The wavelet representation of a signal has many similarities with conventional musical notation. We can think of a sound (for example music) as a result of variations in air pressure which we detect at our ear. The frequency of these variations gives us the pitch of a sound. Higher frequencies result in higher pitched notes and vice-versa. Complex sounds such as a piece of music are made up of many different notes containing different frequencies which change over time as the melody and harmony progress.

The language of reading and writing music is the score. A musical score consists of a stave where higher-pitched notes are written at the top of the stave and lower-pitched notes at the bottom. Looking across a score from left to right we see how the notes change with time (see Figure 1).

Figure 1. Example of musical notation. The five horizontal lines are known as the stave. Higher notes are written higher on the stave. The music is read from left to right.
 

Because wavelets are localized in frequency and space, they tell us about the way in which the frequency of a signal varies with time. Wavelet coefficients tell us (approximately!) how much of a particular frequency is present in a particular part of a signal. The wavelet coefficients of a 1-D signal are usually displayed as an image with the vertical axis showing higher frequencies (smaller scales) at the top and lower frequencies (larger scales) at the base, and time along the horizontal axis (see Figure 2). The colour at each point in the image gives us the magnitude of that particular wavelet in the signal which in turn tells us approximately how much of a particular frequency is present in that part of the signal.

This is very similar to the musical score except that rather than having notes of a fixed duration, the wavelet transform has 'notes' that can continuously change in loudness depending on the magnitude of the wavelet coefficients. If we look at the wavelet coefficients of an aeromagnetic signal and imagine that the horizontal axis is time instead of distance, we can 'play' the aeromagnetic signal!

Figure 2. The continuous wavelet transform of an aeromagnetic profile. The wavelet coefficients are displayed as an image with the smaller scales at the top of the image (eg higher frequencies), the position on the horizontal axis and the magnitude of the wavelet displayed by colour. Clicking on the image will play the accompanying wavelet music.