信号的自然采样与恢复matlab（信号无损失下采样过程）

在不影响计算结果精度的前提下，为了降低计算成本，通常对信号进行采样。

下采样之后的样本仍需满足大于奈奎斯特频率，以避免产生混叠。

为了避免发生混叠，通常应在下采样前施加一个**抗混叠低通滤波器**。

比如一个128Hz的信号，想减采样至32Hz，系数M=4。我们可以先对原始信号进行抗混叠低通滤波，2M=8，截止频率为128/8 = 16Hz。然后进行downsample。减采样之后的样本仍满足大于奈奎斯特频率，避免产生混叠。

decimate

减采样之前，为了防止产生混叠对输入进行低通滤波（By default, decimate uses a lowpass Chebyshev Type I IIR filter of order 8.）

y = decimate(x,r)

减采样系数为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.

指定滤波器阶次，由于数值不稳定，一般阶次不超过13。

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

uses an FIR filter designed using the window method with a Hamming window. The filter has order 30.

使用基于窗方法设计的FIR滤波器，默认阶次为30。

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

使用基于窗方法设计的FIR滤波器，并指定滤波器阶次。

For better results when r is greater than 13, divide r into smaller factors and call decimate several times.

为了获得更好的结果，当r大于13时，将r分成较小的因子，并多次抽取。

```

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.

对x减采样，从第一个样本开始，每n个样本取一个。如果x是矩阵，每一列被看做是一个独立序列。

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

将均匀或非均匀数据重新采样为新的固定采样频率

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.

对x重采样，采样频率是原始采样频率的p/q 倍。如果x是矩阵，每一列被看做是一个独立序列。重采样将抗混叠FIR低通滤波器应用于x并补偿滤波器引入的延迟。

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为滤波器系数向量。

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