EquivalentNoiseBandwidth - Maple Help

SignalProcessing

 EquivalentNoiseBandwidth
 computes equivalent noise bandwidth of a window

 Calling Sequence EquivalentNoiseBandwidth( size, windowtype, samplerate ) EquivalentNoiseBandwidth( windowvector, samplerate )

Parameters

 size - Positive integer for the size of the window. windowtype - (optional) Either a list, name, or string, specifies the windowing command to be applied. The default is "none" (for no windowing to be applied). If a list is passed, the first element provides the name of the windowing command, and any remaining terms are passed as options to the command. windowvector - 1-D rtable or list of numeric values, specifies the Windowing Vector. samplerate - (optional) Positive numeric value for the sampling rate. The default is size or numelems(windowvector), depending on the calling sequence.

Description

 • The value of windowtype, when not passed as a list, should be the name or string, with or without the Window suffix, that corresponds to the windowing command. For example, to use a Hamming window, you can pass Hamming or "HammingWindow". In both cases, the command SignalProcessing[HammingWindow] will be used internally. Similarly, you can pass ["Exponential",0.5] or [ExponentialWindow,0.5] to use SignalProcessing[ExponentialWindow] with parameter value 0.5.
 • Denote $n=\mathrm{size}$ and $r=\mathrm{samplerate}$. For a given windowtype, the windowing Vector $W$ is the Vector of size $n$ formed by applying the window to the Vector of size $n$ filled with ones. Applying the window to any real-valued Vector $X$ of size $n$ is equivalent to multiplying $X$ element-wise by $W$.
 • Define $\mathrm{\rho }$ to be the Root Mean Square (RMS) of $W$, and $\mathrm{\mu }$ to be the mean of $W$. The Equivalent Noise Bandwidth (ENBW) is given by:

$\mathrm{EquivalentNoiseBandwidth}\left(W\right)=\frac{r}{n}{\ast }{\left(\frac{\mathrm{\rho }}{\mathrm{\mu }}\right)}^{2}$

 • The SignalProcessing[EquivalentNoiseBandwidth] command is thread-safe as of Maple 2021.

Examples

 > $\mathrm{with}\left(\mathrm{SignalProcessing}\right):$

Example 1

 > $\mathrm{EquivalentNoiseBandwidth}\left(5,"Hamming",3.5\right)$
 ${1.11328124999999978}$ (1)

Example 2

 > $\mathrm{EquivalentNoiseBandwidth}\left(10,\left["Exponential",0.75\right]\right)$
 ${1.00681781685235361}$ (2)

Example 3

 > $\mathrm{EquivalentNoiseBandwidth}\left(\left[1,2,3,4,3,2,1\right]\right)$
 ${1.20312500000000022}$ (3)

Compatibility

 • The SignalProcessing[EquivalentNoiseBandwidth] command was introduced in Maple 2021.