在不影響計算結果精度的前提下，為了降低計算成本，通常對信號進行減采樣。
減采樣之后的樣本仍需滿足大於奈奎斯特頻率，以避免產生混疊。
為了避免發生混疊，通常應在減采樣前施加一個抗混疊低通濾波器。
https://cnx.org/contents/p8E-T146@5/Decimation-and-Downsampling
https://dspguru.com/dsp/faqs/multirate/decimation/
比如一個128Hz的信號，想減采樣至32Hz，系數M=4。我們可以先對原始信號進行抗混疊低通濾波，2M=8，截止頻率為128/8 = 16Hz。然后進行downsample。減采樣之后的樣本仍滿足大於奈奎斯特頻率，避免產生混疊。
decimate
減采樣之前，為了防止產生混疊對輸入進行低通濾波（By default, decimate uses a lowpass Chebyshev Type I IIR filter of order 8.）
y = decimate(x,r)
減采樣系數為r，length(y) = ceil(length(x)/r)
y = decimate(x,r,n)
uses a Chebyshev filter of order n. Orders above 13 are not recommended because of numerical instability.
指定濾波器階次，由於數值不穩定，一般階次不超過13。
y = decimate(x,r,'fir')
uses an FIR filter designed using the window method with a Hamming window. The filter has order 30.
使用基於窗方法設計的FIR濾波器，默認階次為30。
y = decimate(x,r,n,'fir')
使用基於窗方法設計的FIR濾波器，並指定濾波器階次。
For better results when r is greater than 13, divide r into smaller factors and call decimate several times.
為了獲得更好的結果，當r大於13時，將r分成較小的因子，並多次抽取。
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')
downsample
y = downsample(x,n)
decreases the sampling rate of x by keeping every nth sample starting with the first sample. x can be a vector or a matrix. If x is a matrix, each column is considered a separate sequence.
對x減采樣，從第一個樣本開始，每n個樣本取一個。如果x是矩陣，每一列被看做是一個獨立序列。
y = downsample(x,n,phase)
指定相位偏移
x = [1 2 3 4 5 6 7 8 9 10];
y = downsample(x,3)
y =
1 4 7 10
y = downsample(x,3,2)
y =
3 6 9
resample
Resample uniform or nonuniform data to new fixed rate
將均勻或非均勻數據重新采樣為新的固定采樣頻率
y = resample(x,p,q)
resamples the input sequence, x, at p/q times the original sample rate. If x is a matrix, then resample treats each column of x as an independent channel. resample applies an antialiasing FIR lowpass filter to x and compensates for the delay introduced by the filter.
對x重采樣，采樣頻率是原始采樣頻率的p/q 倍。如果x是矩陣，每一列被看做是一個獨立序列。重采樣將抗混疊FIR低通濾波器應用於x並補償濾波器引入的延遲。
y = resample(x,p,q,n)
uses an antialiasing filter of order 2 × n × max(p,q).
y = resample(x,p,q,n,beta)
specifies the shape parameter of the Kaiser window used to design the lowpass filter.
y = resample(x,p,q,b)
filters x using the filter coefficients specified in b. b為濾波器系數向量。