cubic spline interpolation and upsample ?
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Write down a routine which upsamples the recorded speech by M and uses
cubic spline interpolation on the data to replace the zero samples. Cubic spline
interpolation routines exist in MATLAB toolboxes. You can use lookfor
command of MATLAB to find out how to do it. Then play the upsampled data
for M = 2 and comment on the effect of upsampling in terms of frequency
changes.
[y,Fs]= audioread('sound.wav');
Y=upsample(y,2)
I did the upsampling but couldn't figure out cubic spline interpolation.
2 个评论
John D'Errico
2017-1-14
What did you find when you tried this:
lookfor spline
Why did you not try that?
Eren Çiftçi
2017-1-14
回答（3 个）
Star Strider
2017-1-14
编辑：Star Strider
2017-1-14
0 个投票
Consider that you were told to ‘resample’ your signal, so you should be searching on ‘resample’, not ‘spline’. You will find the resample function, and particularly the method argument section that should guide you to the solution you want.
EDIT — Note that the resample function incorporates a FIR anti-aliasing filter. This is absolutely necessary for signal processing applications. Interpolation without the anti-aliasing filter will not produce reliable results for signal processing purposes.
1 个评论
Charalambos Hadjipanayi
2021-12-17
Why do you need the anti-aliasing filter if you are up-sampling? Doesn't aliasing occur when you downsample?
Image Analyst
2017-1-14
See my spline demo:
% Demo to show spline interpolation.
% Clean up / initialize
clc;
close all;
clear all;
workspace; % Display workspace panel.
% Create the original knot points.
lengthX = 10;
x = 1:lengthX;
y = rand (lengthX,1);
% Plot it and show how the line has sharp bends.
plot(x, y, '-sr', 'LineWidth', 2);
set(gcf, 'Position', get(0,'Screensize')); % Maximize figure.
% Use splines to interpolate a smoother curve,
% with 10 times as many points,
% that goes exactly through the same data points.
samplingRateIncrease = 10;
newXSamplePoints = linspace(1, lengthX, lengthX * samplingRateIncrease);
smoothedY = spline(x, y, newXSamplePoints);
% Plot smoothedY and show how the line is
% smooth, and has no sharp bends.
hold on; % Don't destroy the first curve we plotted.
plot(newXSamplePoints, smoothedY, '-ob');
title('Spline Interpolation Demo', 'FontSize', 20);
legend('Original Points', 'Spline Points');
% Mathworks Demo code from their Help
% x = 0:10;
% y = sin(x);
% xx = 0:.25:10;
% yy = spline(x,y,xx);
% plot(x,y,'o',xx,yy)
slopes = [0, diff(smoothedY)];
plot(newXSamplePoints, slopes, 'k-', 'LineWidth', 3);
% Draw x axis
line(xlim, [0,0], 'Color', 'k', 'LineWidth', 2);
grid on;
legend('Original Points', 'Spline Points', 'Slope');
4 个评论
Eren Çiftçi
2017-1-14
编辑：Eren Çiftçi
2017-1-16
Image Analyst
2017-1-14
Eren, you do know that you can't fit a cubic through just 2 points, don't you? I assume you know the basics of a line needing at least 2 points, a quadratic needing at least 3 points, and a cubic needing at least 4 points, and a polynomial of degree n needing at least (n+1) points. So are you really surprised that you get garbage when you try to use only 2 points to fit a cubic spline? Try it again with at least 4 points.
Eren Çiftçi
2017-1-16
编辑：Eren Çiftçi
2017-1-16
Image Analyst
2017-1-16
So what's the problem? Just replace my data with your data in my code. Did you do that?
kevin cobley
2017-2-28
编辑：kevin cobley
2017-2-28
0 个投票
try 'interp1("original sampletimes","samples","new sample times")'
thats it.. (but you should understand how spline interpolation works, and its relation to matrix algebra... search youtube for cubic spline interpolation - its beautiful stuff..)
2 个评论
N/A
2021-12-13
is there a function for polynomial interpolation
Image Analyst
2021-12-13
Cubic spline is a polynomial interpolation using third order polynomials.
Maybe you could try to do a linear upsampling to get more points, and then use sgolayfilt() if you want some different order.
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