Smoothing Function in Python

Currently you are calculating the mean each time in the loop, so that's slice + sum for each of the len(heightProfile) - smoothingInterval iterations. We can remove this by calculating the mean of first smoothingInterval items and then inside of the loop simply subtract current i^th item from the sum of the previous mean and add (i + smoothingInterval)^th item to the sum and calculate the mean for the current window. With this approach we can do this in almost linear time.

Also as you're using Python 2 don't forget to add this line at the top of the file, otherwise normal division will result in integer division.

from __future__ import division

You can replace:

for i in range(smoothingInterval):
        heightProfile.append(heightProfile[-1])

with:

heightProfile.extend([heightProfile[-1]]*smoothingInterval)

If smoothingInterval is very huge then consider passing a generator expression to list.extend, but in most cases [heightProfile[-1]]*smoothingInterval is as fast as you can get:

last_val = heightProfile[-1]
heightProfile.extend(last_val for _ in xrange(smoothingInterval))

Full Code:

from __future__ import division


def smoothen_fast(heightProfile, travelTime):

    smoothingInterval = 30 * travelTime

    heightProfile.extend([heightProfile[-1]]*smoothingInterval)
    # Get the mean of first `smoothingInterval` items  
    first_mean = sum(heightProfile[:smoothingInterval]) / smoothingInterval
    newHeightProfile = [first_mean]

    for i in xrange(len(heightProfile)-smoothingInterval-1):
        prev = heightProfile[i]  # the item to be subtracted from the sum
        new = heightProfile[i+smoothingInterval] # item to be added
        # Calculate the sum of previous items by multiplying
        # last mean with smoothingInterval
        prev_sum = newHeightProfile[-1] * smoothingInterval
        new_sum = prev_sum - prev + new
        mean = new_sum / smoothingInterval
        newHeightProfile.append(mean)

    return newHeightProfile

Timing comparisons:

>>> from random import sample
>>> heightProfile = sample(xrange(1, 10**5), 10**4)
>>> travelTime = 1000
>>> %timeit smoothen(heightProfile[:], travelTime)
1 loops, best of 3: 11.3 s per loop
>>> %timeit smoothen_fast(heightProfile[:], travelTime)
100 loops, best of 3: 2.69 ms per loop

Note that in my function call I am passing a slice of the list because we are modifying the passed list object using its .extend method, which is usually a not a good idea unless the caller expects such modifications.