An Algorithm for Interpolate Discrete Time Signals
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Transcript of An Algorithm for Interpolate Discrete Time Signals
An algorithm for interpolate discrete time signals
Cs.B. Harmonic interpolation, Budapest, 2010. november 4.. 1
Bertalan CsanádiÓE – KVK – HTI
E-mail: [email protected]
Short introduction
Sometimes the right sampling frequency is not enough for the offline or post processing, that needs a resample or an interpolation for the measurements or simulating
Sometimes the sample number is under the necessary limit
Example:
Some FM radio simulation need at least 2,1MHz sampled audio signal
In the field of the studiotechnic some audio is sampled in 44,1KHz and audio from other source is sampled in 192KHz and the problem is to editthis two sinal in one time line
Cs.B. Harmonic interpolation, Budapest, 2010. november 4. 2
Sampling theorem
Main is the Nyquist-Shannon law, which says the sampling frequency must have two times greater than the highest harmonic member of the input signal
That means, the gate opener signals first harmonic is two times greater than the sampled signal
But this is not the all, it also means that if choose a right sampling frequency, and use a right anti-aliasing filter, the sampled data frequency members are harmonic
Now if we have a method to transform signals to the frequency field, do the steps and transform back, than we get the full harmonic interpolation of the original signal
Cs.B. Harmonic interpolation, Budapest, 2010. november 4.. 3
Continuous and discrete Fourier transformation
Continuous Fourier transform
Discrete Fourier transform
Fast Discrete Fourier Transform
Cs.B. Harmonic interpolation, Budapest, 2010. november 4.. 4
Multidimensional Fourier transform
Method
On the original matrices do the transform by rows and do it by the columns to.
Input matrix X;
Y = fft(X);
Y = fft(Y’);
Results
Cs.B. Harmonic interpolation, Budapest, 2010. november 4.. 5
The algorithm
Input array x;
Output array y;
<y greater than x>
X = fft(x)/lenght(x);
Y(0..(lenght(X)/2)) = X(0..(lenght(X)/2));
Y((lenght(Y)-lenght(X)/2)..(lenght(Y))=X((lenght(X)/2)..(lenght(X)));
y = ifft(Y)*lenght(Y);
Cs.B. Harmonic interpolation, Budapest, 2010. november 4.. 6
Results in vectors
Cs.B. Harmonic interpolation, Budapest, 2010. november 4.. 7
Results in vectors
Cs.B. Harmonic interpolation, Budapest, 2010. november 4.. 8
Results in vectors
Cs.B. Harmonic interpolation, Budapest, 2010. november 4.. 9
Results in matrices
Cs.B. Harmonic interpolation, Budapest, 2010. november 4.. 10
Results in matrices
Cs.B. Harmonic interpolation, Budapest, 2010. november 4.. 11
Results in matrices
Cs.B. Harmonic interpolation, Budapest, 2010. november 4.. 12
References
Numerical Recipes The art of scientific computing, third edition, William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery
ISBN: 978-0-521-88068-8
Mathworks Matlab Online Help
www.Mathworks.com
Matlab Central
www.mathworks.com/matlabcentral
Cs.B. Harmonic interpolation, Budapest, 2010. november 4.. 13
Thanks for Your attention!
14Cs.B. Harmonic interpolation, Budapest, 2010. november 4..
Bertalan Csanádi([email protected])