Applications of Nyquist's Theorem

Radios Image Processing - reconstruction filters & reverse aliasing Audio Engineering Telecommunications

Nyquist's Theorem can be utilized in every field that involves signal processing and signal analysis. Nyquist's Theorem is helpful in working with radio devices, image processing, audio engineering, and telecommunications.

Radios obviously make use of signals, since the radio tower must project the radio signal to your car or portable radio. Radios work by isolating certain frequencies. When someone tunes in to 94.7 FM, they are really isolating frequencies close to 94.7 Megahertz (MHz). Nyquist's Theorem comes into play for radio systems because the radio systems need to effectively analyze the radio waves that they receive. AM and FM stand for Amplitude Modulation and Frequency Modulation. These are the two methods through which radio providers "encode" the information that they send out. When some cars isolates frequencies, they are programmed with Nyquist's Theorem in mind to alter the sampling rate. The sampling rate is altered so that it is a small amount higher than the Nyquist Rate for the given radio station. This enables the most effective and efficient analysis of the signal in order to convert it into audio.

One interesting application of Nyquist's Theorem is in image processing. Images can be thought of as multi-dimensional signals that occur in two-dimensional space, rather than time. This is actually one of the most used methods of analyzing images. Nyquist's Theorem, then, is still relevant, and its impact is familiar. When capturing image data, pixels are the sample rate, since they are the size of each piece of a photograph. [5] The Nyquist Rate is thus twice as small in each dimension as one pixel. Thus, aliasing can occur in images, and this results in a low level of clarity. This is why cameras need to focus. However, if aliasing does occur, many techniques have been created to reconstruct images. These reconstruction filters enable the restoration of some data in images. An example of reverse aliasing is shown below.

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