# Classifying this signal in dimension and number of channels

The question is:

"Weight and height measurements of a child taken every month"

Classify this signal as:

1. one/multidimensional
2. single/multichannel

I'm not understanding how this can be described as a signal and hence how can it be classified.

I don't feel like it's a very well-posed question, as multi-channel signals are sometimes represented as vector-valued, which would make them multidimensional. However, I assume the answer that is being fished for is:

This is a one-dimensional, two-channel setup. The two channels are the child's height and weight. Each signal is one-dimensional, measured across time. The sample rate of each signal is $1\text{ month}^{-1}$. You could state them mathematically as:

$$h[n] \equiv \text{ height of child at month } n$$ $$w[n] \equiv \text{ weight of child at month } n$$

• And what about "a color movie"? I guess It may be 3-dimensional across RGB values, but how many channel? – Sam Sep 28 '13 at 16:15
• You could call a color video as a three-dimensional, three-channel file. The three channels would be the RGB color signals. Each frame is a two-dimensional quantity, while time provides the third dimension. – Jason R Sep 28 '13 at 20:52

The dimension is how many coordinated you need to specify a particular measurement. For example, say you had a GPS:

• GPS speed is 1D
• GPS ground position is 2D [latitude, longitude]
• GPS absolute position is 3D [latitude, longitude, height]

The number of channels is how many measurement you make at one time. E.g. if you are taking speed and position measurements then that is multi-channel. But like @JasonR said, depending on how you define the measurements a signal could be multidimensional or multichannel. If operations such as norms or rotations make sense on a set of individual measurements then they should be grouped into a vector (multidimensional) signal.