decimate (Signal Processing Toolbox)

Decimation -- decrease sampling rate

Syntax

y = decimate(x,r)
y = decimate(x,r,n)
y = decimate(x,r,'fir')
y = decimate(x,r,n,'fir')

Description

Decimation reduces the original sampling rate for a sequence to a lower rate, the opposite of interpolation. The decimation process filters the input data with a lowpass filter and then resamples the resulting smoothed signal at a lower rate.

y = decimate(x,r) reduces the sample rate of x by a factor r. The decimated vector y is r times shorter in length than the input vector x. By default, decimate employs an eighth-order lowpass Chebyshev Type I filter with a cutoff frequency of 0.8*(Fs/2)/r. It filters the input sequence in both the forward and reverse directions to remove all phase distortion, effectively doubling the filter order.

y = decimate(x,r,n) uses an order n Chebyshev filter. Orders above 13 are not recommended because of numerical instability. MATLAB displays a warning in this case.

Note For better results when r is greater than 13, you should break r into its factors and call decimate several times.

y = decimate(x,r,'fir') uses an order 30 FIR filter, instead of the Chebyshev IIR filter. Here decimate filters the input sequence in only one direction. This technique conserves memory and is useful for working with long sequences.

y = decimate(x,r,n,'fir') uses an order n FIR filter.

Examples

Decimate a signal by a factor of four:

t = 0:.00025:1;                      % Time vector
x = sin(2*pi*30*t) + sin(2*pi*60*t);
y = decimate(x,4);

View the original and decimated signals:

stem(x(1:120)), axis([0 120 -2 2])   % Original signal
title('Original Signal')
figure
stem(y(1:30))                        % Decimated signal
title('Decimated Signal')

Algorithm

decimate uses decimation algorithms 8.2 and 8.3 from [1]:

It designs a lowpass filter. By default, decimate uses a Chebyshev Type I filter with normalized cutoff frequency 0.8/r and 0.05 dB of passband ripple. For the fir option, decimate designs a lowpass FIR filter with cutoff frequency 1/r using fir1.
For the FIR filter, decimate applies the filter to the input vector in one direction. In the IIR case, decimate applies the filter in forward and reverse directions with filtfilt.
decimate resamples the filtered data by selecting every rth point.

Diagnostics

If r is not an integer, decimate gives the following error message:

```
Resampling rate R must be an integer.
```

If n specifies an IIR filter with order greater than 13, decimate gives the following warning:

Warning: IIR filters above order 13 may be unreliable.

See Also

cheby1, downsample, filtfilt, fir1, mfilt, interp, resample

References

[1] IEEE. Programs for Digital Signal Processing. IEEE Press. New York: John Wiley & Sons, 1979. Chapter 8.

dct deconv