method = forward, backward, bilinear, prewarp, matched, zoh, or foh

frequency = realcons

The Resample command resamples a discrete-time system sys, discretized with sampling time sys:-sampletime, to create an equivalent discrete-time system with new sampling time T.

The method option specifies the resampling method. The following methods are supported: forward rectangle rule (forward), backward rectangle rule (backward), bilinear rule (bilinear), bilinear with prewarping (prewarp), matched poles and zeros (matched), zero-order hold (zoh), and first-order hold or non-causal triangle-hold (foh).

The bilinear rule is also known as the Tustin or Trapezoid rule.

Not all resampling methods can be applied to all system types. The following table describes the usage. An x indicates that the method can be used by the system type. A D indicates that the method is the default for the system type.

For details on the transformation methods, see the sections Frequency Domain Transformations and Time Domain Transformations in DynamicSystems[ToContinuous] and DynamicSystems[ToDiscrete].

$\mathrm{with}\left(\mathrm{DynamicSystems}\right)\:$

$\mathrm{sys}≔\mathrm{ZeroPoleGain}\left(\left[0.7\right]\,\left[0.5\right]\,1\,\mathrm{discrete}\,\mathrm{sampletime}=0.01\right)\:$

$\mathrm{sys}≔\mathrm{TransferFunction}\left(\mathrm{sys}\right)\:$$\mathrm{PrintSystem}\left(\mathrm{sys}\right)$

$\left[\begin{array}{l}\mathbf{Transfer\; Function}\\ \mathrm{discrete;\; sampletime\; =\; .1e-1}\\ \mathrm{1\; output(s);\; 1\; input(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(z\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(z\right)\right]\\ {\mathrm{tf}}_{1,1}\=\frac{z-0.7000000000}{z-0.5000000000}\end{array}\right.$

$T≔0.001$

$T≔0.001$

$\mathrm{sys\_1}≔\mathrm{Resample}\left(\mathrm{sys}\,T\right)\:$$\mathrm{PrintSystem}\left(\mathrm{sys\_1}\right)$

$\left[\begin{array}{l}\mathbf{Transfer\; Function}\\ \mathrm{discrete;\; sampletime\; =\; .1e-2}\\ \mathrm{1\; output(s);\; 1\; input(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(z\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(z\right)\right]\\ {\mathrm{tf}}_{1,1}\=\frac{1.116129032\left(z-0.9653179191\right)}{z-0.9354838710}\end{array}\right.$

$\mathrm{sys\_orig}≔\mathrm{Resample}\left(\mathrm{sys\_1}\,0.01\right)\:$$\mathrm{PrintSystem}\left(\mathrm{sys\_orig}\right)$

$\left[\begin{array}{l}\mathbf{Transfer\; Function}\\ \mathrm{discrete;\; sampletime\; =\; .1e-1}\\ \mathrm{1\; output(s);\; 1\; input(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(z\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(z\right)\right]\\ {\mathrm{tf}}_{1,1}\=\frac{z-0.7000000000}{z-0.5000000000}\end{array}\right.$

$\mathrm{sys\_2}≔\mathrm{Resample}\left(\mathrm{sys}\,T\,\mathrm{method}=\mathrm{forward}\right)\:$$\mathrm{PrintSystem}\left(\mathrm{sys\_2}\right)$

$\left[\begin{array}{l}\mathbf{Transfer\; Function}\\ \mathrm{discrete;\; sampletime\; =\; .1e-2}\\ \mathrm{1\; output(s);\; 1\; input(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(z\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(z\right)\right]\\ {\mathrm{tf}}_{1,1}\=\frac{z-0.9700000000}{z-0.9500000000}\end{array}\right.$

$\mathrm{sys\_3}≔\mathrm{Resample}\left(\mathrm{sys}\,T\,\mathrm{method}=\mathrm{backward}\right)\:$$\mathrm{PrintSystem}\left(\mathrm{sys\_3}\right)$

$\left[\begin{array}{l}\mathbf{Transfer\; Function}\\ \mathrm{discrete;\; sampletime\; =\; .1e-2}\\ \mathrm{1\; output(s);\; 1\; input(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(z\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(z\right)\right]\\ {\mathrm{tf}}_{1,1}\=\frac{1.327272727\left(z-0.9589041096\right)}{z-0.9090909091}\end{array}\right.$

$\mathrm{sys\_4}≔\mathrm{Resample}\left(\mathrm{sys}\,T\,\mathrm{method}=\mathrm{prewarp}\,\mathrm{frequency}=2\right)\:$$\mathrm{PrintSystem}\left(\mathrm{sys\_4}\right)$

$\left[\begin{array}{l}\mathbf{Transfer\; Function}\\ \mathrm{discrete;\; sampletime\; =\; .1e-2}\\ \mathrm{1\; output(s);\; 1\; input(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(z\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(z\right)\right]\\ {\mathrm{tf}}_{1,1}\=\frac{1.116129582\left(z-0.9653190438\right)}{z-0.9354859315}\end{array}\right.$

$\mathrm{sys\_5}≔\mathrm{Resample}\left(\mathrm{sys}\,T\,\mathrm{method}=\mathrm{zoh}\right)\:$$\mathrm{PrintSystem}\left(\mathrm{sys\_5}\right)$

$\left[\begin{array}{l}\mathbf{Transfer\; Function}\\ \mathrm{discrete;\; sampletime\; =\; .1e-2}\\ \mathrm{1\; output(s);\; 1\; input(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(z\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(z\right)\right]\\ {\mathrm{tf}}_{1,1}\=\frac{z-0.9598197945}{z-0.9330329908}\end{array}\right.$

$\mathrm{sys\_6}≔\mathrm{Resample}\left(\mathrm{sys}\,T\,\mathrm{method}=\mathrm{foh}\right)\:$$\mathrm{PrintSystem}\left(\mathrm{sys\_6}\right)$

$\left[\begin{array}{l}\mathbf{Transfer\; Function}\\ \mathrm{discrete;\; sampletime\; =\; .1e-2}\\ \mathrm{1\; output(s);\; 1\; input(s)}\\ \mathrm{inputvariable}\=\left[\mathrm{u1}\left(z\right)\right]\\ \mathrm{outputvariable}\=\left[\mathrm{y1}\left(z\right)\right]\\ {\mathrm{tf}}_{1,1}\=\frac{1.135736069\left(z-0.9646218822\right)}{z-0.9330329908}\end{array}\right.$

$\mathrm{p0}≔\mathrm{MagnitudePlot}\left(\mathrm{sys}\,\mathrm{range}=0.1..10\,\mathrm{color}=\mathrm{red}\,\mathrm{thickness}=2\,\mathrm{legend}=''discrete''\right)\:$

$\mathrm{p1}≔\mathrm{MagnitudePlot}\left(\mathrm{sys\_1}\,\mathrm{range}=0.1..100\,\mathrm{color}=\mathrm{blue}\,\mathrm{legend}=''bilinear''\right)\:$

$\mathrm{p2}≔\mathrm{MagnitudePlot}\left(\mathrm{sys\_2}\,\mathrm{range}=0.1..100\,\mathrm{color}=\mathrm{green}\,\mathrm{legend}=''forward''\right)\:$

$\mathrm{p3}≔\mathrm{MagnitudePlot}\left(\mathrm{sys\_3}\,\mathrm{range}=0.1..100\,\mathrm{color}=\mathrm{cyan}\,\mathrm{legend}=''backward''\right)\:$

$\mathrm{p4}≔\mathrm{MagnitudePlot}\left(\mathrm{sys\_4}\,\mathrm{range}=0.1..100\,\mathrm{color}=\mathrm{grey}\,\mathrm{legend}=''prewarp''\right)\:$

$\mathrm{p5}≔\mathrm{MagnitudePlot}\left(\mathrm{sys\_5}\,\mathrm{range}=0.1..100\,\mathrm{color}=\mathrm{magenta}\,\mathrm{legend}=''zoh''\right)\:$

$\mathrm{p6}≔\mathrm{MagnitudePlot}\left(\mathrm{sys\_6}\,\mathrm{range}=0.1..100\,\mathrm{color}=\mathrm{black}\,\mathrm{legend}=''foh''\right)\:$

$\mathrm{plots}\left[\mathrm{display}\right]\left(\mathrm{p0}\,\mathrm{p1}\,\mathrm{p2}\,\mathrm{p3}\,\mathrm{p4}\,\mathrm{p5}\,\mathrm{p6}\right)$

The DynamicSystems[Resample] command was introduced in Maple 18.

For more information on Maple 18 changes, see Updates in Maple 18.