Aliased Images

An aliased image is a frequency component that appears in continuous time waveforms being recreated from discrete–time, digital waveforms. The frequencies where these extra components appear are related to both the frequency of the signals being recreated as well as the frequency of the sample rate. Looking only at positive frequencies, the two frequencies are related by the following equation:

f ai = | fo + nf s |
  • where
    • fai = the aliased images
    • fo = the desired waveform frequency
    • fs = the sample rate
    • n = an integer (either positive or negative)

As the equation indicates, there are an infinite number of these aliased images that occur. As n gets larger, however, the power content of these extra frequencies "falls off."

The following figure shows a 1 MHz sine wave generated by a 6 MS/s DAC. The dotted line represents an aliased image signal that shows up as a 5 MHz component. In this case, fo is 1 MHz, n is –1, and f s is 6 MHz; resulting in the following formula:

fai = 5 MHz = |1 MHz + (–1)(6 MHz)|

The other possible frequencies of sine waves can be calculated and superimposed onto the sampling points of the image.

Figure 4. Nyquist Theorem

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The following figure shows the frequency domain representation of the previous example. The vertical arrow at fo represents the frequency and signal power of the desired generated signal. The other vertical arrows represent the frequencies and signal powers of the aliased image frequency components that appear in the frequency spectrum.


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In systems where you want to generate accurate signals using sampled data, you must introduce an optional lowpass filter after the DAC to restrict the bandwidth of the output signal to meet the sampling criteria (Shannon's Sampling theorem).