# Sine Wave "Lobes" (Basics, and probably a dumb question)

I am beginning my journey on trying to understand a little deeper on signal processing. I wonder if the effect I am seeing is worth any spit or is there a deeper level of understanding is apparent I do not grasp.

I was initially using Jupyter Notebook to make some examples of Aliasing so that I could see the frequency foldback, and give myself a workspace to intuitively understand this concept. And after playing around with drawing sine waves, If I didn't create a sine wave at frequencies based on power 2 of my "sampling rate" then I would create what looked like lobes in my sine wave.

My initial code looks like this

# Aliasing Example
import numpy as np
import matplotlib.pyplot as plot
import math

%matplotlib qt
plot.ion()

# Number of samples
N = pow(2,14) # 16,384 Samples

# Sampling Frequency
Fs = pow(2,14) # 16,384 Samples/second

# Sampling Frequency
T = 1/Fs # 1 second of data

# The amount of sampling time
time = np.linspace(0.0,(N-1)*T,N)

#Nyquist Frequency
Fn = (Fs/2)

# Number of lobes
num_lobes = 4

#Signal 1
f1 = 4096 - num_lobes/4
str1 = "Sine Wave @" + str(f1) + "Hz"
w1 = 2*math.pi*f1
sig1 = np.sin(w1*time)

fig1 = plot.figure()
ax.plot(time,sig1)
ax.set_title(str1)
ax.set_xlabel('Time')
ax.set_ylabel('Amplitude')


The plot of the above graph looks something like It looks like there is an accumulation of phase difference based between my "sampling frequency" of 16384 Hz and the signal frequency 4097 Hz. I don't think I have explored if this actually means anything? Does this have any real-world implications on how I capture data? On a relationship I need to try to satisfy to correctly recreate/capture data? That if I run an FFT or get any other signal information, am I still getting the correct value on the power of the spectrum?

I guess I am looking at this thinking if I were to capture this on a scope I would think I am getting multiple signals going on at once, but it's only a single wave. And that I don't have proper understanding of setting sampling for my signals of concern?

• Your graph is perfectly fine & correct. Why do you think there is something wrong or unusual about it ? What did you expect to see ? Sep 4 '20 at 19:30  