File:Multirate upsampling (interpolation) filter.svg
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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)
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Summary[edit]
| 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. |
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| 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:
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| SVG development |  This W3C-invalid vector image was created with LibreOffice. |
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| 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");
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![{\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&action=edit§ion=1){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 (talk | contribs) | add a vertical line for filter delay arrow to point at |
| 15:12, 23 December 2019 |  | 900 × 630 (43 KB) | Bob K (talk | contribs) | replace random noise with more realistic signal | |
| 15:54, 22 December 2019 |  | 855 × 585 (41 KB) | Bob K (talk | contribs) | Label y-origin. Indicate filter delay. | |
| 14:43, 21 December 2019 |  | 855 × 585 (36 KB) | Bob K (talk | contribs) | User created page with UploadWizard |
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