Fail:Aliasing between a positive and a negative frequency.png

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Aliasing_between_a_positive_and_a_negative_frequency.png ‎(694 × 452 piksel, saiz fail: 44 KB, jenis MIME: image/png)

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Keterangan

English: This figure depicts two complex sinusoids, colored gold and cyan, that fit the same sets of real and imaginary sample points. They are thus aliases of each other when sampled at the rate (f_s) indicated by the grid lines. The gold-colored function depicts a positive frequency, because its real part (the cos function) leads its imaginary part by 1/4 of one cycle. The cyan function depicts a negative frequency, because its real part lags the imaginary part.

Tarikh

27 Mac 2013

Sumber

Karya sendiri

Pengarang

Bob K

Kebenaran
(Penggunaan semula fail ini)

Dengan ini, saya selaku pemegang hak cipta karya ini, menerbitkannya di bawah lesen yang berikut:

Fail ini disediakan di bawah Dedikasi Domain Awam Sejagat CC0 1.0 Creative Commons.

Pihak yang mengaitkan karya ini dengan surat ikatan ini telah mendedikasikan karya ini kepada domain awam dengan melepaskan segala haknya kepada karya ini di seluruh dunia di bawah undang-undang hak cipta, termasuk semua hak berkaitan dan berjiran, sejauh mana yang dibenarkan oleh undang-undang. Anda boleh menyalin, mengubah suai, mengedarkan dan mempersembahkan karya ini, termasuk untuk tujuan komersil, semuanya tanpa meminta kebenaran.

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Versi lain

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Dalam bahasa lain

Alemannisch ∙ Bahasa Indonesia ∙ Bahasa Melayu ∙ British English ∙ català ∙ čeština ∙ dansk ∙ Deutsch ∙ eesti ∙ English ∙ español ∙ Esperanto ∙ euskara ∙ français ∙ Frysk ∙ galego ∙ hrvatski ∙ Ido ∙ italiano ∙ lietuvių ∙ magyar ∙ Nederlands ∙ norsk bokmål ∙ norsk nynorsk ∙ occitan ∙ Plattdüütsch ∙ polski ∙ português ∙ português do Brasil ∙ română ∙ Scots ∙ sicilianu ∙ slovenčina ∙ slovenščina ∙ suomi ∙ svenska ∙ Tiếng Việt ∙ Türkçe ∙ vèneto ∙ Ελληνικά ∙ беларуская (тарашкевіца) ∙ български ∙ македонски ∙ нохчийн ∙ русский ∙ српски / srpski ∙ татарча/tatarça ∙ українська ∙ ქართული ∙ հայերեն ∙ বাংলা ∙ தமிழ் ∙ മലയാളം ∙ ไทย ∙ 한국어 ∙ 日本語 ∙ 简体中文 ∙ 繁體中文 ∙ עברית ∙ العربية ∙ فارسی ∙ +/−

PNG genesis

This PNG graphic was created with LibreOffice.

Octave/gnuplot source

click to expand

This graphic was created with the help of the following Octave script:

graphics_toolkit gnuplot
gold = [251 159 3]/256;         % arbitrary color choice
sam_per_sec = 1;
T = 1/sam_per_sec;              % sample interval
dt = T/20;                      % time-resolution of continuous functions
cycle_per_sec = sam_per_sec/8;  % sam_per_sec = 8 * cycle_per_sec (satisfies Nyquist)

figure
subplot(3,1,1)
xlim([-2 10])
ylim([-1.3 1.3])

% Plot cosine function
start_time_sec = -2;
stop_time_sec = 10;
x = start_time_sec : dt : stop_time_sec;
y = cos(2*pi*cycle_per_sec*x);
plot(x, y, "color", gold, "linewidth", 4)
box off           % no border around plot please
hold on           % same axes for next 3 plots

% Plot sine function
start_time_sec = 0;
stop_time_sec = 10;
x = start_time_sec : dt : stop_time_sec;
y = sin(2*pi*cycle_per_sec*x);
plot(x, y, "color", gold, "linewidth", 4)

% Sample cosine function at sample-rate (1/T)
start_time_sec = 0;
stop_time_sec = 8;
x = start_time_sec : T : stop_time_sec;
y = cos(2*pi*cycle_per_sec*x);
plot(x, y, "color", "black", ".")

% Sample sine function
y = sin(2*pi*cycle_per_sec*x);
plot(x, y, "color", "black", ".")

set(gca, "xaxislocation", "origin")
set(gca, "yaxislocation", "origin")
set(gca, "xgrid", "on");
set(gca, "ygrid", "off");
set(gca, "ytick", [0]);
set(gca, "xtick", [0:8]);

subplot(3,1,2)
xlim([-2 10])
ylim([-1.3 1.3])
cycle_per_sec2 = cycle_per_sec - sam_per_sec;   % negative frequency

% Re-plot same cosine function on new axes
start_time_sec = -2;
stop_time_sec = 10;
x = start_time_sec : dt : stop_time_sec;
y = cos(2*pi*cycle_per_sec*x);
plot(x, y, "color", gold, "linewidth", 4)
box off
hold on

% Plot other cosine function
start_time_sec = -2;
stop_time_sec = 10;
x = start_time_sec : dt : stop_time_sec;
y = cos(2*pi*cycle_per_sec2*x);
plot(x, y, "color", "cyan", "linewidth", 4)

% Sample cosine functions at sample-rate (1/T)
start_time_sec = 0;
stop_time_sec = 8;
x = start_time_sec : T : stop_time_sec;
y = cos(2*pi*cycle_per_sec*x);
plot(x, y, "color", "black", ".")

set(gca, "xaxislocation", "origin")
set(gca, "yaxislocation", "origin")
set(gca, "xgrid", "on");
set(gca, "ygrid", "off");
set(gca, "ytick", [0]);
set(gca, "xtick", [0:8]);

subplot(3,1,3)
xlim([-2 10])
ylim([-1.3 1.3])

% Re-plot original sine function on new axes
start_time_sec = 0;
stop_time_sec = 10;
x = start_time_sec : dt : stop_time_sec;
y = sin(2*pi*cycle_per_sec*x);
plot(x, y, "color", gold, "linewidth", 4)
box off
hold on

% Plot other sine function
start_time_sec = -2;
stop_time_sec = 10;
x = start_time_sec : dt : stop_time_sec;
y = sin(2*pi*cycle_per_sec2*x);
plot(x, y, "color", "cyan", "linewidth", 4)

% Sample sine functions at sample-rate (1/T)
start_time_sec = 0;
stop_time_sec = 8;
x = start_time_sec : T : stop_time_sec;
y = sin(2*pi*cycle_per_sec*x);
plot(x, y, "color", "black", ".")

set(gca, "xaxislocation", "origin")
set(gca, "yaxislocation", "origin")
set(gca, "xgrid", "on");
set(gca, "ygrid", "off");
set(gca, "ytick", [0]);
set(gca, "xtick", [0:8]);

Sejarah fail

Klik pada tarikh/waktu untuk melihat rupa fail tersebut pada waktu itu.

	Tarikh/Waktu	Gambar kenit	Ukuran	Pengguna	Komen
semasa	05:26, 27 Mac 2013		694 × 452 (44 KB)	Bob K	User created page with UploadWizard

Penggunaan fail

Laman berikut menggunakan fail ini:

Pengaliasan

Penggunaan fail sejagat

Fail ini digunakan oleh wiki-wiki lain yang berikut:

Penggunaan di sr.wikipedia.org
- Алијасинг

Metadata

Fail ini mengandungi maklumat tambahan daripada kamera digital atau pengimbas yang digunakan untuk menghasilkannya. Jika fail ini telah diubah suai daripada rupa asalnya, beberapa butiran dalam maklumat ini mungkin sudah tidak relevan.

Komen fail PNG	Created with GIMP
Leraian mengufuk	28.35 dpc
Leraian menegak	28.35 dpc
Tarikh dan waktu fail diubah	04:59, 27 Mac 2013

Fail:Aliasing between a positive and a negative frequency.png

Ringkasan

Captions

Items portrayed in this file

menggambarkan

pencipta

some value

status hak cipta

copyrighted, dedicated to the public domain by copyright holder ^Inggeris

lesen hak cipta

CC0

tarikh penubuhan

27 Mac 2013

sumber fail

original creation by uploader ^Inggeris

media type ^Inggeris

image/png

hasil tambah semak

176af466b89d1b29d7b8c6750686d08053d33e6f

saiz data

44,646 bait

tinggi

452 piksel

lebar

694 piksel

Sejarah fail

Penggunaan fail

Penggunaan fail sejagat

Metadata

Ringkasan

Captions

Items portrayed in this file

some value

copyrighted, dedicated to the public domain by copyright holder Inggeris

27 Mac 2013

original creation by uploader Inggeris

media type Inggeris

image/png

176af466b89d1b29d7b8c6750686d08053d33e6f

44,646 bait

452 piksel

694 piksel

Sejarah fail

Penggunaan fail

Penggunaan fail sejagat

Metadata

copyrighted, dedicated to the public domain by copyright holder ^Inggeris

original creation by uploader ^Inggeris

media type ^Inggeris