed communication over thousands of miles, but I ignored it knowing I wouldn’t get into it this summer (the equipment is just too expensive for me to justify purchasing). Now, after sitting in front of a rig for several hours, I wish I had the time to upgrade my license, earn a little cash to blow on a HF radio, and spend a few weeks sitting in front of it scouring the waves for random voices around the world. I know it’s a little morbid, but I’d probably have to compare the feeling I’m experiencing with what an old person feels like when they realize their end is near and that they won’t be able to do the things they always dreamed they would. Oh well, at least I’ll be able to fill holes in teeth soon. [smiles convincingly]

After the tents, antennas, and radios were mostly set up, everyone was exhausted. I was ready to make some contacts! I fired-up my ‘ol netbook and tried communicating over 40m using psk (a digital mode), a mode I’ve never used, with software I’ve never used, on a band I’ve never used. It wasn’t working either. I spent the first several hours in frustration because what I was trying to do wasn’t working, and I couldn’t figure out why. This photo was taken at the height of my frustration.

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Flipping Bits in C

June 24, 2009

Bitwise programming techniques (manipulating the 1s and 0s of binary numbers) are simple, but hard to remember if you don’t use them often. Recently I’ve needed to perform a lot of bitwise operations. If I’m storing true/false (1-bit) information in variables, it’s a waste of memory to assign a whole variable to the task (the smallest variable in C is a char, and it contains 8 bits). When cramming multiple values into individual variables, it’s nice to know how to manipulate each bit of a variable.

// set the Nth bit of x to 0
x &= ~(1 << n);

// set the Nth bit of x to 1
x |= (1 << n); 

// store the Nth bit of x in y (y becomes 0 or 1)
y = (x >> n) & 1; 

// leave the lowest N bits of x alone and set higher bits to 0.
x &= (1 << (n + 1)) - 1;

// toggle the Nth bit of x
x ^= (1 << n);

// toggle every bit of x
x = ~x;
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Reading PCM Audio with Python

June 19, 2009
python obsolete

When I figured this out I figured it was simply way too easy and way to helpful to keep to myself. Here I post (for the benefit of friends, family, and random Googlers alike) two examples of super-simplistic ways to read PCM data from Python using Numpy to handle the data and Matplotlib to display it. First, get some junk audio in PCM format (test.pcm).

import numpy
data = numpy.memmap("test.pcm", dtype='h', mode='r')
print "VALUES:",data

This code prints the values of the PCM file. Output is similar to:

VALUES: [-115 -129 -130 ...,  -72  -72  -72]

To graph this data, use matplotlib like so:

import numpy, pylab
data = numpy.memmap("test.pcm", dtype='h', mode='r')
print data
pylab.plot(data)
pylab.show()

This will produce a graph that looks like this:

Could it have been ANY easier? I’m so in love with python I could cry right now. With the powerful tools Numpy provides to rapidly and efficiently analyze large arrays (PCM potential values) combined with the easy-to-use graphing tools Matplotlib provides, I’d say you can get well on your way to analyzing PCM audio for your project in no time. Good luck!

FOR MORE INFORMATION AND CODE check out:

Let’s get fancy and use this concept to determine the number of seconds in a 1-minute PCM file in which a radio transmission occurs. I was given a 1-minute PCM file with a ~45 second transmission in the middle. Here’s the graph of the result of the code posted below it. (Detailed descriptions are at the bottom)

Figure description: The top trace (light blue) is the absolute value of the raw sound trace from the PCM file. The solid black line is the average (per second) of the raw audio trace. The horizontal dotted line represents the threshold, a value I selected. If the average volume for a second is above the threshold, that second is considered as “transmission” (1), if it’s below the threshold it’s “silent” (0). By graphing these 60 values in bar graph form (bottom window) we get a good idea of when the transmission starts and ends. Note that the ENTIRE graphing steps are for demonstration purposes only, and all the math can be done in the 1st half of the code. Graphing may be useful when determining the optimal threshold though. Even when the radio is silent, the microphone is a little noisy. The optimal threshold is one which would consider microphone noise as silent, but consider a silent radio transmission as a transmission.

### THIS CODE DETERMINES THE NUMBER OF SECONDS OF TRANSMISSION
### FROM A 60 SECOND PCM FILE (MAKE SURE PCM IS 60 SEC LONG!)
import numpy
threshold=80 # set this to suit your audio levels
dataY=numpy.memmap("test.pcm", dtype='h', mode='r') #read PCM
dataY=dataY-numpy.average(dataY) #adjust the sound vertically the avg is at 0
dataY=numpy.absolute(dataY) #no negative values
valsPerSec=float(len(dataY)/60) #assume audio is 60 seconds long
dataX=numpy.arange(len(dataY))/(valsPerSec) #time axis from 0 to 60
secY,secX,secA=[],[],[]
for sec in xrange(60):
    secData=dataY[valsPerSec*sec:valsPerSec*(sec+1)]
    val=numpy.average(secData)
    secY.append(val)
    secX.append(sec)
    if val>threshold: secA.append(1)
    else: secA.append(0)
print "%d sec of 60 used = %0.02f"%(sum(secA),sum(secA)/60.0)
raw_input("press ENTER to graph this junk...")

### CODE FROM HERE IS ONLY USED TO GRAPH THE DATA
### IT MAY BE USEFUL FOR DETERMINING OPTIMAL THRESHOLD
import pylab
ax=pylab.subplot(211)
pylab.title("PCM Data Fitted to 60 Sec")
pylab.plot(dataX,dataY,'b',alpha=.5,label="sound")
pylab.axhline(threshold,color='k',ls=":",label="threshold")
pylab.plot(secX,secY,'k',label="average/sec",alpha=.5)
pylab.legend()
pylab.grid(alpha=.2)
pylab.axis([None,None,-1000,10000])
pylab.subplot(212,sharex=ax)
pylab.title("Activity (Yes/No) per Second")
pylab.grid(alpha=.2)
pylab.bar(secX,secA,width=1,linewidth=0,alpha=.8)
pylab.axis([None,None,-0.5,1.5])
pylab.show()

The output of this code:

46 sec of 60 used = 0.77

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pySquelch - Frequency Activity Reports via Python

June 18, 2009
amateur radio python obsolete

Update: this project is now on GitHub https://github.com/FredEckert/pySquelch

I’ve been working on the pySquelch project which is basically a method to graph frequency usage with respect to time. The code I’m sharing below listens to the microphone jack on the sound card (hooked up to a radio) and determines when transmissions begin and end. I ran the code below for 24 hours and this is the result:

__This graph represents frequency activity with respect to time. __The semi-transparent gray line represents the raw frequency usage in fractional minutes the frequency was tied-up by transmissions. The solid blue line represents the same data but smoothed by 10 minutes (in both directions) by the Gaussian smoothing method modified slightly from my linear data smoothing with Python page.

I used the code below to generate the log, and the code further below to create the graph from the log file. Assuming your microphone is enabled and everything else is working, this software will require you to determine your own threshold for talking vs. no talking. Read the code and you’ll figure out how test your sound card settings.

If you want to try this yourself you need a Linux system (a Windows system version could be created simply by replacing getVolEach() with a Windows-based audio level detection system) with Python and the alsaaudio, numpy, and matplotlib libraries. Try running the code on your own, and if it doesn’t recognize a library “aptitude search” for it. Everything you need can be installed from packages in the common repository.


# pySquelchLogger.py
import time
import random
import alsaaudio
import audioop
inp = alsaaudio.PCM(alsaaudio.PCM_CAPTURE, alsaaudio.PCM_NONBLOCK)
inp.setchannels(2)
inp.setrate(1000)
inp.setformat(alsaaudio.PCM_FORMAT_S8)
inp.setperiodsize(100)
addToLog = ""
lastLogTime = 0

testLevel = False  # SET THIS TO 'True' TO TEST YOUR SOUNDCARD


def getVolEach():
    # this is a quick way to detect activity.
    # modify this function to use alternate methods of detection.
    while True:
        l, data = inp.read()  # poll the audio device
        if l > 0:
            break
    vol = audioop.max(data, 1)  # get the maximum amplitude
    if testLevel:
        print vol
    if vol > 10:
        return True  # SET THIS NUMBER TO SUIT YOUR NEEDS ###
    return False


def getVol():
    # reliably detect activity by getting 3 consistant readings.
    a, b, c = True, False, False
    while True:
        a = getVolEach()
        b = getVolEach()
        c = getVolEach()
        if a == b == c:
            if testLevel:
                print "RESULT:", a
            break
    if a == True:
        time.sleep(1)
    return a


def updateLog():
    # open the log file, append the new data, and save it again.
    global addToLog, lastLogTime
    # print "UPDATING LOG"
    if len(addToLog) > 0:
        f = open('log.txt', 'a')
        f.write(addToLog)
        f.close()
        addToLog = ""
    lastLogTime = time.mktime(time.localtime())


def findSquelch():
    # this will record a single transmission and store its data.
    global addToLog
    while True:  # loop until we hear talking
        time.sleep(.5)
        if getVol() == True:
            start = time.mktime(time.localtime())
            print start,
            break
    while True:  # loop until talking stops
        time.sleep(.1)
        if getVol() == False:
            length = time.mktime(time.localtime())-start
            print length
            break
    newLine = "%d,%d " % (start, length)
    addToLog += newLine
    if start-lastLogTime > 30:
        updateLog()  # update the log


while True:
    findSquelch()

The logging code (above) produces a log file like this (below). The values represent the start time of each transmission (in seconds since epoch) followed by the duration of the transmission.

#log.txt
1245300044,5 1245300057,4 1245300063,16 1245300094,13 1245300113,4 1245300120,14 1245300195,4 1245300295,4 1245300348,4 1245300697,7 1245300924,3 1245301157,4 1245301207,12 1245301563,4 1245302104,6 1245302114,6 1245302192,3 1245302349,4 1245302820,4 1245304812,13 1245308364,10 1245308413,14 1245312008,14 1245313953,11 1245314008,6 1245314584,4 1245314641,3 1245315212,5 1245315504,6 1245315604,13 1245315852,3 1245316255,6 1245316480,5 1245316803,3 1245316839,6 1245316848,11 1245316867,5 1245316875,12 1245316893,13 1245316912,59 1245316974,12 1245316988,21 1245317011,17 1245317044,10 1245317060,6 1245317071,7 1245317098,33 1245317140,96 1245317241,15 1245317259,14 1245317277,8 1245317298,18 1245317322,103 1245317435,40 1245317488,18 1245317508,34 1245317560,92 1245317658,29 1245317697,55 1245317755,33 1245317812,5 1245317818,7 1245317841,9 1245317865,25 1245317892,79 1245317972,30 1245318007,8 1245318021,60 1245318083,28 1245318114,23 1245318140,25 1245318167,341 1245318512,154 1245318670,160 1245318834,22 1245318859,9 1245318870,162 1245319042,57 1245319102,19 1245319123,30 1245319154,18 1245319206,5 1245319214,13 1245319229,6 1245319238,6 1245319331,9 1245319341,50 1245319397,71 1245319470,25 1245319497,40 1245319540,8 1245319551,77 1245319629,4 1245319638,36 1245319677,158 1245319837,25 1245319865,40 1245319907,33 1245319948,92 1245320043,26 1245320100,9 1245320111,34 1245320146,8 1245320159,6 1245320167,8 1245320181,12 1245320195,15 1245320212,14 1245320238,18 1245320263,46 1245320310,9 1245320326,22 1245320352,27 1245320381,15 1245320398,24 1245320425,57 1245320483,16 1245320501,40 1245320543,43 1245320589,65 1245320657,63 1245320722,129 1245320853,33 1245320889,50 1245320940,1485 1245322801,7 1245322809,103 1245322923,5 1245322929,66 1245323553,4 1245324203,15 1245324383,5 1245324570,7 1245324835,4 1245325200,8 1245325463,5 1245326414,12 1245327340,12 1245327836,4 1245327973,4 1245330006,12 1245331244,11 1245331938,11 1245332180,5 1245332187,81 1245332573,5 1245333609,12 1245334447,10 1245334924,9 1245334945,4 1245334971,4 1245335031,9 1245335076,11 1245335948,16 1245335965,27 1245335993,113 1245336107,79 1245336187,64 1245336253,37 1245336431,4 1245336588,5 1245336759,7 1245337048,3 1245337206,13 1245337228,4 1245337309,4 1245337486,6 1245337536,8 1245337565,38 1245337608,100 1245337713,25 1245337755,169 1245337930,8 1245337941,20 1245337967,6 1245337978,7 1245337996,20 1245338019,38 1245338060,127 1245338192,30 1245338227,22 1245338250,15 1245338272,15 1245338310,3 1245338508,4 1245338990,5 1245339136,5 1245339489,8 1245339765,4 1245340220,5 1245340233,6 1245340266,10 1245340278,22 1245340307,7 1245340315,28 1245340359,32 1245340395,4 1245340403,41 1245340446,46 1245340494,58 1245340554,17 1245340573,21 1245340599,3 1245340604,5 1245340611,46 1245340661,26 1245340747,4 1245340814,14 1245341043,4 1245341104,4 1245341672,4 1245341896,5 1245341906,3 1245342301,3 1245342649,6 1245342884,5 1245342929,4 1245343314,6 1245343324,10 1245343335,16 1245343353,39 1245343394,43 1245343439,62 1245343561,3 1245343790,4 1245344115,3 1245344189,5 1245344233,4 1245344241,6 1245344408,12 1245344829,3 1245345090,5 1245345457,5 1245345689,4 1245346086,3 1245347112,12 1245348006,14 1245348261,10 1245348873,4 1245348892,3 1245350303,11 1245350355,4 1245350766,5 1245350931,3 1245351605,14 1245351673,55 1245351729,23 1245351754,5 1245352123,37 1245352163,21 1245352186,18 1245352209,40 1245352251,49 1245352305,8 1245352315,5 1245352321,6 1245352329,22 1245352353,48 1245352404,77 1245352483,58 1245352543,17 1245352570,19 1245352635,5 1245352879,3 1245352899,5 1245352954,4 1245352962,6 1245352970,58 1245353031,21 1245353055,14 1245353071,52 1245353131,37 1245353170,201 1245353373,56 1245353431,18 1245353454,47 1245353502,13 1245353519,106 1245353627,10 1245353647,12 1245353660,30 1245353699,42 1245353746,28 1245353776,29 1245353806,9 1245353818,21 1245353841,10 1245353853,6 1245353862,224 1245354226,4 1245354964,63 1245355029,4 1245355036,142 1245355180,148 1245355330,7 1245355338,23 1245355363,9 1245355374,60 1245355437,142 1245355581,27 1245355609,5 1245355615,2 1245355630,64 1245355700,7 1245355709,73 1245355785,45 1245355834,85 1245355925,9 1245356234,5 1245356620,6 1245356629,12 1245356643,29 1245356676,120 1245356798,126 1245356937,62 1245357001,195 1245357210,17 1245357237,15 1245357258,24 1245357284,53 1245357339,2 1245357345,27 1245357374,76 1245357452,28 1245357482,42 1245357529,14 1245357545,35 1245357582,74 1245357661,30 1245357693,19 1245357714,38 1245357758,11 1245357777,37 1245357817,49 1245357868,19 1245357891,31 1245357931,48 1245357990,49 1245358043,24 1245358082,22 1245358108,17 1245358148,18 1245358168,7 1245358179,6 1245358186,19 1245358209,17 1245358229,5 1245358240,9 1245358252,10 1245358263,6 1245358272,9 1245358296,26 1245358328,49 1245358381,6 1245358389,38 1245358453,19 1245358476,24 1245358504,21 1245358533,76 1245358628,24 1245358653,10 1245358669,105 1245358781,20 1245358808,14 1245358836,6 1245358871,61 1245358933,0 1245358936,44 1245358982,11 1245358996,25 1245359023,15 1245359040,32 1245359076,19 1245359099,13 1245359117,16 1245359138,12 1245359161,33 1245359215,32 1245359249,14 1245359272,7 1245359314,10 1245359333,36 1245359371,21 1245359424,10 1245359447,61 1245359514,32 1245359560,42 1245359604,87 1245359700,60 1245359762,23 1245359786,4 1245359791,8 1245359803,6 1245359813,107 1245359922,29 1245359953,22 1245359978,86 1245360069,75 1245360147,22 1245360170,0 1245360184,41 1245360239,15 1245360256,34 1245360301,37 1245360339,1 1245360342,28 1245360372,20 1245360394,32 1245360440,24 1245360526,3 1245360728,3 1245361011,4 1245361026,35 1245361064,137 1245361359,5 1245362172,11 1245362225,21 1245362248,51 1245362302,20 1245362334,42 1245362418,12 1245362468,7 1245362557,9 1245362817,3 1245363175,4 1245363271,4 1245363446,3 1245363539,4 1245363573,4 1245363635,1 1245363637,3 1245363740,5 1245363875,3 1245364075,4 1245364354,14 1245364370,19 1245364391,49 1245364442,34 1245364478,23 1245364502,80 1245364633,15 1245364650,8 1245364673,16 1245364691,47 1245364739,53 1245364795,39 1245364836,25 1245365353,4 1245365640,11 1245365665,5 1245365726,8 1245365778,7 1245365982,4 1245366017,13 1245366042,6 1245366487,4 1245366493,4 1245366500,4 1245366507,3 1245366622,5 1245366690,5 1245366946,4 1245366953,16 1245366975,8 1245366996,7 1245367005,7 1245367031,6 1245367040,9 1245367051,7 1245367059,23 1245367084,76 1245367166,158 1245367740,4 1245367804,3 1245367847,4 1245367887,9 1245369300,10 1245369611,12 1245370038,10 1245370374,8 1245370668,5 1245370883,5 1245370927,7 1245370945,9 1245370961,16 1245370978,414 1245371398,135 1245371535,252 1245371791,238 1245372034,199 1245372621,4 1245372890,5 1245373043,7 1245373060,9 1245373073,6 1245373081,68 1245373151,10 1245373162,49 1245373212,79 1245373300,12 1245373313,38 1245373353,20 1245373374,59 1245373435,28 1245373465,94 1245373560,11 1245373574,53 1245373629,22 1245373654,6 1245373662,334 1245373998,169 1245374176,41 1245374219,26 1245374246,51 1245374299,31 1245374332,57 1245374391,55 1245374535,4 1245374759,7 1245374769,200 1245374971,215 1245375188,181 1245375371,81 1245375455,59 1245375516,33 1245375552,19 1245375572,56 1245375629,220 1245375850,32 1245375884,26 1245375948,7 1245375964,114 1245376473,4 1245376810,13 1245378296,10 1245378950,12 1245379004,3 1245379569,4 1245379582,4 1245379615,6 1245380030,3 1245380211,4 1245380412,14 1245380727,4 1245380850,4

This log file is only 7.3 KB. At this rate, a years’ worth of log data can be stored in less than 3MB of plain text files. The data presented here can be graphed (producing the image at the top of the page) using the following code:

# pySquelchGrapher.py
import numpy
import datetime
import pylab
print "loading libraries...",
print "complete"


def loadData(fname="log.txt"):
    print "loading data...",
    # load signal/duration from log file
    f = open(fname)
    raw = f.read()
    f.close()
    raw = raw.replace('n', ' ')
    raw = raw.split(" ")
    signals = []
    for line in raw:
        if len(line) < 3:
            continue
        line = line.split(',')
        sec = datetime.datetime.fromtimestamp(int(line[0]))
        dur = int(line[1])
        signals.append([sec, dur])
    print "complete"
    return signals


def findDays(signals):
    # determine which days are in the log file
    print "finding days...",
    days = []
    for signal in signals:
        day = signal[0].date()
        if not day in days:
            days.append(day)
    print "complete"
    return days


def genMins(day):
    # generate an array for every minute in a certain day
    print "generating bins...",
    mins = []
    startTime = datetime.datetime(day.year, day.month, day.day)
    minute = datetime.timedelta(minutes=1)
    for i in xrange(60*60):
        mins.append(startTime+minute*i)
    print "complete"
    return mins


def fillMins(mins, signals):
    print "filling bins...",
    vals = [0]*len(mins)
    dayToDo = signals[0][0].date()
    for signal in signals:
        if not signal[0].date() == dayToDo:
            continue
        sec = signal[0]
        dur = signal[1]
        prebuf = sec.second
        minOfDay = sec.hour*60+sec.minute
        if dur+prebuf < 60:  # simple case, no rollover seconds
            vals[minOfDay] = dur
        else:  # if duration exceeds the minute the signal started in
            vals[minOfDay] = 60-prebuf
            dur = dur+prebuf
            while (dur > 0):  # add rollover seconds to subsequent minutes
                minOfDay += 1
                dur = dur-60
                if dur <= 0:
                    break
                if dur >= 60:
                    vals[minOfDay] = 60
                else:
                    vals[minOfDay] = dur
    print "complete"
    return vals


def normalize(vals):
    print "normalizing data...",
    divBy = float(max(vals))
    for i in xrange(len(vals)):
        vals[i] = vals[i]/divBy
    print "complete"
    return vals


def smoothListGaussian(list, degree=10):
    print "smoothing...",
    window = degree*2-1
    weight = numpy.array([1.0]*window)
    weightGauss = []
    for i in range(window):
        i = i-degree+1
        frac = i/float(window)
        gauss = 1/(numpy.exp((4*(frac))**2))
        weightGauss.append(gauss)
    weight = numpy.array(weightGauss)*weight
    smoothed = [0.0]*(len(list)-window)
    for i in range(len(smoothed)):
        smoothed[i] = sum(numpy.array(list[i:i+window])*weight)/sum(weight)
    while len(list) > len(smoothed)+int(window/2):
        smoothed.insert(0, smoothed[0])
    while len(list) > len(smoothed):
        smoothed.append(smoothed[0])
    print "complete"
    return smoothed


signals = loadData()
days = findDays(signals)
for day in days:
    mins = genMins(day)
    vals = normalize(fillMins(mins, signals))
    fig = pylab.figure()
    pylab.grid(alpha=.2)
    pylab.plot(mins, vals, 'k', alpha=.1)
    pylab.plot(mins, smoothListGaussian(vals), 'b', lw=1)
    pylab.axis([day, day+datetime.timedelta(days=1), None, None])
    fig.autofmt_xdate()
    pylab.title("147.120 MHz Usage for "+str(day))
    pylab.xlabel("time of day")
    pylab.ylabel("fractional usage")
    pylab.show()
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UCF Tailgate June 2009

June 13, 2009

This morning I woke up at 4:45am, hopped out of bed, and raced to the university parking lot for field day. It’s pretty much a flea market with an emphasis in ham radio and associated electronics. This is a panorama of the parking lot the tailgate was held in, taken from the roof of a parking garage at about 9am. The UCF ARC (the amateur radio club which sponsored the event) is stationed under the white tent.

My goal was to purchase a [working] oscilloscope, and I lucked-out. I ended-up purchasing two, and I’m glad I did! The 1st one (the one with the green circular screen) crapped-out on me after literally 1 minute. (By crapped-out I mean it started spurring thick gray smoke and made my whole apartment smell like a burned marshmallow). At $5, I’m not crying over it. The second one is a 1969 Tektronix 561A 10 MHz oscilloscope. Just think, these things just started started being produced the same year Neil Armstrong walked on the moon. I tested it and it seems to be functioning well. At $10, I’m very happy!

Here you can see it attached to my prime number generator described in agonizingly-boring detail over the last several weeks’ posts. It’s attached to one of the microcontroller pins responsible for multiplexing the LED display. Finally, a way to assess high speed power output as a function of time. The output of the microcontroller isn’t performing like I expected, and since it’s a series of pulses I can’t use a volt meter to measure its output. Thus, the need [more like desire] for an oscilloscope.

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