cubic spline interpolation and upsample ?

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.

[John D'Errico]

What did you find when you tried this:

lookfor spline

Why did you not try that?

[Eren Çiftçi]

I tried

lookfor spline

but around 50 codes apear and I don't know which to use for my assigment

Answer 1

[Star Strider]

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.

[Charalambos Hadjipanayi]

Why do you need the anti-aliasing filter if you are up-sampling? Doesn't aliasing occur when you downsample?

Answer 2

[Image Analyst]

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');

[Eren Çiftçi]

Y=[1,2,3,4];
y=upsample(y,2);

after this 'y' will be [1 0 2 0] I got it until this part but.

Use cubic spline interpolation on the data to replace the zero samples I am lost here I am changing the zero samples with what? And how do I change them? is it

x = 0:3;
y = [1,0,2,0,3,0,4,0];
xx = 0:.25:3;
yy = spline(x,y,xx);

like this?

[Image Analyst]

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]

well it is not actually two points(it is 76160 points) I just write like that to show what I am trying to do.

[Image Analyst]

So what's the problem? Just replace my data with your data in my code. Did you do that?

Answer 3

[kevin cobley]

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..)

[N/A]

is there a function for polynomial interpolation

[Image Analyst]

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.