French
DeutschFile:Multirate upsampling (interpolation) filter.svg
Size of this PNG preview of this SVG file: 800 × 560 pixels. Other resolutions: 320 × 224 pixels | 640 × 448 pixels | 1,024 × 717 pixels | 1,280 × 896 pixels | 2,560 × 1,792 pixels | 900 × 630 pixels.
Original file (SVG file, nominally 900 × 630 pixels, file size: 43 KB)
 | This is a file from the Wikimedia Commons. Information from its description page there is shown below. Commons is a freely licensed media file repository. You can help. |
 | This SVG image contains embedded raster graphics.[1] Such images are liable to produce inferior results when scaled to different sizes (as well as possibly being very inefficient in file size). If appropriate to do so, they should be replaced with images created using vector graphics. Note: This template is only supposed to be used if the SVG file mixes vector and raster graphics. If the SVG file only contains raster graphics {{FakeSVG}} is supposed to be used. See also {{TopoSVG}}. |  |
Summary
| Description | English: Depiction of one dot product, resulting in one output sample (in green), computed by a multirate filter. This illustrates the formula at Upsampling by an integer factor, for the case L=4, n=9, j=3. Three (L-1) conceptual "inserted zeros" are depicted between each pair of input samples. Omitting them from the calculation is what distinguishes a multirate filter from a monorate filter. | |||
| Date | ||||
| Source | Own work | |||
| Author | Bob K | |||
| Permission (Reusing this file) | I, the copyright holder of this work, hereby publish it under the following license:
| |||
| SVG development |  This W3C-invalid vector image was created with LibreOffice. | |||
| Gnu Octave source | click to expand This graphic was created with the help of the following Octave script: pkg load signal graphics_toolkit gnuplot M = 1000; darkgreen = [33 150 33]/256; interpolation_factor = 4; % Generate M+1 samples of a Gaussian window (filter type not important) filter = .3*exp(-.5*(((0:M)-M/2)/(.4*M/2)).^2); % Sample the window. N=24; sam_per_hop = M/N; window_dots = filter(1+(0:N)*sam_per_hop); normalize = sum(window_dots)/interpolation_factor; window_scale_factor = 0.5; sam_per_hop = sam_per_hop*window_scale_factor; %------------------------------------------------------------------ figure("position", [100 200 900 600]) % Plot the continuous filter function xoffset = sam_per_hop*15; yoffset = 0.1; plot(xoffset+(0:M)*window_scale_factor, yoffset+filter, "linestyle",":", "linewidth",1, "color","black") set(gca, "xaxislocation", "origin") xlim([0 M]) ylim([-.06 .45]) % allows space for negative samples (in case I change the signal) set(gca, "ygrid","off"); set(gca, "xgrid","on"); set(gca, "ytick",[0], "fontsize",14); xticks = [0:4*sam_per_hop:M]; set(gca, "xtick",xticks) set(gca,"xticklabel",[0:length(xticks)]) % Plot the filter coefficients hold on plot(xoffset+(0:N)*sam_per_hop, yoffset+window_dots, "color","red", ".", "markersize",10) % Create signal to be interpolated samples_per_cycle = 4*M; signal = .2*sin(2*pi*(0:M)/samples_per_cycle); signal_dots = signal(1:sam_per_hop:end); % Simulate "inserted zeros", for display signal_dots(2:4:end) = 0; signal_dots(3:4:end) = 0; signal_dots(4:4:end) = 0; % Plot the data L = length(signal_dots); plot((0:L-1)*sam_per_hop, signal_dots, "color","blue", ".", "markersize",10) % Compute dot product, and plot it dot_product = sum(window_dots(24:-4:4).*signal_dots(17:4:37))/normalize; x = 27*sam_per_hop; plot(x, dot_product, "color",darkgreen, ".", "markersize",14) plot([x,x],[0,.45]); % vertical line % xlabel('\leftarrow n \rightarrow', "fontsize",16) text(465, -.05, '\leftarrow n \rightarrow', "fontsize",16) text(18, .1, "X[n]", "fontsize",16, "color","blue") title("Multirate interpolation filter", "fontsize",16, "fontweight","normal"); |
![{\displaystyle y[j+nL]=\sum _{k=0}^{K}x[n-k]\cdot h[j+kL],\ \ j=0,1,\ldots ,L-1,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7da35f9a584e9e41e8405a5319ab151a2cf3b48f)
_filter.svg){kind=link}
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 13:44, 24 December 2019 | | 900 × 630 (43 KB) | Bob K | add a vertical line for filter delay arrow to point at |
| 15:12, 23 December 2019 |  | 900 × 630 (43 KB) | Bob K | replace random noise with more realistic signal | |
| 15:54, 22 December 2019 |  | 855 × 585 (41 KB) | Bob K | Label y-origin. Indicate filter delay. | |
| 14:43, 21 December 2019 |  | 855 × 585 (36 KB) | Bob K | User created page with UploadWizard |
File usage
The following page uses this file:
Global file usage
The following other wikis use this file:
- Usage on ca.wikipedia.org
_filter.svg){kind=link}