# Graph examples

To understand how to use the interactive graphs, try some of these examples:

### Basic unmodified data

To start with, here are some of the data sets in their unmodified form:

### Selecting parts of the data

Sometimes we might only be interested in particular parts of the data:

### Cleaning up the data

The raw data is quite 'noisy', so to see patterns we need to clean it up:

In particular, notice how the annual mean of the CO_{2} completely removes the annual oscillation.

### Deeper cleaning

Sometimes we need to do some deeper cleaning to find longer-term patterns:

Note the bowl curve in the detrended CO_{2} shows that the rate of increase has not been constant, and has increased over the period.

### Capturing the detail

Alternatively, sometimes the detail is the interesting part:

### Estimating trends

The most interesting thing might be just the general trend over time:

It's usually better to plot trend lines together with the data, because the auto-scaling of the graphs means they always look the same otherwise - although the vertical scale is useful, of course.

### Fourier analysis

Fourier analysis is a very powerful technique, but needs care to get right. Put simply, Fourier analysis divides a series of data into its individual waves of different frequencies. We can then study this "frequency domain", or manipulate it, and then convert back to the real-world "time domain" by reversing the process:

- Temperature data with a "band-pass" filter - this selects cycles between around 6 and 75 years
- Frequency spectrum of the CO
_{2}series - note the strong signal at 'harmonic 50' - this is the annual oscillation.

### In the mix

One of the most interesting things we can do is compare different datasets. By clicking "Add series" you can add multiple series on the same graph. Each one can have different processes applied to it, but you do have to be careful that the data is still comparable afterwards. Also, the time range and values cover the maximum of any series, so get any detail you may have to ensure they cover the same range. Here are some examples:

In the Fourier example, we normalise the signal so it fits cleanly on the same graph. We can still compare the peaks and troughs of the signals, but the relative sizes are meaningless.

### Test signals

To help test the system and demonstrate the processes, you can start with some internal test signals:

- Sine wave test - trying listening to the audio; you should hear a pure tone.
- Square wave test - the audio is harsher.
- Pure random noise - audio not recommended!
- Fourier analysis of pure noise - beware of finding signals where there are none; always check the amplitude!