Basic sampling excercise - unsure of rationale informing np.arange parameters for time array

Question

I'm extremely new to DSP, so I apologise if it's a very basic question.

I'm having issues understanding the following exercise:

"Create an array of 201 samples containing a sin wave with a frequency , f, of 2 Hz, i.e. the period is 0.5 seconds. Use a sampling rate, fs of 100 Hz, i.e 100 samples per second. Use the numpy method arange to generate the array. The first step is to declare the variables for f and fs and then create an array of times for the samples in a 2 second range, i.e.

t = np.arange(−1,1+1/fs,1/fs)

which gives a array starting at -1 and ending at 1.01."

I get how you create a range in Python, and I get that the parameters are the starting value, the end value, and the steps. However, I'm not quite sure what this is doing: why does it start at -1? Why does it end at 1+1/fs? Why are the time steps 1/fs? And lastly, what exactly is this giving me? Just the times at which the wave is sampled?

I've tried Googling, but I don't really know what I should be looking for. Even a pointer to the right keyword to Google to answer those questions would be greatly appreciated.

Answer 1

The Hz values are used to get your parameters for defining your signal.

I don't think there is any reason that they went from -1 to 1 instead of, say, 0 to 2. Notice that the end point is not included in the range.

The spacing in your sampling is 1/100 of a second. Yes, the array is giving you values on a time scale.

To generated the signal your are going to need:

f = 2
signal = np.sin( f * 2*np.pi * t )

The $2\pi$ comes as a unit conversion of radians per cycle. Therefore the argument, in units is:

$$ \frac{cycles}{second} \cdot \frac{radians}{cycle} \cdot seconds = radians $$

Hope this helps.

Ced

================================

Followup:

Here is a sample program.

import numpy as np
import matplotlib.pyplot as plt

f = 2.0
fs = 100.0

t = np.arange( -1.0, 1.0+1.0/fs, 1.0/fs )
signal = np.sin( f * 2*np.pi * t )

plt.plot(t, signal, c='g')
plt.show()

Notice that I added a bunch of ".0"s to force Python into using floats. Without it, the program passed 1/fs as the integer 0 to arange.