Handy Numpy FFT crash course to revise the main concepts

fft-review.py

import numpy as np
from numpy.fft import fft, fftfreq
import matplotlib.pyplot as plt
# Input: Sine wave with 30º offset
# Expected results: discrete impulse with A/2 amplitude at fc
# Phase equal to 90 - phase offset
#
# Phase may be noisy given lower oversampling rate
# Have to adjust the threshold parameter
A = 2
fc = 10
fs = 32 * fc # oversampling rate
phi_offset_deg = 30
t = np.arange(0, 4, 1/fs)
window_size = 1024
N = window_size
df = fs / N

sig = A * np.sin(2 * np.pi * fc * t + np.deg2rad(phi_offset_deg)) 

sig_freq = fft(sig, N) / N #normalize amplitude
f = fftfreq(sig_freq.size, 1/fs)


# Signal plot
plt.figure(figsize=(16,9));
plt.plot(t, sig);

# Amplitude plot
plt.figure(figsize=(16,9));
plt.stem(f, np.abs(sig_freq));

# Phase plot
sig_freq_filtered = 1 * sig_freq
sig_freq_filtered[sig_freq < np.max(np.abs(sig_freq))/10000] = 1e-16
plt.figure(figsize=(16,9));
phase = np.rad2deg(np.angle(sig_freq_filtered))
plt.plot(f, phase);