MATLAB: Unexpected shift after downsampling using decimate

decimatedownsampleresample

n = 1000;
t = 1:n;
x = rand(1,n) - 0.5; 
x = sin(2*pi/100*t);
y = decimate(x,4);
figure('color','w');
ha = axes('nextplot','add','box','on');
plot(ha,t,x,'k','marker','.');
plot(ha,t(1:4:end),y,'r','marker','o'); addkeycb;

There is a shift of 3 points.

Best Answer

Add the default filter to produce the correct decimation:

y = decimate(x,4,'fir');

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MATLAB: Fir and iir filtering

You have to know your filter specifications. If you do, you can do both with fdesign.lowpass and fdesign.highpass

fdesign.lowpass and fdesign.highpass have different specification strings which support different filter designs.

The default string 'Fp,Fst,Ap,Ast' supports both FIR and IIR designs.

Here is an example:

Design a lowpass filter with a passband frequency of 1 kHz, a stopband frequency of 1.5 kHz, passband ripple of 0.5 dB, and stopband attenuation of 40 dB. The sampling frequency is 20 kHz

   d = fdesign.lowpass('Fp,Fst,Ap,Ast',1e3,1.5e3,0.5,40,20e3);
   designmethods(d)  %shows which designs are valid for this spec
   Hdeq = design(d,'equiripple'); % FIR filter
   Hbutt = design(d,'butter'); %IIR design

MATLAB: Matlab coding for downsampling……..……

If you have the Signal Processing Toolbox, you can use downsample() to simply downsample without lowpass filtering. Or use decimate() or resample() to first lowpass filter and then downsample.

 n = 0:159;
 x = cos(pi/4*n);
 % downsample by 2 starting with the first value
 y = downsample(x,2,0);
 % downsample by 2 starting with the second value
 y1 = downsample(x,2,1);

You can of course do the above with simple MATLAB commands:

 y = x(1:2:end);
 y1 = x(2:2:end);

In general, do consider either decimate()or resample() as these afford anti-aliasing through filtering.

Best Answer

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MATLAB: Fir and iir filtering

MATLAB: Matlab coding for downsampli​ng……..​……

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MATLAB: Matlab coding for downsampling……..……