APC_Australia_Issue_442_June_2017

howto » coding masterclass
Enter resistor and
capacitor values to
calculate the 3dB
cut-off frequency.
d = ( v2 x sin(2Ð) ) / g
...where ‘d’ is the distance travelled,
‘v’ is the initial velocity, theta (‘θ’)
is the initial projection angle off
the ground and ‘g’ is gravity
(9.8 metres per second-squared).
Rearranging the equation so that ‘v’
is the subject, we get:
This is true even if you’re just
mucking around in the Python Shell,
but from then on, you can use the
module functions as you like —
and there are plenty to play with,
including in other modules.
One common need is the rounding of
real numbers, or turning real numbers
into integers. Say, for example, you
have a real number ’12.65’. You may
decide you want to round it up to 13,
or you may want to round it down to
12. Try these in the Python Shell:
print(math.ceil(12.65))
print(math.floor(12.65))
The first returns the ‘ceiling’ integer
of 12.65 (i.e. 13), while the second
returns the ‘floor’ integer, which,
in this example will be ‘12’. In other
words, ‘math.ceil()’ rounds up to the
nearest integer, while ‘math.floor()’
108 www.apcmag.com
The dds.py code
creates a DDS table
to any sample count
you choose.
rounds down to the nearest integer.
Negative numbers give the impression
of working in reverse — ‘floor’ gives
you the next integer towards minusinfinity
and ‘ceil’, the next towards
zero, but it makes sense.
GOAL-LINE DROP-OUT
Let’s try something more practical.
In rugby league, a goal-line drop-out
is taken when a player drop-kicks the
ball from underneath the cross-bar on
the try-line down the field towards
the opposition try-line. These days, a
typical drop-out travels 50 metres on
the fly (before the first bounce). Using
the math module and some projectile
motion theory, we can get Python to
calculate the initial velocity required
to kick the ball that distance. The
mathematical equation for the
maximum horizontal distance
travelled is:
v = sqrt( (d x g) /
sin(2θ) )
...where ‘sqrt’ is the square-root.
Now we’re ready to create a small
Python app.
Download the source code for this
month from our website (apcmag.com/
magstuff) and unzip it, then open up
the Python IDLE editor and load
‘dropout.py’. You’ll see we’ve included
both of these equations, to calculate
either the required speed given the
distance and angle, or the distance
given the initial speed and angle.
The key to the code is the math
module’s ‘sqrt()’, ‘sin()’ and ‘radian()’
functions. The ‘math.sqrt()’ function
takes the square-root of the supplied
parameter, the ‘math.sin()’ calculates
the sine of the given value. However,
this function expects to see the value
in ‘radians’, not degrees. One radian
is (180/pi) degrees, but rather than
do the conversion by-hand, Python
includes the ‘math.radian()’ function,
which converts degrees into radians
more accurately. You’ll see by
embedding the math.radian()
function inside the math.sin()
function, we send the output of the
radian() function immediately as
input to the sin() function and get
the right result.
DIRECT DIGITAL SYNTHESIS
In electronics, a popular new method
for generating sinewaves is ‘direct
digital synthesis’ and it’s used in
everything from radio transmission
to music synthesisers. It takes a table