File:DFT 2sin(t) + cos(4t) 25 points.svg
Original file (SVG file, nominally 583 × 414 pixels, file size: 52 KB)
Captions
Discrete Fourier Transform of . This plot illustrates how the DFT of a real signal is symmetric around the middle point, and so only half of the transform points are needed to reconstruct the original signal. We also see how the phase of the sinusoids determines if their DFT components are real or imaginary.
Generated with:
#!/usr/bin/env python
import math
import matplotlib.pyplot as plt
import numpy as np
N = 25
x = np.array([2 * math.sin(i * 2 * math.pi / N) + math.cos(i * 2 * math.pi * 4 / N) for i in range(N)])
X = np.fft.fft(x)
fig, axs = plt.subplots(3, 1)
fig.suptitle('X = DFT(x)')
fig.tight_layout(rect=[0, 0.03, 1, 0.94])
ax = axs[0]
ax.set_title('x(t) = 2 sin(t) + cos(4t)')
#ax.set_title('x(t) = 2 sin(t) + sin(4t) = $-25 e^{1 \\times 2\\pi i t/25} -12.5 e^{4 \\times 2\\pi i t/25} + 12.5 e^{21 \\times 2\\pi i t/25} + -25 e^{24 \\times 2\\pi i t/25}$')
ax.plot(np.arange(0., N, 1.), x, '.')
ax.axis([-0.5, N, -3.5, 3.5])
ax.set_yticks([-3, 0, 3], minor=False)
ax.grid()
ax = axs[1]
ax.set_title('Re(X(t))')
ax.plot(np.arange(0., N, 1.), np.real(X), '.')
ax.axis([-0.5, N, -30, 30])
ax.set_yticks([-25.0, -12.5, 0.0, 12.5, 25.0], minor=False)
ax.grid()
ax = axs[2]
ax.set_title('Im(X(t))')
ax.plot(np.arange(0., N, 1.), np.imag(X), '.')
ax.axis([-0.5, N, -30, 30])
ax.set_yticks([-25, -12.5, 0.0, 12.5, 25], minor=False)
ax.grid()
plt.savefig(
'fft.svg',
format='svg',
dpi=1000/plt.gcf().get_size_inches()[1],
bbox_inches='tight',
)
on:
matplotlib==3.5.2 numpy==1.24.2
on Ubuntu 23.04.
Summary
[edit]DescriptionDFT 2sin(t) + cos(4t) 25 points.svg |
English: Discrete Fourier Transform of 2sin(t) + cos(4t) with 25 points |
Date | |
Source | Own work |
Author | Cirosantilli2 |
Licensing
[edit]- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 13:21, 25 September 2023 | 583 × 414 (52 KB) | Cirosantilli2 (talk | contribs) | Add correct scaling of 2 * pi / 25 on the definition of x(t). | |
21:39, 22 September 2023 | 583 × 414 (48 KB) | Cirosantilli2 (talk | contribs) | Uploaded own work with UploadWizard |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.
File usage on other wikis
The following other wikis use this file:
- Usage on en.wikipedia.org
Metadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
Width | 466.712812pt |
---|---|
Height | 331.518125pt |