Decimation — decrease sampling rate
Decimation reduces the original sampling rate of a sequence to a lower rate. It is the opposite of interpolation. decimate lowpass filters the input to guard against aliasing and downsamples the result.
y = decimate(x,r) reduces the sampling rate of x, the input signal, by a factor of r. The decimated vector, y, is shortened by a factor of r so that length(y) = ceil(length(x)/r). By default, decimate uses a lowpass Chebyshev Type I IIR filter of order 8.
Input signal, specified as a vector.
Data Types: double
Decimation factor, specified as a positive integer scalar.
Data Types: double
Filter order, specified as a positive integer scalar. When using the IIR filter, avoid values above 13 because sometimes the results are unreliable.
Data Types: double
Create a sinusoidal signal sampled at 4 kHz. Decimate it by a factor of four.
t = 0:.00025:1; x = sin(2*pi*30*t) + sin(2*pi*60*t); y = decimate(x,4);
Plot the original and decimated signals.
subplot 211 stem(0:120,x(1:121),'filled','markersize',3) grid on xlabel 'Sample number',ylabel 'Original' subplot 212 stem(0:30,y(1:31),'filled','markersize',3) grid on xlabel 'Sample number',ylabel 'Decimated'
Create a signal with two sinusoids. Decimate it by a factor of 13 using a Chebyshev IIR filter of order 5. Plot the original and decimated signals.
r = 13; n = 16:365; lx = length(n); x = sin(2*pi*n/153) + cos(2*pi*n/127); plot(0:lx-1,x,'o') hold on y = decimate(x,r,5); stem(lx-1:-r:0,fliplr(y),'ro','filled','markersize',4) legend('Original','Decimated','Location','south') xlabel('Sample number') ylabel('Signal')
The original and decimated signals have matching last elements.
Create a signal with two sinusoids. Decimate it by a factor of 13 using an FIR filter of order 82. Plot the original and decimated signals.
r = 13; n = 16:365; lx = length(n); x = sin(2*pi*n/153) + cos(2*pi*n/127); plot(0:lx-1,x,'o') hold on y = decimate(x,r,82,'fir'); stem(0:r:lx-1,y,'ro','filled','markersize',4) legend('Original','Decimated','Location','south') xlabel('Sample number') ylabel('Signal')
The original and decimated signals have matching first elements.
decimate uses decimation algorithms 8.2 and 8.3 from .
decimate creates a lowpass filter. The default is a Chebyshev Type I filter designed using cheby1. This filter has normalized cutoff frequency 0.8/r and passband ripple 0.05 dB. Sometimes, the specified filter order produces passband distortion due to roundoff errors accumulated from the convolutions needed to create the transfer function. The filter order is automatically reduced when distortion causes the magnitude response at the cutoff frequency to differ from the ripple by more than 10–6.
When the 'fir' option is chosen, decimate uses fir1 to design a lowpass FIR filter with cutoff frequency 1/r.
When using the FIR filter, decimate filters the input sequence in only one direction. This conserves memory and is useful for working with long sequences. In the IIR case, decimate applies the filter in forward and reverse directions using filtfilt to remove phase distortion. This in effect doubles the filter order. In both cases, the function minimizes transient effects at both ends of the signal by matching endpoint conditions.
Finally, decimate resamples the data by selecting every rth point from the interior of the filtered signal. The resampled sequence is such that y(end) matches x(end) when the IIR filter is used and y(1) matches x(1) in the FIR case.
 Digital Signal Processing Committee of the IEEE Acoustics, Speech, and Signal Processing Society, eds. Programs for Digital Signal Processing. New York: IEEE Press, 1979, chap. 8.